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Lfi-..x.?x LIST OF MODEL VARIABLES Descrimion area opening effectiveness mass diffusivity of water diameter view factor height heat transfer coefficient mass transfer coefficient latent heat of vaporization analogous current (flow) radiosity thermal conductivity length mass mass flow rate Nusselt number pregnancy state volumetric flow rate heat transfer rate analogous resistance Reynolds number sweating rate temperature thickness free stream velocity air velocity weight humidity ratio distance milk yield XV Basic units m2 mzls m m W/m2 K m/s J/kg W or kg/s Wlm2 W/m K 0.6, or (3.6.5) NuL = (0.337 Rolf” - 871) Pr"3 for mixed flow, 0.6 0.7, where the (3.6.7) constant m is experimentally derived, and is generally near 0.5. Sphere: Nun = 2 + (0.4 Rep"2 «1» 0.06 Rep”) Pr°" (u. In) (3.6.8) for 3.5 38.6) (3.9.1) where: aqm,’ ” = muscle metabolism increase from increased respiration, W/m’; qmb’ ” = basal muscle metabolism of normal respiration, WIm’; Q, = respiratory ventilation rate, m3lhr/m2; and T, = average body core temperature, °C. The rise in body temperature associated with therrnolability necessarily increas- es the metabolic rate according to the van’t Hoff effect which relates the rate of thermochemical reactions to the temperature at which the reaction occurs. Metabolism is directly affected as shown in Equation 3.9.2 (Blaxter, 1962). Hp = H; em (3.9.2) where: Hp = heat production at elevated body temperature (W); H,’ = heat production at thermoneutral temperature (W ); k = van’t Hoff coefficient (°C‘); and AT = increase in body temperature (°C). Cows stand during hot weather to expose more body surface area for convec- tive and evaporative cooling. This action requires an additional expenditure of energy, albeit the amount is comparatively very small (1 or 2% of total expenditure, Blaxter, 1962). Origins and site of thermoregulatory control. Temperature regulation has been the subject of considerable research. A very brief review of the research is necessary to better define where and when the physiological temperature control mechanisms are activated. How the control takes place is of lessor importance for this research. 67 Reviews of thermoregulation (Curtis, 1983; Ingram and Mount, 1975) converge toward consensus that thermoregulation is under central, exterior and peripheral con- trol. Central control occurs in the hypothalamus. This organ receives neural stimuli from other sites and monitors core temperature in a manner similar to a central room thermostat in a house. When body temperature deviates from the desired setpoint or outside stimuli are received, the hypothalamus activates appropriate mechanisms to restore homeothenny. The hypothalamus utilizes both the nervous and hormonal networks to bring about the desired reactions. The spinal cord and possibly other internal body organs facilitate and accentu- ate the activity of the hypothalamus. It is believed that the spinal cord, called external because it is located outside the brain, primarily initiates, transmits and disperses ther- moregulatory signals that are processed by the hypothalamus. However, when the hypothalamus is nonfunctional, thermoregulation of the body is still maintained at a reduced capacity. The spinal cord has been credited maintaining this activity. Peripheral organs, such as the skin, tongue, lung surface tissue, etc., are primar- ily responsible for sensing local temperatures, sending signals to and responding to feedback from the hypothalamus. However, it has been demonstrated that some peripheral temperature control mechanisms are stimulated directly by peripheral control sites. Modeling therhroregulatory control. In modeling heat flow in animals, reliable information is needed regarding the source of control and the primary stimuli for certain acclimatory responses. For example, the onset of a physiological activity and the rate at which it proceeds could be controlled by the hypothalamus, control 68 sites in the skin or a combination of the two. Also, the stimuli may be absolute temperature, a change in temperature, the magnitude of a surface vapor pressure gradient, exposure to light or a combination of stimuli. Control of physiological activities is obviously a complex subject. Although considerable research has been performed in this area, the intricacies of the control of thermoregulatory actions are not yet well understood. Feed and metabolizable energy intake. Feed consumption, which is a primary determinant of the release of energy during metabolism, is likely under both voluntary and involuntary control. Blaxter (1962) summarizes research that establishes a clear relationship between feed intake and function of the hypothalamus -- the thermoregula- tory control center. Hypothalamic control means that feed intake is automatically (i.e., involuntarily) adjusted to meet the thermal energy demands of the body. This largely explains the fall in feed intake that inevitably results from persistently hot conditions. Considerably less is known about the nature of the stimuli and control strategy that initiate adjustment of feed intake. Voluntary control of appetite, on the other hand, has more to do with feed quality and the physical-chemical processes in an animal’s stomach. Blaxter also shows that the food and metabolizable energy intake rises when high quality feed is available, regardless of the species or stomach system. Feed quality can be defined by the proportion of metabolizable energy present in the food -- with high quality feed having a greater metabolizable energy content. In this case, feed intake is not a direct function of the animal’s thermal environment or thermal energy status, but rather of some level of satiety. 69 Since the metabolic heat increment of a foodstuff is inversely related to its metabolizable energy content, high quality feed can supply an animal’s energy needs with less release of heat to the body. Nutritional management strategies are beyond the scope of this research. However, it is clear that feeding strategies are another very important tool that can be used to limit heat stress in cattle during hot weather. Sweating. Sweating has been shown to be under the control of peripheral thermoregulation sites as well as central control. In cattle, this is clearly evident as sweating is initiated at about 18 °C compared to 29°C in man, even though no change in body temperature occurs until ambient temperature rises considerably (Kibler & Brody, 1950a). Respiration. The control pattern and mechanisms of control are considered by Murray (1986). The response of many animals to hot conditions has been shown to include increased respiratory activity which benefits the animal by increasing the total heat loss from the lungs. The studies of respiratory activity in dairy cattle that are referenced in Table 3.8.2 generally attempted to use environmental parameters such as ambient air temperature as variables controlling respiration. The results obtained provide useful insights, but, because of the considerable scatter in the data, relation- ships that were developed for assessing control of respiration are not very accurate. When ambient environmental conditions are utilized as the stimuli for a respi- ratory response, the inherent assumption is that control occurs within the lungs or at the surface of the animal’s body. A few studies have specifically related respiratory parameters to body temperature. Bianca and Findlay (1962) presented the measured rise in respiration rate, respiratory volume and resulting ventilation rate of bull calves 70 exposed to hot environmental conditions as a function of rectal temperature. The results showed that each of the measures was fairly accurately predicted by rectal temperature. Hales (1976) developed relationships to predict the respiratory ventila- tion rate per unit of surface area as a function of rectal temperature based on the results of the work of Bianca and Findlay. Q,” = 0.90 (for T, s 38.6) (3.9.3) Q,” = 0.90 + 1.322 (1‘, - 38.6)“2 (for 38.6 s T, s 40.5) (3.9.4) Q,” = 2.64 + 0.75 (i, > 40.5) (3,9,5) where: Q,” = respiratory ventilation rate per unit surface area, mi'Vhr/m2 and Tc = average body core temperature, °C. Roller and Goldman (1969) found that in swine, respiration rate was well correlated with rectal temperature and that the standard error of the relationship was virtually the same for differing numbers of animals tested; i.e., there was little vari- ability among animals. This approach assumes that respiration is centrally controlled and that equivalent respiratory responses could be achieved by an unlimited combina- tion of environmental conditions 3.10 Models of Animal Interactions with their Thermal Environment Stevens (1982) promotes the concept of making models isomorphic, which means that the components of models should progressively be designed and integrated to more closely resemble the components of the physical and physiological systems being modeled. Such models have the advantages of i) having measurable inputs and outputs at each component modeling stage of the overall model, ii) allowing for 71 independent development of the component models and iii) facilitating the swift improvement of the model by updating individual components of the model. Several varieties of models have been developed to describe how animals interact with their environment. Production. Early models attempted to predict the growth rate and production of livestock in various thermal environments. Modeling work continues in this area as the need remains to describe the productive processes of ever higher producing live- stock. Such models have been developed by Greninger, et al. (1982) for layers, Nienaber, et al. (1982) for swine, and Timmons and Gates (1988) for Tom turkeys. Thermal load exerted by environment. Hahn, et al. (1961) used scale mod- els of livestock housing to evaluate the relative importance of shelter components toward the resulting interior thermal environment. By using black globe thermometry and a radiant energy balance, the heat loads contributed by various enclosure surfaces were determined. Other models predict interior thermal conditions of livestock housing (Diesch and Froehlich, 1988). A few have incorporated an index of thermal stress into the model, while others have predicted the heat deficit or surplus that exists for optimum production. Reece and Lott (1982) developed a computer model to predict fuel con- sumption needs of broiler houses based on chicken characteristics and stocking densi- ty, climatic conditions, and house design. Oliveira and Esmay (1982) developed a model to predict temperature-humidity and black globe humidity indices within various cattle barn enclosures. This model evaluated the performance of barns based on the calculated indices as a function of 72 solar radiation, shade material, walls, cave height, floor type, air velocity, inside and outside air temperatures and dewpoint temperature. The steps that were followed were: 1) determine shape factor of each part of the surroundings with respect to the sphere; 2) determine the radiosity of each part of the surroundings with respect to the sphere; 3) multiply the shape factors by the respective radiosities; and 4) add the parts to obtain the total radiant heat load. Unique aspects of this model were that it i) accommodated a variety of build- ing configurations and materials, ii) included radiant heat load through the sidewall ventilation openings and iii) modeled an animal as a sphere to eliminate questions concerning orientation with respect to the radiant heat load. A limiting feature of the model was that no attempt was made to determine the net heat exchange for the animal or enclosure surfaces. All surface temperatures were estimated based on weather conditions and construction materials. When evaluated against real field measurements, the model overestimated the value of the heat stress indices. The critical calculation was determined to be that of the surface temperature of the roofing materials. Further investigation suggests that the model underestimated the cooling capac- ity of ventilating air, both on the enclosure and animal surfaces. Also, the model gave little or no insights concerning the actual or potential evaporative cooling from the animal. For most livestock species, and dairy cattle in particular, this is of consid- erable importance. 73 Energy balance models. Several models have been developed to perform energy balances on animals. McArthur (1982) proposed a method of modeling the energy exchange of animals with their environment that has the advantage that knowl- edge of skin temperature is not required. Beckett (1965) modeled the internal heat generation and external heat loss of 150 lb pigs. Their model partitioned heat loss amongst several transfer mechanisms and did so with reasonable accuracy. Resistance circuit analogies are commonly used to model heat transfer in animal systems (Jordan and Barwick, 1965). Hoff, et al. (1993b) modeled the radia- tive and convective interactions of the newborn piglet with its surroundings. The piglets were modeled as cylinders having an established core temperature. The resis- tance to heat flow from the core to the skin was defined as tissue resistance and included the convective resistance of the cardiovascular system and the standard resistance to conduction offered by the vascular tissue and skin. Then the radiant heat exchange of newborn piglets in various enclosures was calculated by solving the matrix of equations resulting from summation. Use of this model was limited to ambient temperatures below 30°C for the piglets, however, because it neglected the effects of evaporation. Such a model has little direct value for use with hot weather dairy housing where evaporation is very important. Turner, et al. (1987a) modeled the dynamic heat transfer from cattle using finite element analysis. The model was quite intensively designed in that it analyzed the impact of differing components (muscle, fat, water, etc.) of the body individually. It included provisions for modeling thermoregulatory control, establishing relationships for predicting respiratory ventilation rate, the increase in muscle metabolism due to ' 74 panting or shivering, sweating rate, vasoconstriction/vasodilation and feed intake. The model was found to correctly simulate the trends of core temperature response of beef cattle exposed to high temperature environments (Turner, et al., 1987b). However, considerable error was present in estimating the magnitude and phase of the response. The error in the predictions was attributed primarily to the fact that the model did not account for warming of the ingesta although it is not clear from the data how this feature would improve the correlation of the predicted and measured data. Chastain (1991) deve10ped a model to evaluate a direct evaporative cooling cycle in terms of the heat flux to or from the cow’s body relative to the heat loss by evaporation. The model considers convection, evaporation and any radiant heat loads placed on the animal. Ehrlemark and Stillvik (1996) modeled the heat and moisture dissipation from cattle based on thermal properties of the animals and the heat load of the surround- ings. Their model, ANIBAL, predicts the heat loss of cows based on a relative mea- sure, the thermal load index, they defined as shown in Equation 3.10.1. TLI = 100(t,,,,,,- LCT)/(t,,,,,,— LCT) (3.10.1) where: TLI = thermal load index; rm, ,tbody = ambient and body temperature, respectively (C); and LCT = lower critical temperature (C); and ANIBAL was developed to account for deficiencies in existing heat loss pre- diction equations of high producing cattle, principally underestimation of evaporative losses of cows in warm environments. The model they produced provided satisfactory results in this regard compared to values derived from experiments. The model did 75 not incorporate a housing type or varied environment, however, as is desired in this study. 3.11 Ventilation Rate in Naturally Ventilated Buildings Air flow through naturally ventilated buildings can be induced by either wind or thermal buoyancy forces. Wind-induced ventilation is of primary interest for this study and is highlighted in greater detail in this section. Thermal buoyancy will be overwhelmed by the action of the free stream if free stream velocities are sufficiently high. The critical air velocity for modeling heat loss in animal shelters was deter- mined to be 0.12 mls (Hoff, et al., 1993a). Above this value, convective heat loss is governed by standard Reynolds number relations. Wind effect. Air enters openings due to the presence of wind pressure. The dynamic pressure and resulting air flow rate through wall openings are given by ASHRAE (1989) in Equations 3.11.1 and 3.11.2, respectively. AP, = C,"2 pv2 (3.11.1) where: AP, = wind pressure (Pa); Cp = surface pressure coefficient; p = air density (kg/m3); and v = wind speed (mls). Q.v = C. Av (3.11.2) where: Q, = air flow rate (m3/s); C, = effectiveness coefficient; and A = free area of inlet openings (m2). 76 an area. Bottcher, et al. (1986) studied a scale-model naturally ventilated building to evaluate the ventilation rate, pressure coefficients and opening resistance as open area in the sidewalls varied from 0 to 75%. They determined that a straight-line relationship existed between the mass flow rate through the structure and the wall open area as shown in Equation 3.11.3. Pressure drops measured across the barn and opening resistance decreased in a non-linear fashion with increased wall open area, but since they act against each other when determining flow rate, the ventilation rate rose linearly. m = - 0.006 + 0.00334 A (3.11.3) pV,,, LH where: m = mass flow rate of air through the building (kg/s); = mass density of air (kg/m3); ,, = reference velocity (mls); = building length (m); = building ridge height (m); and >iIII"<'° == percentage opening area. Bottcher and Willits (1987) modeled the flow of ventilation air around and through a peaked roof building using numerical methods. The analysis was cumber- some for high Reynolds number flow, but, for low Reynolds numbers, the results matched well those given by algebraic solutions and ASHRAE recommendations. (_)pgning effectiveness and barn orientation. The effectiveness C, of an opening is primarily a function of the opening’s discharge coefficient, CD, when the direction of flow is parallel to the open area’s surface normal (i.e. flow is perpendicular to 77 opening). The average value of C, was 0.82 in the experiments performed by Bot- tcher, et al. (1986). As the experiments were performed with air flowing directly at the sidewalls and other parameters were controlled, C, - CD. Discussion with Bot- tcher (1995) revealed that this value was unrealistic for practical applications since both the opening characteristics and flow conditions were more favorable than could be expected in the field. He recommended that a value of 0.5 to 0.6 be used (similar to that given by ASHRAE above). When the flow approaches in a direction different from normal to the opening, net flow through the opening will be reduced. This effect has been incorporated into the opening effectiveness term in a number of ways. Fundamental principles of fluid flow specify that the reduction factor is sin 0, where 0 is the angle the wind vector makes with respect to the planar opening surface. This would require that there be no flow across a barn for wind directions parallel to the axis of the barn (i.e., 0 = 0°). Measurements in real facilities, however, indicate that there is always some minimal level of flow across buildings with parallel winds due to leakage and other real con- struction imperfections. Barrington, et al. (1994) recommended the use of Equation 3.11.4 which produces a range of C, values that vary from 0.15 to 0.40 as wind direction changes from parallel to perpendicular to the sidewall openings. Ventilation rates for modeled building orientations calculated using this equation varied from 7.0 to 37.0 m3/s on a seasonal basis when evaluated against weather data. Equation 3.11.4 was developed for buildings that used tilt panels to regulate the opening size. The panels increase the 78 opening’s resistance to air flow and therefore have a lower discharge coefficient than do clear openings. C, = 0.15 + 0.25 lsin 0| (3.11.4) Zhang, et al. (1989), developed and validated a model for natural ventilation that included the combined action of both wind and thermal forces. The resulting model demonstrated that thermal buoyancy effects dominated when wind speed was below 0.5 mls and that wind induced flow dominated when wind speed was greater than 3 rn/s. Stack effect. Thermal buoyancy is the driving force in the free convection or as its commonly referred to as the stack effect. Bruce (1982) developed an equation for determining airflow velocities due to the stack effect. Timmons, ct al. (1984) present nomographs for determining ventilation rates from an open building ridge using descriptive geometric parameters for the ridge, the temperature difference be- tween inside and outside air, and the absolute outside air temperature. Down, et a1. (1990) verified the conditions under which the equations developed by Bruce were valid. Pearson (1993) presents an improved equation for use in calculating the ventila- tion rate achieved via the stack effect. His equation utilizes pressure drop coefficients that, if known for the given opening, provide more accurate predictions of air flow. Air distribution. The interior air flow patterns during ventilation via the stack effect have been modeled recently. Timmons and Baughman modelled ventilation in a livestock structure using dimensional analysis. Tanguy and DuPuis (1986) utilized a finite-element model to assess distribution patterns in naturally ventilated buildings having an interior heat source. 79 Effect of natural ventilation design features. A number of studies have been performed in the laboratory and in the field to measure the impact of barn features on the quality of ventilation achieved. Stowell and Bickert (1994) presented results of monitoring the thermal environment of sixteen free stall barns. They found that the gross amount of open area provided per cow was the chief determinant of maintaining low inside air temperature. Barn features that directly influence this parameter are sidewall height, percent of sidewall open and the stocking density. Barn orientation and gable open area were found to be related in their impact on the thermal environ- ment of the barn. 3.12 Radiant Heat Exchange of Buildings The heat contributed to the environment within a building by solar radiation can be substantial. At night, heat loss to the sky may also greatly affect the energy balance of a facility. The effects and modeling requirements of each of these condi- tions are considered in this section. Solar radiation. The effect of solar radiation on building heat load is depen- dent on the astronomical factors that determine the amount and nature of radiation that reaches the building, the orientation of building surfaces with respect to the sun’s rays, and the radiative characteristics of the building surfaces. Astronomical factors. Due to the earth’s shape, axial tilt with respect to the sun and rotation about its axis, radiation is received from the sun at differing angles with respect to horizontal at differing locations on the earth. The resulting angle is commonly called the solar elevation angle. As the solar elevation decreases from 80 normal, the net radiant flux incident on the surface also decreases according to Lam- bert’s Cosine Law (Rosenberg, et al., 1983 throughout subsection). I = Io sin 8 (3.12.1) where: I = flux density on unit horizontal surface (W/mz); IO = flux density on unit normal surface (W/mz); and B = solar elevation angle (°). The solar elevation angle is a function of the time of day, location on the earth and season. It is calculated according to Equation 3.12.2. sin 8 = cos(l) cos(h) cos(D) + sin(l) sin(D) (3.12.2) where: l = latitude; h = hour angle; and D = solar declination. The solar declination is the sun’s angular distance north or south of the equator and determined by Equation 3.12.3. D = 23.5 cos[21t(d - 172)/365] (3.12.3) wherein d = the day (integer) of the year. The amount and nature of the radiation that reaches the earth’s surface is also greatly affected by the conditions of the atmosphere. Clouds, water vapor and particu- late matter absorb and scatter some of the direct beam solar radiation. Trenberth (1992) illustrates that in the radiation balance of the earth, roughly half of the incoming solar radiation reaches the earth’s surface (global solar radiation) and another quarter is absorbed by the atmosphere. Of the solar radiation reaching the earth, some is received directly and the remainder is scattered by the components of 81 the atmosphere. Scattered radiation is called diffuse because it reaches the earth at nearly all hemispherical angles. On a clear day, about 10-30% of the solar radiation reaching the earth is diffuse scattered radiation, whereas, on overcast days, virtually all of the incoming solar radiation is scattered. Clouds and the gases that comprise the atmosphere selectively absorb solar radiation at the very short (UV and shorter) and longer infrared wavelengths (Peixoto and Oort, 1992), meaning most of the remaining incoming solar radiation is in the visible and infrared range. Details on radiation energy balances, the mechanisms of atmospheric scattering and absorption as well as equations for use in modeling radiation incident to the earth’s surface are provided by Rosenberg, et al. (1983), Peixoto and Oort (1992) and Trenberth (1992). Longwave atmwpherlc radiation. The aunosphere is always emitting radia- tion in accordance with its temperature. Clouds, and the atmosphere in general, tend to insulate the earth. In addition to intercepting solar radiation during the day, they absorb nearly 90% of the terrestrial radiation emitted by the earth at all times (Rosen- berg, et al., 1983). The absorbed energy is stored in latent form and then is emitted as longwave radiation, with much of this re-emitted energy being directed back toward the earth. The total radiation flux (direct and diffuse solar plus longwave atmospheric) incident on the earth is called total hemispherical radiation. Rosenberg submits an equation developed by Swinbank (1963) to predict longwave atmospheric radiation from the air temperature measured in a standard shelter 2 m aboveground. The accuracy of Equation 3.12.4 has been confirmed to be 82 reasonable for modeling night-time radiation and dry atmospheric conditions, but greater errors are involved when used during the day or in humid conditions. q,,,” = 5.31x10’” T‘ (3.12.4) where: q,,,” = longwave sky radiation flux, W/m2 and T = shelter air temperature, K. The earth’s surface, including buildings, are at temperatures on the order of the atrnosphere’s. Thus, terrestrial radiation is emitted in the longwave range and Equa- tion 3.12.5 relates the net flux of thermal longwave energy between the sky and a surface. (1...... = q... - oT.‘ (3.12.5) where: q,,,,,,, = net longwave radiation flux WM”); 6 = Stefan-Boltzman constant (567le8 W/m2 K‘); and T, = absolute surface temperature (K). Bond, et al. (1967) demonstrated a means of measuring the various components of radiation that are incident on buildings. Representative zenith radiation measure- ments during summer Califomia conditions (8/18/64, clear sky, noon) indicated the diffuse solar component was about 50 Btu/hr/ftz compared to 125 for the longwave atmospheric. This ratio would likely change considerably in more humid regions where the diffuse solar component can be much larger. Effectiveness of shading devices. Provision of shade is one of the primary roles of the livestock barn. The effectiveness and benefits offered to cattle by various shading materials and arrangements may vary widely. Neubauer and Cramer (1965) performed tests of shading materials arranged in several orientations. They determined 83 that the slope and orientation greatly influenced the all-day (average) surface tempera- ture. Steeper slopes and exposure to the north sky resulted in the lowest daytime heat gain. A slope of 70° from horizontal experienced the smallest temperature rise, being an order of magnitude less than that of the flat arrangement. At night, the shades with less slope did lose more thermal energy to the night sky, however. These findings were incorporated into suggested roof and shade configurations. Shade height. Givens (1965) determined that low shades (6 ft) were preferable to taller (9 and 12 ft) shades in the southeastern United States based on black-globe temperature measurements. [Black-globe thermometers have a temperature sensor enclosed within a black, conductive sphere. Black-globe temperature is a measure of the maximal radiant heating that may occur in a given environment] He attributed the added heating effect in the tall shades to the cloudy conditions that prevail in that area. Cloud cover increases the proportion of radiation that is diffusely received by the earth and the tall shades evidently permitted more of this radiation to enter the building. Bond, et al. (1967) monitored the radiation load under galvanized steel shades of similar heights as those of Givens’ study, but in clear sky, dry California condi- tions. The measurements from the center of the shade indicated that the diffuse shortwave energy. from the zenith sky at noon was 35 Btu/hr/ft2 under a 12 ft shade compared to 15.6 under a 6 ft shade. It was evident from measurements and predic- tion that animals under a tall shade are exposed to greater amounts of diffuse solar energy. Substantial amounts of terrestrial longwave emission entered the buildings since more longwave radiation was consistently measured under the 12 ft shade when 84 the longwave emission from the taller shade should have been less than that from a shorter shade. They also determined that 20-25% of the total radiation received by a surface under shade is diffuse solar radiation and half of that is reflected by the ground. They noted that the benefit of the taller shade should increase if animals were able to follow the shadow throughout the day. Garrett, et al. (1967) tested this theory using the same shade facilities and beef cattle. The cattle were found to indeed be able to take advantage of the larger shadow cast by taller shades if they moved with the shadow. The advantage is most obvious under ambient conditions that otherwise imposed mild to medium heat stress on the animals. Rectal temperature, surface temperature and respiration rate were each significantly reduced under the taller shade compared to no shade and a 6 ft shade height. Under more severe conditions, the differences in the physiological responses were more variable and were not statistically significant. Roof materials. Shade materials are generally characterized by their reflective and transmissive properties. Bond, et al. (1969) investigated the effect of radiant heating on three building materials -- unpainted plywood, white painted plywood and embossed aluminum. They concluded that a building’s material surface does present a significant source of radiant heating to nearby animals on a sunny day. The more reflective aluminum and white painted surfaces reduced the resulting heating load. While nonconductors, such as white enamel paint, are highly reflective to radiation in the shorter visible wavelengths, they are known to be virtually black to infrared radiation (Sparrow and Cess, 1978). Also, aging of roofing surfaces can reduce their reflectance through oxidation or simply by being contaminated. Birkebak, 85 et al. (1964) reported that surface roughness decreases both the total hemispherical and specular reflectance of metallic surfaces, although not equally. When metals oxidize, their surfaces generally become pitted and rough. Various coatings have been applied to roofs in an attempt to add or restore surface reflectance to the roofing. There is evidence that some of these coatings do reduce the solar heat gain to a livestock building (Bottcher, et al., 1990), although their longevity and effectiveness in naturally ventilated buildings with large sidewall openings is still unknown. Dolby and Jeppsson (1993) recently reported on the thermal environment inside naturally ventilated dairy facilities having transparent roof covering. They determined that the interior thermal environment was well maintained as long as the ventilation rate was reasonably high. Considerable variation in the daily environment was evident in their results although it was not directly attributed to the effects of radiant heating and cooling. Insulation is frequently installed below the roof sheeting. During hot weather, insulation under the roof is expected to reduce radiant heating of the roof on housed animals. The effect has been questioned for barns with tall open sidewalls, however. There appears to be little value of having reflective insulation for reducing radiant heat exchange in livestock buildings because it soon becomes covered with dust (Bottcher, et al., 1990). Generally, many problems must be addressed when installing insulation in naturally ventilated livestock buildings if it is to perform as desired (Muehling, 1967). 86 Convective cooling. The effective roof surface temperatures are a function of both the radiative and convective thermal environment. Movement of air over the roofing material tends to counteract the effects of radiant heating or cooling, thus limiting the difference between the temperature of the roof and ambient air. When convective heat transfer from a roof is modeled as that from an inclined surface under laminar flow, equations developed by King and Reible (1991) for calculating Nusselt numbers may be applied. It is difficult to apply these equations to buildings, however, since real flows are generally turbulent and because total building geometries don’t match that of a flat plate in a freestrearn. Brand and Nelson (1962) performed model studies of the convective cooling effect of metal roofs that were exposed to both radiant heating and convective heat transfer (generally cooling). Their study examined thin, uninsulated roofs over sym- metrical gable roof shelters with the wind direction normal to the eaves. Dimensional analysis was utilized to develop an equation relating the convective heat transfer rate to the incident radiant energy intensity as a function of ambient temperatures, the Reynolds number and position on the roof. After validating their model with field data, they concluded that shelters having a high roof with low absorptivity had a thermal advantage due to greater exposure to stronger winds and less solar heating. More recently, Pieters et al. (1994) developed a static one-dimensional model describing heat transfer by conduction, convection, radiation, and phase change to, through and from single greenhouse covers. This model was utilized to determine the influence of condensation and evaporation on static heat losses from greenhouses. 4 - MODEL DEVELOPMENT The model of heat transfer for the animals, in this case dairy cattle, was created by first developing a conceptual model of the various thermal interactions between the animal and the environment within the barn. This conceptual model considered the pertinent effects of weather conditions on the barn environment. A few basic assumptions and constraints were established before developing the conceptual model. Next, a physical representation of the animals was selected. Then the production and dissipation of heat and moisture from their bodies were characterized. Theoretical and empirical relationships developed previously by others to describe heat flow from cows were utilized extensively. The combined actions of the various heat transfer mechanisms operating simultaneously were then modeled. With the animals’ heat loss mechanisms modeled, defining and modeling the animals’ surroundings and general thermal environment remained. Weather was not modeled. Instead, real weather data were utilized as inputs. The weather inputs were included in the estimation of ventilation air characteristics and radiant heating impacts. Following the development of the conceptual model, the appropriate theoretical and empirical relationships were incorporated into a computer program that quickly calculates the modeled cows’ thermal energy status. The computer model was named ANTRAN (from "ANimal heat TRAster model"). 87 88 4.1 Basic Assumptions of the Conceptual Model Primary model assumptions were, i) mass and energy flows are two-dimen- sional, ii) air flows through the barn due only to wind forces, iii) air enters and exits the enclosure through the sidewall openings and iv) steady-state conditions prevail. Two-dimensional model. A two-dimensional constraint was applied to both the animal model and the housing model. Figure 4.1.1 illustrates the two-dimensional nature of the modeled physical system. Livestock buildings are commonly modeled in this manner, converting the three-dimensional directional nature of wind to solely transverse flow of air across the width of the building. This assumed condition accu- rately represents buildings that are much longer than they are wide (as might exist in barns housing large numbers of cattle) as well as buildings that are situated with sidewalls facing the wind. Less accurate model results are obtained for barns of shorter relative length under real, varying weather conditions. The cows are modeled as horizontal cylinders oriented perpendicular to the flow of ventilation air across the barn envelope. Specific implications of the cylindri- cal model assumption for dairy cattle are detailed in Section 4.2. The two-dimensional model assumption implies that the not flow of heat in the axial direction (along the length of the barn and cow rows) is zero. Wind-induced flow. The assumption that the flow of ventilation air due to thermal buoyancy forces can be neglected is valid only if the Grashof number is very small compared to the Reynolds number (see discussion following Equation 3.6.9). Under relatively calm conditions, this assumption will not hold true and a different flow regime must be applied. That analysis is left for further study. 89 Solar - ener jib Barn 9y enclosure / / Ventilation Exhaust 8" —/ Heal Moisture \—0 air —————e ——-——e '\ /—-O AMmm Figure 4.1.1 The two-dimensional nature of the animals and the naturally venti- lated barn as modeled in ANTRAN. Exclusive airflow through sidewalls. Real barns often have openings in the ridge of the roof and in endwalls. Flow through the endwalls has already been pre- cluded from consideration in ANTRAN by the two-dimensional constraint. When warm season ventilation is due to wind forces, a ridge opening usually serves as an exhaust vent. The roof was assumed to be of gable construction (having uniform slope in both directions joining at the peak) and closed at the peak. The closed peak assumption was made to eliminate the consideration of numerous available ridge designs and because flow through the peak under conditions governed by wind was assumed to have minimal effect on the airflow in the vicinity of the animals. The presence of a ridge Opening and the design of the opening would need to be consid- ered for a more detailed evaluation of roof temperature or of calm weather conditions. 90 Steady-state conditions. The steady-state assumption eliminates the need to account for heat storage or to have specific knowledge of the time-varying nature of the animals’ physiological reactions to the environment. A dynamic model would have to consider both the heat storage capacity of the building materials and the capacity of the animals to retain heat. The steady-state model assumption neglects storage of heat in the animal’s body when an increase in body core temperature occurs. Since any rise in body temperature will typically be slight and the objectives of this study are concerned with heat exchange potential once body and surface temperatures have essentially equili- brated rather than during any rise in body temperature, calculation of heat storage within the animal was considered to be of minimal importance and was not perfortned. The model also assumes that all building component surfaces, except those of the roof, are at ambient air temperature unless explicitly assigned a different tempera- ture. The roof is usually under additional radiant heat load and ANTRAN handles the roof separately. Since air temperature may change more rapidly than the temperature of other building components that have substantial thermal mass; e.g., the floor/ground system, building component temperatures are not precisely represented by the model. However, only the surface temperatures are necessary for calculating heat exchange with the animals and it was assumed that the surface temperature of these components would rapidly approach inside air temperature. Little data are available on the thermal condition of floor surfaces in naturally ventilated buildings. Dolby and Jeppsson (1993) did find that in well ventilated buildings having transparent coverings, the daily average temperature of the upper 91 region of the alley floors closely followed average ambient outdoor air temperature regardless of the season. In this study, it was assumed that floor surface temperature would be roughly equal to inside air temperature for all conditions. The effect of varying surface temperature or of the effect of moisture evaporation from the cow alleys were left for later consideration. 4.2 Representation of the Animals within the Barn The cows were modeled as horizontal cylinders that are standing and are aligned end-to-end in rows extending continuously along the length of the barn. All animals were assumed to be homogeneous in size, shape and dimension. Figure 4.2.1 illustrates the positioning of a row of animals within the modeled barn enclosure. Cylindrical form. The cows were modeled as cylinders for a number of reasons. First, modeling the animals as horizontal cylinders fits the two-dimensional nature of ANTRAN very well. Other modeled shapes, such as spheres or ellipsoids, possess a depth dimension that complicates modeling the animals. Also, most of the heat transfer relationships that have been developed and accepted for use with cattle, as well as other livestock, utilized a cylindrical animal form. Lastly, the cow is simply well-described physically by a cylinder, as are many other animals. One disadvantage of the cylindrical form in a two-dimensional model is that the orientation of the animals must be pre-established. Another is that the distinct effects of appendages, such as the legs, are either ignored or muddled into the com- bined effect of an extended trunk. Although the effects of appendages and their substantial surface area play a role in heat transfer from the animal body, Wiersma Barn enclosure O I HT Floor [ : ,,,,, : Figure 4.2.1 Illustration of the modeled cow dimensions and the location of the row of cows within the barn enclosure. (1967) implied that equivalent results are obtained from heat transfer studies with physical cow models by using a single cylinder having an equivalent total surface area and a diameter equal to that of the modeled animal’s mean trunk diameter. The diameter and length of each cow were modeled according to Wiersma’s suggestion. That is, the diameter was modeled as the mean trunk diameter of the cow and the modeled length was initially calculated as the total surface area divided by the cylinder circumference. Mean trunk diameter can be obtained from ASAE Standards (1991) for several livestock species either directly or based on trunk circumference. A question arose as to whether surface area should be assigned to the individu- al cylinder ends and, if so included, whether the ends would participate in heat loss 93 from the animal. The assumption was made that the model cow’s total surface area should be divided between both the outer cylinder area and the area required to cover the ends of the cylinder. This assumption was made because animals logically should be modeled as closed bodies and also because animal lengths were more realistic when modeled in this manner. Then it was assumed that the cylinder ends would not participate in heat exchange since they were butted up against the ends of adjacent animals and were not exposed to air flow. Standing position. The cows are assumed to be in a standing position. Real cows do not always stand up. Actually, the purpose of the stalls in the barn is to provide a comfortable place for the cows to lie down. However, cows do spend a substantial portion of the day standing. Even more time is spent standing during hot weather as the cows attempt to expose more body surface area to air movement. Thus the standing position representation may be accurate for potentially stressful environ- mental conditions but doesn’t hold for continuous or mild weather modeling purposes. Row alignment. The assumption that the cows are lined up end-to-end or head-aside-head in one or more continuous rows cannot immediately be justified as an accurate description of real conditions in livestock buildings. Figure 4.2.2 illustrates four possible ways that cows might align themselves in a free stall barn. The first distribution suggests that the cows randomly choose a location within the barn and also assume a random orientation. In reality, however, they can only locate them- selves within the alleys or stall spaces, so the completely random arrangement is an unrealistic representation. 94 /\. 60v ALLEY DRIVE-"Tm“ cav ALLEY my ' FEED ALLEY ‘ ALLEY i fl fir \I w BARN CRUSS SECTIUN --+-— DRIVE-THRU I FEED ALLEY CW “‘5’ _ - -_ M I din) __ -_ . . map- A I __-_._-_ I I iii i) ii) iii) ' i v) CCUPIE F U R P AN Figure 4.2.2 A free stall barn cross section and an occupied floor plan showing possible representations of cow position and alignment within the barn; i) completely random, ii) randomly-located transverse align- ment, iii) rows of transversely aligned cows and iv) in-line rows. 95 The arrangement of stalls and the placement of feed in typical free stall barns affects where and how a cow positions herself within the barn. Because of these features, cows will tend to assemble in rows running the length of the barn and align themselves aside one another with their bodies perpendicular to the sidewalls. The most accurate model of cow positioning is likely some variation of the second and third schemes shown. Unfortunately, the more realistic representations pose several difficulties in modeling heat loss from the animals via any one heat transfer mecha- nism, much less via several in combination. Hence, the simplified in-line representa- tion of the cows was chosen. In real free stall barn environments, there is no rigid constraint to make the cows distribute themselves along the length of the barn. In fact, cows tend to bunch into huddled masses during repressively hot conditions. However, the assumption was made that the regular distribution of stalls and feeding space along the length of the barn justifies a continuous row representation for most summer environmental conditions and for basic thermal energy status comparisons. In its current form, ANTRAN models only one row of animals within the barn enclosure. It was not assumed that all the animals that would normally be housed in a livestock barn would, nor could, position themselves into a single lengthwise row. The single row assumption is purely a starting point from which to develop improved methods of modeling the entire herd of housed animals. 4.3 Modeling the Thermal Energy Status of the Cows Certain assumptions had to be made to model the thermal energy status of the animals. Acclimatization, acclimation and the method of determining the cows’ 96 present thermal state were considered in the development of the model. The resulting process block diagram is presented in Figure 4.3.1. Thermal environment I Acclimatized Energy balance I metabolic heat Output of animal on the animal dissipated? model results 4? l... is the Acclimatory .__"9_ animal fully Y” actions taken acclimated? Figure 4.3.1 Block diagram of the decision process used in modeling the thermal energy status of the animals. Acclimatization. The animals were assumed to be acclimatized to warm conditions. For dairy cows, this means that the hair coat is in summer condition, minimal tissue resistance and maximal sweating rates are readily maintained, and the cow is not constrained from further acclimating to the surroundings. Although tropical breeds of cattle may make seasonal adjustments in body temperature, it was assumed that this effect was not common in European breeds in temperate regions, so body temperature adjustment was modeled as a mechanism of acclimation only. Thermal energy status. A fundamental assumption incorporated into AN - TRAN was that feed intake and metabolic heat production are not immediately re- duced by hot conditions. An animal’s thermal energy status in the model is indicated 97 both by the skin temperature that can be maintained and by the difference between the heat produced by the cow and the heat that can be dissipated to the environment at normal pro-stress metabolic rate. Thus, if a critical temperature difference cannot be maintained between the body core and skin surface or if heat production exceeds dissipation, then a rise in body temperature is impending. If such a situation exists even when the animals have taken full acclimatory actions, physiologic reality dictates that heat production must be reduced and milk yield will be adversely impacted. It is important to understand that the underlying assumption throughout the model is that heat production is not reduced and that homeothermy may not be achiev- able at all times. Stated another way, ANTRAN emphasizes the projected heat dissi- pating capacity of the animal within its environment and the projected not heat load on the animal if metabolic activity is not reduced. This approach was taken largely because, although there are a number of relationships that have been developed to predict feed intake and milk production in warm environments, the limitations on the appropriate use of available relationships were generally substantial. No relationships were found that were adequately demon- strated to be accurate outside the environmental conditions in which they originated and none was suitably tied to skin temperature or a projected thermal energy imbal- ance. As shown in Figure 4.3.1, heat flow from the body and the thermal energy status of the animals were initially modeled at thennoneutral acclimatized conditions. If the cow’s thermal energy status reveals that a surplus of thermal energy exists, then the energy balance was performed again with the cow being in a more acclimated 98 state. This process is continued until either a thermal energy balance is achieved or all acclimatory actions are exhausted by the animal. Acclimation. It was assumed that, beyond sweating, the principal means of acclimation utilized by the cows were elevated respiratory activity and an allowance for some rise in body temperature. Although some research reports suggest that respiratory activity responds directly to the environment and a rise in respiration rate precedes any rise in body temperature, no suitable relationship exists to confidently define when the two mechanisms are exercised. Also, a larger body of literature suggests that elevated respiration rate is a coincident signal that homeothermy is already not being maintained. Consequently, respiratory ventilation rate and body temperature are increased simultaneously if additional dissipation of body heat is required, each being constrained within some maximum allowable level. It was assumed that if the cow can maintain homeothermy without expending resources to acclimate to the surroundings, then milk production is fully maintained. If cows must acclimate to the environment, then milk production may still be main- tained. But, more likely, feed intake will fall to help offset the need to maintain the mechanisms of acclimation and, consequently, milk yield will fall slightly also. The interactions involved in these situations and the related implications on the production and health of the cow are not well understood (Beede, 1995). Certainly, if the cow is not able to increase the rate of heat dissipation through physiological acclimation, heat production must be reduced and the cow’s health and productivity will likely suffer. 99 4.4 Modeling Heat Transfer from the Animal’s Body Heat flow from the body was assumed to occur via the respiratory system and from the exterior body surface of the animal as shown in Figure 4.4.1. Here, the various forms of heat transfer from the body surface are lumped together into q”, for simplicity. Other minor avenues of heat loss were considered negligible. One such avenue that has been considered by others (Turner, et al., 1987a) is heat loss when ingested food and water are warmed to body temperature before being excreted. As with other purely conduction processes, it was assumed that this minor mode of heat loss would become negligible under warm conditions. If the drinking water or feed was chilled, this assumption would need reconsideration. q'.” Qaurl Skin 008i surface ’ _ surface I I I '1. \ \ ‘ \ 1” '2 q." \\ - \ I / \ I 2 \ I, chnd 2 QCOIv “ l ." —-' :....———-‘. I : Q'eone'; Qrad : ‘ ' l ‘. Peripheral ; ’i ‘. tissue gAmbient’. ‘\ Hair 3 a" I \ coat 3 / Body surface Animal body Figure 4.4.1 Schematic of modeled heat flow from the cow detailing heat loss from the two-dimensional body surface. 100 Uniform body core temperature. Metabolic heat was assumed to be pro- duced and distributed throughout the body at a constant rate and in a manner that produces a uniform core temperature. Metabolism does not really occur at a constant rate, but the digestion process in lactating cattle is extended throughout the day suffi- ciently to justify that assumption. Warm blooded animals have a cardiovascular system that supports a large heat-carrying capacity. This makes the uniform body temperature assumption plausible. It must be recognized, however, that body extremi- ties, especially in appendages, may not be at body temperature. It has already been stated that the cylindrical representation of the animals restricts the modeling of heat loss from appendages. It was assumed that the variability of temperature within the body is, at most, slight during warm environmental conditions. Respiratory heat loss. Both sensible and latent heat loss from the lungs are accounted for within ANTRAN. In warm conditions, heat loss is largely in latent form, but it is convenient to model sensible heat loss from respiration so it was includ- ed. The expired air was assumed to be saturated at a temperature slightly cooler than body temperature per the research of Stevens (1981) described earlier. Respiration rate and respiratory ventilation rate were not assumed to be func- tions of ambient temperature alone, however, as was assumed by Stevens. The equa- tion for estimating expired air temperature was quite accurate (R2 = 0.96), but those for respiration rate and tidal volume were less accurate (R2 = 0.94 and 0.81, respec- tively). The assumption employed in the formulation of ANTRAN was that respirato- ry activities are not strictly a function of one or more ambient conditions, but are a 101 function of the thermal energy status of the cow. Therefore, respiratory activity is modeled as a mechanism of acclimation that is directly related to body temperature. Heat loss from the surface of the body. In the model, respiratory heat loss is subtracted from metabolic heat production. Any excess heat must be dissipated across the body surface. It was assumed that this heat is carried in the arterial blood stream to the vascular tissues and that this process does not limit heat flow from the body. Heat is then transferred to the peripheral tissues below the skin by the vascular blood supply system. From there, the entire balance of residual body heat must be trans- ferred by conduction across the peripheral tissue. Heat is lost from the skin by sensible mechanisms and by evaporation of surface moisture. It was assumed that the heat required to evaporate the moisture comes entirely from the skin rather than from the air within the hair coat. Sensible heat loss occurs by conduction, radiation and local convection currents. However, the flow of heat from these mechanisms is frequently described using an effective thermal conductivity of the hair coat in the heat transfer calculation as is highlighted in the review of literature. The resulting all-inclusive sensible heat loss component is ac- cordingly labeled q.m.. The water lost from the skin was assumed to be transported directly to the surface of the hair coat and away from the body by the movement of air about the body. No condensation or evaporation within the hair coat is accounted for in the model unless the cow is soaked with water. Sensible heat that reaches the outer surface of the hair coat was assumed to be lost to the environment via the convective cooling of the ventilation air and by radiant 102 heat exchange with interior enclosure surfaces. It was recognized that either of these processes could add heat to the hair coat under extreme conditions. Positive heat flow implies that heat leaves the hair coat, negative flow is a heat gain in the model. Metabolic heat production. Several equations for estimation of the metabolic heat production of lactating dairy cattle within the thermoneutral zone were presented in the review of literature. The criteria used in selecting an appropriate relationship were that the equation should consider the combined effects of maintenance, pregnan- cy and milk production and yet should provide realistic estimates of total heat produc- tion. Based on these criteria, either Equation 3.8.2 or 3.8.3 was acceptable. Assumptions had to be made about the weight and productive status of the animals to arrive at an estimate of heat production. Hence it was assumed that all the cows weigh the same, are of the same reproductive standing and produce equivalent quantities of milk. Of course, this assumption never holds true on real farms, espe- cially on a herd-wide basis. It does closely approximate groupings of cattle that are often sorted on the basis of these characteristics within large herds. If herd averages are used for input values in the equations, the user should be aware that model results may not be truly representative of the herd since any cows differing substantially from the average modeled cow will not be accurately modeled and because cows of differ- ing size and productive standing are seldom uniformly distributed throughout the barn. Body surface area. A single value of surface area to model all of the mecha- nisms of heat loss from the skin was desired. The effect of disregarding the thickness of the dairy cow’s summer hair coat (1 to 3 mm) when calculating surface area for convection was examined. The error in neglecting any difference in surface area due 103 to the presence of the hair coat is at most three percent for a 0.6 m diameter (ASAE, 1991) cow modeled as a cylinder or sphere. This margin of error is certainly small compared to the errors introduced when measuring or estimating hair coat depth, trunk diameter and base surface area. The surface area used for all heat transfer calculations was determined by subtracting the area of the cylinder ends from the area given by the Meeh relationship, Equation 3.8.5. If ANTRAN is used with animals having propor- tionately thicker hair coats, then a separate surface area for convection or modification of the sensible insulation provided (per Equation 3.8.11) must be determined. Resistance circuit model. A resistance circuit approach was used to model heat flow from the outer surface of the cow. Figure 4.4.2 illustrates how the physical flows of heat and mass, the temperature and vapor pressure gradients that drive the flows and the circuit representation are interrelated. The physical flow portion of the figure illustrates in detail how the flows must equilibrate at each surface. A liquid layer of unspecified thickness is also shown on the outer surface of the skin. Prolific sweating or sprinkling with water are example situations that might require this repre- sentation. The liquid layer is drawn for illustrative purposes primarily as it was assumed that the sweating rate of cattle would not be sustained at a level that would form a thick layer of moisture and sprinkling of the animals was not assessed. A surface energy balance is applied at the skin and outer hair coat surface to establish the equations relating the various heat flows. First, the heat leaving the skin surface must equal that entering. Similarly, the heat leaving the outer surface of the hair coat must also equal that entering with the requirement that the effective conduc- tion of sensible heat through the hair coat, mm», be the same in both equations. 104 Body Peripheral . Free air core 3 tissue 3: Ha" coat 3 stream . > (5' 0 ° o r}, ——> g. —> m. —> ; ——-p m" ewt O '5' . 0 El (5 _ t l a I , . E ' : a... Qmete-Qresp . q°°"d % :/ Qewt _’./' 4. : —'_—' I :/ Qred . '\ q'cond' —--' I a) l .\ Cl...“ l I : pveet b) lewt=Qewt=rfiwhtg lrnd=Qred lune: q mete-qresp Rites Rolf: the/(kettAe) Rconv=1/(hAe) E») . re . W W—0 Th Terr Toe Rdlll=the/(DeflA-) R°°""=1/(h"‘A') I..= rfi .. ”—W a a c) W Figure 4.4.2 Model representations of the a) physical flow, b) driving potential and c) resistance circuitry of heat and mass transfer from an animal’s outer body surface. 105 Heat approaching the skin is the residual metabolic heat that is being conducted across the peripheral surface tissue, hence the designation qmd. Heat is removed from the evaporative surface as sweat or other moisture evaporates. Since evaporative heat loss q,“ is in latent form, it is not involved in the heat balance at the hair coat surface although conservation of mass must be satisfied throughout the system. At the outer surface of the hair coat the thermal energy balance is comprised entirely of sensible heat flows. The rate of sensible heat flow through the hair coat must equal that of convection qm, and radiation q“, which occur simultaneously to remove heat from the coat. qcond = q'cond' + c1m (4-4-1) qr...- = (1.... + Cl... (4.42) If a liquid layer developed over the skin, the effects of the layer on the liquid’s surface temperature and saturation vapor pressure, the effective conductivity of the coat and the resistance to diffusion of water vapor through the coat each would need to be addressed. And if the moisture was incrementally applied by external means, the dynamic character of the ensuing drying layer would have to be considered. Since moisture for vaporization from the skin comes entirely from internally supplied sweat, these concerns are not relevant in this study and the requirement for conservation of mass reduces to one of constant flow of moisture with the limitation that vaporization rates do not exceed the animal’s maximal sweating rate. Turning to the thermal and vapor density gradient diagrams, it should be evident that skin temperature must be maintained below body temperature for heat to flow by conduction from the body. Normally, a continuously decreasing temperature 106 gradient will exist from the skin to the ambient air as well. However, at extremely high ambient air temperature or under substantial radiant heat load, the thermal gradi- ent may be reversed within the hair coat so that the temperature of the skin is below the temperature of the coat itself. The vapor pressure at the skin surface of sheltered animals will be at or above that of the ambient air during summer conditions even if the animal is not sweating. This ever-present vapor pressure gradient within the hair coat is the driving force that feeds the vaporization process that cools the skin. Finally, the analogous resistance model defines how the heat and mass flows from the animal are modeled within ANTRAN. Each flow (electric current analogy) is either modeled as a difference in potential (as in voltage) and an equivalent resis- tance or as a heat (current) source/sink. Surface moisture flow. Starting with the simple water vapor circuit, moisture flows from points of high vapor pressure to lower vapor pressure. Thus, moisture must move from the skin to the ambient air for all realistic warm weather circumstanc- es encountered. The movement of moisture is resisted by both the nature of the hair coat and the character of the air moving about the body. These resistances act in series which simplifies the model since the mass flow rate can thus be expressed as the total vapor pressure difference divided by the sum of the resistances. mw 5 1.. = (0.... - Pt.)/(R.m + Rs...) (4.43) where: ritw = mass flow rate of water vapor (kg/s); Iw = analogous current for water vapor flow (kg/s); pvsat = saturation vapor density at liquid interface (kg/m3); P... = vapor density of free stream air (kg/m3); 107 Rdiff = resistance of hair coat to diffusion of water vapor (slm’); and Rm, = resistance to convection of water vapor from hair coat (slm’). The resistances were modeled as shown in Equations 3.8.26 and 3.8.27 except that the resistance terms include the surface area A,. This was done so that heat flow is described rather than heat flux. Also, the rate of moisture loss by evaporation was limited to the maximal sweating rate that could be sustained by the cows. Rdiff = tlac/(1)61 As) (444) RM, = 1/(hm A.) (4.4.5) where: thc 2 thickness of the hair coat (m); Deff = effective mass diffusivity of water vapor into air (mzls); and hm = convective mass transfer coefficient (mls). Surface heat flow. A few mechanisms of heat flow were modeled as heat (analogous current) sources or sinks. The residual metabolic heat load is modeled as a vascular source, I,“ , vaporization from the skin as a latent sink, 1,", and the net radiant heat load from the surroundings as a radiant sink, Ind. The vascular and latent currents are modeled in Equations 4.4.6 and 4.4.7. The radiant current is determined from a matrix solution of the radiant energy exchange within the enclosure which is described later. Energy required to evaporate the surface moisture was assumed to be provided by the body via the skin rather than by the air within the hair coat. The literature shows this assumption holds as long as evaporation occurs from the skin. Ivase = qmen - qmp (4.4.6) where: qml = rate of metabolic heat production (W) and qmp = rate of respiratory heat loss (W). 108 Iswt = [1]" ha (447) where: 1“,, = analogous current for evaporative heat flow (W); rhw = mass transfer rate of water vapor (kg/s); and hr 8 = latent heat of vaporization of water (J/kg). Heat flow through the peripheral tissue was modeled as in Equation 3.6.8. The thermal resistance (or insulation) of the peripheral tissue is held constant within the model at its minimum value. In reality, tissue insulation is rapidly lowered to a minimum level under hot conditions, but it also varies with the environment to balance heat loss with the residual metabolic heat load. The objective of this effort was not to model the exact nature of heat flow under mild conditions, but rather to model heat flow in stressful thermal environments. Therefore, excess heat loss was accounted for solely through decreased sweating rate. It seems logical that if too much heat is being lost from the skin, reducing the amount of moisture that can be vaporized from the skin is the most expedient means available to the animal to maintain a reasonable skin temperature and rate of heat loss from the body. Sensible heat flow through the hair coat is evaluated as a conduction phenome- non using a thermal resistance that incorporates an effective thermal conductivity as shown in Equations 4.4.8 and 4.4.9. Q-m- = (T a - Tc. YR.“ (4.4-8) where: mom. = rate of sensible heat flow through the hair coat (W); Tsk, Tc, = skin and hair coat surface temperature, respectively (°C); and Reff = thermal resistance of the hair coat (°C/W). Reff = the [(keff A. ) (4.4.9) 109 where: thc = thickness of the hair coat (m); keff = effective thermal conductivity of hair coat (W/m °C); and As = exposed body surface area (m2). The rate of convective heat loss from the coat is modeled as shown in Equation 4.4.10 where the external resistance to convection is presented in Equation 4.4.11. qconv = (Tc: ' Ta )IRcoov (4°4-10) where: qconv = convective heat loss from the hair coat (W); T, = free stream air temperature (°C); and Rm, = external thermal resistance of the hair coat (°C/W). Rm, = l/(hA,) (4.4.11) wherein: h = convective heat transfer coefficient (W/m2 °C). The convective heat transfer coefficient is calculated using the relations report- ed by Wiersma rewritten in Equations 4.4.12 through 4.4.14. These relationships and the previous equations are in harmony with the selected animal physical model as long as the hair coat remains relatively thin. h = Flu(kld,) (4.4.12) Nu = 0.65 Re,“3 for 8 x 10’ < Red < 1.5 x 10’. (4.4.13) Red = U..d,,/v (4.4.14) where: Nu, Re = Nusselt and Reynolds number, respectively; k = thermal conductivity of air (W/m K); db = mean trunk diameter (m); U” = free stream air velocity (mls); and v = kinematic viscosity of air (mzls). 110 4.5 Structure of the Computer Program ANTRAN was written in the Fortran programming language using the MS Fortran° software package. The program is designed to operate using input that could either be entered by the user at the keyboard or retrieved from an ASCII data file. The basic structure of the program is illustrated in Figure 4.5.1. . Data input 8 Enclosure Animal energy Introduction [ processing specifications balance I I l I l l l l l I l I l i l l Describe program File specification Ventilation status Initialize conditions Define variables Data retrieval Roof/surface Respiratory heat loss temperature Declare variables Data processing Heat exchange at . * barn dimensions hair coat surface Initialize variables ' cow characteristics * convection ' row location * radiation ' air conditions Heat exchan e at " interior air flow 9 . skin surface barn properties * evaporation * solar conditions ' sensible heat ’ s cial features pe Net heat loss Data storage Output of results Figure 4.5.1 Structure of the computer model, ANTRAN. After providing a brief introduction to the program user, ANTRAN defines and declares all the required program variables. Constant values and variables that are rarely modified are initialized so the program can gather input data. In the data input and processing portion of the program, sources of input and output data are specified, as are names and paths for data files. Then input data are retrieved and subsequently processed to provide values having units appropriate to the basic model variables. 111 Default values are provided for each variable based on Holstein cows in a partially Open four-row barn located in Lansing, MI during solar noon on a summer day. The user may accept the defaults or enter new input values. Input data are screened for values that are unrealistic or that might produce an error in the program. Brief descriptions of the inputs that are needed in the program follow. Once all required data are entered, the variable values are sent to a storage file. This allows the user to define default input data which may be very helpful for multiple model runs. a) b) d) Structural dimensions - the program user is first requested to enter the barn width, wall height, roof pitch and wall open area. From these data, the seg- ments of the barn enclosure and the cow row are described in Cartesian coordi- nates and their surface dimensions are calculated. Livestock characteristics - the species, weight, production level, gestation state and other details describing the animal are entered next. From these data, all the necessary physical characteristics of the cows are determined in preparation for calculating the flow of heat to, through and from the body. Animal position - the location of the row of cows is determined with input from the user. By default, ANTRAN initially locates the row of cows inside the windward sidewall by one-third the width of the barn. This generally coincides with a cow alley along a feeding area. Ambient air conditions - air temperature, relative humidity and atmospheric pressure must be provided. ANTRAN uses these data to calculate all the pertinent psychrometric values that may be utilized within the model, as well as to compute the temperature humidity index for reference. e) 8) h) 112 Air flow parameters - wind speed and direction and the coefficient of discharge for the wall openings are entered next. ANTRAN calculates the air speed in the animal zone based on the building ventilation rate and continuity. Altema- tively, velocities obtained from other models can be entered. The ventilation rate through the building is calculated according to Equation 3.11.2 using 0.5 to 0.6 for the opening effectiveness as recommended by Bottcher (1995). Ventila- tion rate is reduced for angled winds according to Equation 3.11.4. Surface properties and level of insulation - emissivity values of the building components are specified for both long-wave and short-wave radiation. The bam’s roof is initially uninsulated. A fully-insulated roof can be simulated wherein the underside temperature is assumed to equal inside air temperature. Solar conditions - for some advanced model applications, the solar date and time, orientation of the barn, and other data are required. In this study the ambient radiant conditions are entered directly. Special features - some of the model relationships can be used in situations where water is applied to the skin surface. Since soaking cows with sprinklers was not considered in this study, evaporation from the cows was limited to the cows’ maximal sweating rate. The next segment of the program specifies the nature of the enclosure. This small segment of the program accommodates use of the model under special circum- stances. As described in the following chapter, special considerations are taken to allow the program to simulate laboratory conditions. 113 Lastly, a thermal energy balance is calculated for the animals within the enclo- sure through an iterative process. When performing the energy balance, the program first performs an energy balance on the acclimatized, but unacclimated animals as described previously in this chapter. Heat generation by and dissipation from the cows is calculated. The radiant energy balance of the row of cows is performed using a program called RADENC (Copyright W.A. Thelen, 1993). This program calculates the net heat flux of each pertinent surface within an enclosure given the complete set of view factors and either a constant temperature or heat flux value for each surface. View factors for the building enclosure surfaces and the row of animals are deter- mined through the use of basic two—dimensional view factor equations. Because the row of cows blocks the view of some interior surfaces by others, extensive use of Hottel’s equation (Gray and Mtlller, 1974 and Siegel and Howell, 1980), sometimes referred to as the method of strings, is employed. If the cows are not in a state of thermal equilibrium, ANTRAN simulates acclimatory actions on their part and performs the energy balance again. If equilibri- um can be attained through temporary acclimatory actions, the program terminates and creates a summary of output data. If equilibrium cannot be achieved via acclimatory actions other than through a reduction in metabolic heat generation, the program terminates at the maximal allowed acclimation level, reports that thermal equilibrium is not attainable for the given conditions and creates a summary of output data which includes the surplus heat load upon termination of the program run. A sample listing of program output is provided in Appendix B. 5 - MATERIALS AND METHODS The heat transfer model was evaluated and utilized in two stages: i) The computer program was used to model the response of dairy cattle housed within artificial environments simulating the conditions of a previous research study conducted in environmentally controlled facilities and the model results were qualitatively compared to measurements taken during that study; and ii) The computer model was used to project the impact of some features of natu- rally ventilated dairy facilities on the thermal status of the housed animals during various weather conditions. 5.] Comparing Model Results with Environmental Chamber Measurements Two references cited in the literature review, Kibler and Brody (1954) and Thompson, et a1. (1954), report results from controlled environmental chamber studies with dairy cattle that assessed the effect of varied air speeds on cows’ thermoregulato- ry responses. The interior chambers were sufficiently insulated and isolated so that chamber surface temperatures were maintained very close to interior air temperature. ANTRAN was modified to simulate such an environmental chamber by approx- imating the chamber size, covering the sidewall openings, prescribing that surface temperatures equal air temperature and artificially imposing on the cows a stream of 114 115 air that was equivalent to that used in the chamber studies. The option of covering the sidewall openings was provided to avoid any difficulties that might arise in the calcu- lation of shape factors with zero surface area. In the environmental chamber study, several breeds of cows were monitored at different temperature and air velocity combinations. Air speed was controlled within the chamber and within the model at three velocity levels characterized as follows: Low = 0.2 mls (0.4 to 0.5 mph); Medium = 2.0 mls (3 to 6 mph); and High = 4.0 mls (8 to 9 mph). Comparisons of model output and data obtained from the environmental cham- ber study were made for the low and medium air flow conditions. The air speeds used in the high velocity (4.0 mls) chamber trials are beyond the appropriate use of this model in its current form (Reynolds number exceeds 150,000 upper limit), so those conditions were not simulated. Conditions at low air velocities were modeled, but it should be recognized that Reynolds numbers for such conditions are at the lower fringe of ANTRAN’s usable range (Re ~ 8000). ANTRAN was used to simulate only those environmental conditions with air temperature above 15 °C (59 °F) because the model components were primarily derived and intended for use in warm conditions. Air temperature was raised from 10°F to nearly 100 °F in the chamber study and the relative humidity was generally maintained at 60 to 70%. Each of the following temperature and humidity combinations were simulated at the low and medium air velocity levels: 15, 20, 25, and 30 °C @ 65% RH; 35 °C @ 60% RH; and 40°C @ 50% RH. The relative humidity was lowered 116 slightly as the temperature rose since the physical relationship of relative humidity with temperature and the wording of the reports suggest that the variation in moisture content of the air would result in lower humidities at higher temperature. Lastly, to simplify predictions and comparisons, only Holstein cows were considered. Three Holstein cows were used in the chamber study. Average character- istics were used as inputs to the model and the results were compared to the reported averages for that breed. The specific inputs that were held constant for the simulation runs are provided in Table 5.1.1. Table 5.1.1 Cattle and building inputs for validation simulations. Cow characteristics Building characteristics Weight: 600 kg Width (length of flow): 8 m Production: 24 kg/d Wall height: 2.75 m Gestation: 0 days pregnant Roof slope: 1: 12 Trunk diameter: 0.65 m Surface emissivity: 0.95 Coat thickness: 2.0 mm Max. sweating rate: 300 g/mzlhr Coat emissivity: 0.95 Normal body temperature: 38.5 °C Maximal short-term rise in body temperature: 3.0 °C Normal respiratory ventilation rate: 100 L/min. _—__————— The Holstein cows in the chamber study were larger and higher producing than the average 1950’s era cow. Because of their size and production, their cylindrical representation was assumed to be typical of today’s animals and the trunk diameter reflects that assumption. Also, the warm weather portion of the chamber study was 117 performed in early spring. It was assumed that the cows would retain some remnants of their winter coat as might be observed in warm housing; i.e., a thick summer- condition coat was assumed. No published value exists for the maximal short-term rise in body temperature that can occur without affecting production. Several producers and at least one experi- enced researcher in this area (Beede, 1995) were confident that some rise in body temperature and respiration rate can be tolerated by cows for a few hours a day with- out affecting production as long as the cows had opportunities later in the day to dissipate that excess internal heat. From these contacts, an extreme value of 3 “C was selected for the maximal rise in body temperature allowed during the simulations. The simulations were conducted under the assumption that elevated body temperature and respiration rate over a short duration would not affect daily feed intake and milk production, without considering potential effects on reproduction or other health measures. ANTRAN does allow this value to be reduced during input and preliminary output is always produced during the initial simulation iterations corresponding to the assumption that feed intake falls as soon as body temperature begins to rise. Simulations were then performed given the parameters just described. Simulat- ed skin and hair coat surface temperatures were compared to values measured (with thermocouples) in the chamber study. Due to the limited amount of experimental data, statistical measurements were not performed and few statistical measures were provid- ed to evaluate the reliability of the chamber data. The data from the series of environ- mental chamber studies, of which these trials are a part, are still the best of very limited data of this nature available. 118 5.2 Projecting the Effect of Weather and Barn Features on Heat Loss Next, the model was used to evaluate how heat transfer from the cows was impacted by different weather conditions and changes in pertinent building design features. The cow representation used for this portion of the study was that of H01- stein cows in mid-lactation on a modern dairy operation. In addition to being with calf, these animals possess a somewhat larger frame and level of production than were used for the previous validation simulations. The revised characteristics of the cows are given in Table 5.2.1. Table 5.2.1 Cattle characteristics used as model input for projections. Weight: 635 kg Production: 30 kg/d Gestation: 120 days pregnant Trunk diameter: 0.70 m Coat thickness: 1.4 mm Max. sweating rate: 300 g/mzlhr Coat emissivity: 0.95 Normal body temperature: 38.5 °C Maximal short-terrn rise in body temperature: 3.0 °C Normal respiratory ventilation rate: 100 L/min. w Effect of varied weather conditions. Each trial was evaluated for mid-day conditions from atypical days characterized as i) ‘hot & breezy’ and ii) ‘calm & muggy’. Weather data for Lansing, M1 were obtained from the Michigan Meteorolog- ical Resources Program at Michigan State University. These data are archived by the National Climatic Data Center in Asheville, NC and include measured and modeled solar radiation values. Weather conditions are summarized in Table 5.2.2. 119 Table 5.2.2 Summary of weather conditions on comparison days. Parameter Hot & breezy Calm & muggy Date 6/25/88 8/27/90 Time (local) 1:00 pm 1:00 pm Dry-bulb temperature (°C) 36.1 29.4 Relative humidity (%) 35 75 Wind speed (mls) 13.4 3.6 Wind direction (degrees from north) 270 (W) 230 (SW) Direct beam shortwave solar (W/mz) 848 117 Diffuse solar on horizontal (W/mz) 142 341 The weather data are mid-day values recorded near solar noon. This time was selected to best represent highly shaded conditions inside the barn so that only diffuse radiation would enter through sidewall openings. The hot & breezy day weather conditions were relatively dry with clear skies. By comparison, the calm & muggy day conditions were not as hot, much more humid, and included the effects of hazy skies. These weather conditions are rather extreme for the Lansing area and were selected primarily for illustrative use. Effect of varied building parameters. Simulations of heat loss from a row of dairy cows were made as one building design feature was varied during each simula- tion. The features evaluated were barn width, percentage sidewall open, sidewall height and roof insulation level. Descriptions of the control barn features and of the variations considered are shown in Table 5.2.3. Ample insulation was taken to imply that the interior roof surfaces would be at ambient air temperature. Without insulation, the roof underside temperature was assumed to be at least 10 °C warmer than the air temperature. This approximation was derived by assessing roof underside temperature 120 measurements taken at six locations within each of two free stall barns in mid-Michi- gan over a one-month summer period (8/95). Table 5.2.3 Summary of barn features and alterations evaluated in the model. Barn feature Control Alteration Width 27 m 18 m Wall height 3 m 2 & 4 m Percent open 60% 30 & 80% Roof slope 4:12 «- Ridge opening none «- Surface emissivity 0.95 --- Insulation none ample Orientation N-S -- 6 - RESULTS AND DISCUSSION 6.1 Comparison of Model Results with Environmental CWber Measurements Skin and hair surface temperature. In this section, ANTRAN simulation results are compared to reported data that were obtained from studies conducted in environmental chambers at the University of Missouri. Skin and hair surface tempera- tures obtained using the model and measured in the chamber experiments are shown alongside one another in Figures 6.1.1 and 6.1.2. Figure 6.1.1 displays the cow surface temperatures where the interior air speed was 0.2 mls. Modeled and average measured skin temperatures for low air speed conditions varied by no more than one degree Celsius at each of the three chamber study temperatures. The modeled skin temperature is higher than that measured at the lowest environmental temperature, but is lower at the warmer chamber temperatures. Modeled hair coat surface temperatures, on the other hand, were always less than measured values. Additionally, the difference between modeled and measured hair temperatures was almost 2 °C at the intermediate (26.8 °C) chamber temperature. A similar comparison is shown for results at a 2.0 mls air velocity in Figure 6.1.2. It should be noted that measurement data from the chamber study were not available for a chamber temperature beyond 30 °C. but data at the two lower chamber temperature levels were reported. The differences between modeled and measured 121 122 45 ‘ Modeled skin @ Measured skin Modeled hair [2 Measured hair Temperature (C) 17.9 26.8 35.0 Environmental temperature maintained (0) Figure 6.1.1 Comparison of modeled cow surface temperatures with reported controlled environment measurements where air velocity is 0.2 ads and environmental temperatures are varied (RH ~ 65%). skin temperatures are roughly 0.5 °C. In this case, differences between hair coat surface temperatures are smaller than those between skin temperatures at both chamber temperatures. The model slightly overestimated the amount of cooling that occurs at the skin surface for most of the air temperatures and velocities considered while hair coat surface temperatures are modeled with greater accuracy at the 2.0 mls air speed. In general, there is good agreement between measured and modeled temperatures at the higher air velocity. With limited measurement data available in the literature, it is difficult to assess why differences between the modeled and measured surface temperatures 123 45 .Modeied skin @Maasured akin .Modelod hair lXMeasured hair 00 0| Temperature (C) (a) O 10 (ll 20 1 8.3 26.7 Environmental temperature maintained (C) Figure 6.1.2 Comparison of modeled cow surface temperatures with reported controlled environment measurements where air velocity is 2.0 mls and environmental temperatures are varied (RH ~ 65%). occurred. At the lower air speed, the comparatively larger deviations may have arisen because of inaccuracies in the application of the model’s governing heat transfer equations for low Reynolds number flows or, more likely, due to differences between the modeled animal representation and actual conditions. In the environmental cham- ber studies, air flow was fairly evenly distributed amongst the cows, but the cows were not arranged in conveniently modeled lengthwise rows. Thus, radiant heat exchange was taking place between cows and not solely between a row of cows and the chamber enclosure as was assumed by the model. At each chamber temperature, the measured hair coat surface temperature was warmer than the temperature of the chamber surfaces. Under such conditions, there would be a not transfer of radiant heat 124 from the cows to the exposed chamber surfaces, but there would be no not exchange between cows having a similar hair coat surface temperature. Since the cows in the chamber study were partially shielded from the chamber enclosure whereas the mod- eled row of cows was not, the chamber study cows would lose less heat by radiant means than was assumed by ANTRAN at low air velocities. This is a possible expla- nation for the higher hair coat surface temperatures in the experiment compared to modeled temperatures. Further temperature results. Figures 6.1.3 and 6.1.4 illustrate the animal temperature data produced by ANTRAN for a range of modeled environmental tem- peratures at 0.2 and 2.0 m/s air velocity levels, respectively. In each figure, tempera- tures are shown after the cow has acclimated to the thermal surroundings established by the modeled environmental chamber. Thus, a steady-state condition is described. If the environmental temperature is raised or lowered, the temperatures given by the figures are either those at the newly achieved steady-state equilibrium point (meaning the cow is dissipating as much heat as is produced) or the maximal body temperature condition (implying there is still an excess of metabolic heat). In these figures, the dashed line labeled "Equilibrium skin" represents the skin temperature that would need to exist to achieve equilibrium without exceeding the allowed body temperature or decreasing metabolic heat production. This line further illustrates the environmental conditions at which equilibrium can no longer be achieved without decreasing feed intake. The magnitude of the difference between modeled values of skin temperature and equilibrium skin temperature indicates the level of excess heat load the cows may be experiencing. 125 45 ‘ Short-term maximal temperature 40 —: Q . 335': E :30... ............................................................................ l— _ 25— ............................................................................... *Body alt-sum «II-Hair +tiqumbrlum akin 20...r,++4.,....r4.+.,1-.. 15 20 25 30 35 40 Environmental temperature maintained (C) Figure 6.1.3 Modeled cow body core and surface temperatures within a simulated environment with a 0.2 mls air velocity vs. temporary steady-state environmental ternperature maintairied (RH ~ 65%). In both Figure 6.1.3 and 6.1.4, it is evident that hair and skin temperatures approach body temperature under warmer ambient environmental conditions. The clear goal of the cow in a hot environment is to maintain as large a temperature difference between the body core and the skin surface as is reasonably possible. If some temporary rise in body temperature occurs during acclimation, an improved thermal gradient results which allows either for greater heat dissipation at environmen- tal temperatures below body temperature or for less heat gain when near or above body temperature. The cooling potential of vaporization from the skin of the cow and the buffer- ing capacity of the hair coat for sensible heat gain at high ambient temperature are 126 45 c: : , 2‘“ 35— .......................................................................... o I? 1 ______ +- ----- e -------- 4 § .. an— ........................................................................... .2 25.1 .............................................................................. 2° ‘ *Body *Skln *Hair +Equillbrium akin .e..,..e-,....,rr-.re... 15 20 25 30 35 40 Environmental temperature maintained (0) Figure 6.1.4 Modeled cow body core and surface temperatures within a shnulated environment with a 2 m air velocity vs. temporary steady-state environmental temperature maintained (RH ~ 65 96). evident as well. The vaporization of sweat keeps the skin surface cooler than the surrounding body mass for all conditions and even keeps the skin cooler than the haircoat at the most oppressive temperatures. The hair coat serves both a positive and negative role when it becomes warmer than the skin. It protects the skin from the direct action of radiant and convective heating on the one hand, but it also limits moisture loss as is detailed later. The increase in air velocity from 0.2 to 2 mls shifted the modeled surface temperature curves to the right which results in a cooler surface temperature at the higher air speed for any given environmental temperature. The model results suggest that, when greater air movement exists in the animal area, a satisfactory temperature 127 gradient between the body core and skin surface can be more readily maintained, reducing the need for body temperature to rise as environmental temperature increases. Heat loss. Figures 6.1.5 through 6.1.8 show the modeled cows’ sensible and latent heat losses in comparison to the thennoneutral-state metabolic heat production rate for the two air speeds and for either unacclimated or acclimated conditions. The reader is reminded that real cows would naturally take actions to acclimate to their environment if such actions were required to maintain a thermal energy balance. Heat losses were modeled and are shown for the unacclimated condition only to gain an appreciation for the positive effects of acclimation actions, especially increased respi- ratory activity, on the cow’s ability to approach a thermal energy balance. In these figures, latent heat losses clearly become a larger share of the total heat lost by the animals in hot weather. The relative magnitude of the latent heat loss varied little with ambient temperature, however. Because less heat is lost by sensible means under warmer ambient conditions and latent heat losses remain relatively constant, the modeled cows experienced a thermal energy imbalance at the higher ambient temperatures. This state of imbalance would require that measures be taken to restore the thermal energy balance. Comparison of Figure 6.1.5 with Figure 6.1.6 and Figure 6.1.7 with Figure 6.1.8 shows that the modeled acclimation responses of the cows achieve an energy balance for a substantially greater range of environmental temperatures. In the low air velocity environment, the cows would not have been able to maintain a constant body temperature even at 15 °C were respiratory activity not increased and body temperature not allowed to rise some amount. 128 ngenalble lose mutant loee *- Baaal production g Q E E, x Q :r: -200 i i i + Jr i 15 20 25 so 35 40 Environmental temperature maintained (C) Figure6.l.5 Modeled heatlossofa rowofcowswithin asimuiated environment with a 0.2 mls air velocity vs. steady-state environmental temperature maintained(RH~65%)ifaccfimatlonhinhiblted. In the environmental chamber study, the cows were reported to have expanded thennoneutral zones when supplied with good air movement during hot conditions. This effect was simulated by the model for the step increase from 0.2 to 2 mls when Figures 6.1.5 and 6.1.7 or Figures 6.1.6 and 6.1.8 are compared. The resulting in- crease in convective heat loss, including the convection of water vapor from the cow’s body is effective in maintaining an energy balance to beyond 25 °C with better air movement. The Holstein cows in the environmental chamber study were reported as having maximal vaporization rates at 35 °C of 500 g/hr and 260 g/hr from the skin and lungs, respectively, at low air velocity. By comparison, ANTRAN modeled maximal vapor 129 ESenslbie lose matent Ioee * Basal production E E. 0 E a e x O 15 O 1: -200 i i i i % if 15 20 25 so 35 40 Environmental temperature maintained (C) Figure6.l.6 Modeled heat loss of a row of acclimated cows within a simulated environment with a 0.2 mls air velocity vs. temporary steady-state ummmmnnmuutunpuannenmmMNde(RHL~65%». loss rates of 620 glhr and 440 glhr. At 2 mls air velocity, the rates from the environ- mental chamber study were about 350 g/hr and 150 g/hr compared to the modeled rates of 950 g/hr and 420 g/hr. If the vaporization measurement techniques used in the environmental chamber study are assumed to be accurate, there is evidently some difference in the partitioning of heat loss or methodology taken by ANTRAN and that of real cows when managing thermal stress. No decline in feed intake, heat production or milk production is modeled in ANTRAN. Rather, the program predicts an impending decline whenever excess heat production exists. In the Missouri chamber study, the cows’ feed intake did decline. Thus, much of the difference in moisture vaporization results may be 130 “‘00 Emirate ioae ZLatent lose at- Basal production V >‘&\\\\\\\\\\\\\\\\\\ A0 .V V A O V A Heat exchange rate (W/cow) O V A O OI , 1 -200 i l +~ % i 15 20 25 so 35 40 Environmental temperature maintained (C) Figure 6.1.7 Modeled heat loss of a row of cows within a simulated environment with a 2 mls air velocity vs. steady-state environmental temmrature maintained (RH ~65%)ifaccllmationls inhibited. attributed to the fact that data were gathered over several days under hot conditions, while ANTRAN models the cow’s response to conditions over a shorter period of time and without an allowance for reduced feed intake. Also, the cows were reported to have lost weight during the course of the chamber study and it was presumed that body reserves were utilized to produce milk at a lower metabolic energy expenditure than if only consumed feed was used to produce the milk. More recent data (Monsan- to, unpublished 1987 data) indicates that high producing cows exposed to a 30 °C environment may easily have vaporization rates from the skin and lungs that are higher than those produced by the model. 131 ESeneible lose ELatent loee *- Baeal production ’5 § 5 2 8 g, o x o E -200 i 1r i 1r Jr a 1 5 20 25 3O 35 40 Environmental temperature maintained (C) Figure 6.1.8 Modeled heat loss in a row of acclimated cows within a simflated environment with a 2 mls air velocity vs. temmrary steady-state environmental temperature maintained (RH ~ 65%). The inherent differences between the assumptions incorporated into the model and the situation where cows are exposed to constant environmental temperatures for an extended period of time likely affect the results. Recall that ANTRAN allows for acclimation to temporary conditions. Temporary, in this case, means that adverse conditions may persist for a matter of hours before cooler conditions arrive. Experi- ence in the field indicates that temporary acclimation often allows cows to endure such temporary conditions without decreasing feed intake or experiencing unmanageable body temperatures. In the environmental chamber studies, however, the cows were generally kept in a constant temperature environment for several days. The negative consequences to the cows when body temperatures and respiration rates are elevated 132 for extended periods of time would soon preclude the continued dependency on these mechanisms as the only means of acclimation. The cows would, of necessity, resort to reductions in feed intake and metabolic heat production to prevent a potentially life threatening situation from developing. 6.2 Use of the Model in Predicting Heat Losses ANTRAN was used to assess the impact of weather and naturally ventilated barn features on the ability of a row of cows to dissipate heat. The results are pre— sented in stacked bar chart format in the following figures. Modeled absolute rates of heat loss are partitioned according to the primary heat transfer mechanisms involved: respiration, evaporation from the skin surface and radiant and convective heat losses from the hair coat surface. Also shown is any resulting excess heat load which exists when the rate of heat loss is less than the normal rate of metabolic heat production. This quantity is expressed as "heat loss needed" in the figures. The figures are used to draw implications about the effects of weather condition or barn design on the various heat transfer mechanisms and the overall thermal energy balance. Effect of weather. As described in the methods section, model simulations were run and comparisons made for acclimatized Holstein cows, each producing 30 kg/day of milk, under two rather extreme summer, mid-day conditions in Lansing, MI. Figure 6.2.1 highlights the model results obtained for the reference or control barn for these two conditions. Weather conditions have considerable impact on the rate of heat loss available to the cows and thus on the excess heat load they experience. 133 . ‘ Heat loss INeeded @ Respiration DZOIOIOIOIOZOIOIOX Heat transfer rate (W/cow) Hot & breezy Calm & muggy Weather condition Figure 6.2.1 Magnitude of modeled heat loss via primary heat transfer mechanisms and the net heat loss available to cows in the control barn for two extreme mid-day weather conditions in Lansing, MI. On the ‘hot & breezy’ day, substantial evaporative cooling potential existed to facilitate heat loss. Both the relatively high wind speed and the low humidity contrib- uted to the large evaporative losses. The hot roof and diffuse radiation entering the sidewalls were significant heat loads on the cows, however. When the heat gained by radiant means was subtracted from the heat losses, each modeled cow still needed to dissipate 350 W of excess heat (represented as the solid-fill, "heat loss needed" area in the figures). By comparison, the evaporative losses from the cows’ body surface area on the ‘calm & muggy’ day were only about half those modeled on the ‘hot & breezy’ day. 134 As a result, the net heat load on each cow was about 500 W. This resulted even though the radiant heat load, as modeled, was minimal for the ‘calm & muggy’ day. Effect of variation in barn features. In the following figures, the heat loss potential of a single row of cows in barns of varied construction is compared to that of cows in the reference barn. In each instance, the comparison is presented for mid-day conditions for the ‘hot & breezy’ day and the ‘calm & muggy’ day previously de- scribed. In these figures, the left-hand set of bars compares heat loss results for the ‘hot & breezy’ conditions while the right-hand set shows the same comparison for the ‘calm & muggy’ day conditions. Barn width. Figure 6.2.2 compares heat loss results for two barns having widths of 18 m and 27 m, for the two mid-day weather conditions. In each barn, the row of cows was positioned one-third of the barn width from the windward sidewall and other barn features were unchanged. The gross impact of barn width on the energy balance of a single row of cows is minimal under these circumstances. There is a slight advantage to the narrow barn in terms of heat loss capacity still needed (10- 20 chow). Most of the advantage in each case can be attributed to a small increase in evaporation from the skin surface. The velocity of air approaching a row of cows in the interior of a narrow barn would be expected to be slightly greater than that in a wide barn, other things being equal, because the air is not spread out over as wide a cross-sectional building area. Thus evaporation from the skin surface reflects that very small advantage. During the ‘calm & muggy’ day, much of the narrow bam’s advantage in evaporative capacity was offset by radiant heating effects. Due to the hazy sky and 135 2,000 Hot & breezy Calm & muggy 1,500 Heat loss 1,000 I Needed Respiration @ Evaporation (skin) Heat transfer rate (W/cow) 500 , Radiant E Convection 0 -500 18 27 18 27 Barn width (m) Figure 6.2.2 Effect of ham width on the modeled heat loss potential of a row of cows within the barn during mid-day of two extreme summertime weather conditions in Lansing, M1. the more moderate dry-bulb temperature, the small mid-day radiant heat load on the row of cows, as modeled, was impacted more by exposure to diffuse solar radiation entering-the sidewall than by the effect of the warm roof. The cows in a narrow barn have greater exposure to the open sidewall and thus are under a very slight disadvan- tage for radiant heat exchange under these conditions. In realistic situations, a greater advantage would be expected with the narrow barn since a wider barn would likely have more cows (rows of cows) per unit of building length and more heat to dissipate. Sidewall open area. The effect of open area provided on heat loss and net heat load on the row of cows is shown in Figure 6.2.3. The most obvious change occurs in the modeled evaporation from the skin surface, with heat loss from that mechanism 136 increasing for both weather conditions with increasing open area provided. This is a result of the greater air flow through the building and higher air velocities that result within the barn due to greater sidewall opening. It is also evident, however, that the increase in evaporative heat loss is not directly proportional to the open area provided, but rather the effect diminishes as more of the sidewall is opened up. The diminishing returns can largely be explained by the fact that convection of heat and mass are approximately a function of the square root of velocity (refer to Equation 3.6.7). Thus, doubling the air velocity past the animals would be expected to generate, at most, only forty percent greater convective heat loss (i.e. evaporation). 2000 Hot & breezy Calm & muggy 1.500 Heat loss 1,000 I Needed Respiration @ Evaporation (skin) Radiant E Convection Heat exchange rate (W/cow) -500 Percent sidewall open Figure 6.2.3 Effect of sidewall open area provided on the modeled heat loss potential of a row of cows within the barn during mid-day of two extreme summertime weather conditions in Lansing, MI. 137 Another major consideration is that the resistance to evaporation from the skin surface is affected by the hair coat in addition to the basic air conditions. As de- scribed in the review of literature, the resistance of the hair coat to diffusion of mois- ture is not significantly affected by the low to moderate air velocities that exist within naturally ventilated buildings. Therefore, the hair coat resistance remains largely unaffected by increased ventilation rate and actually becomes the increasingly larger resistor on a percentage basis in the overall mass transfer circuit. Simultaneous increases in the convective heat loss and radiant heat load also resulted with greater sidewall open area, although to a much smaller extent. The explanation for increased convective heat loss is analogous to that just described for evaporative heat loss. The slight increase in radiant heat gain by the row of cows can again be attributed to increased exposure to diffuse solar radiation, in this case due to the larger wall opening. For both of the weather conditions modeled, the increased convective sensible heat losses essentially offset the added radiant heat load with more sidewall open area. Sidewall height. Figure 6.2.4 illustrates the results of the modeling runs with barns having varied sidewall heights. In each case, the sidewalls were open 60% and other features were unchanged. The effect of sidewall height on the heat exchange potential of a single row of cows in the barn is very small, being in favor of the barns with taller sidewalls. The benefit of greater wall height is less than that observed for the increase in sidewall open area percentage provided. With taller sidewalls, there is an increase in the building’s ventilation rate. For example, the ventilation rate through the barn with 138 2,000 Hot & breezy Calm & muggy —L 0'! O O Heat loss I Needed Respiration E Evaporation (skin) Radiant 8 Convection A O O O 01 O O Heat transfer rate (W/cow) Sidewall height (m) Figure 6.2.4 Effect of sidewall height on the modeled heat loss potential of a row of cows within the barn during mid-day of two extreme summertime weather conditions in Lansing, MI. 4 m sidewalls would essentially be twice that of the one with 2 m sidewalls if they both have the same percentage opening. However, since the cross-sectional area of the barn’s interior also increases, the air velocity past the cows in the taller barn is not double that of the shorter barn. There is very minor impact from greater diffuse radiation entering the sidewalls. This is likely due to the fact that the row of cows is located in the interior of a fairly wide building (each barn is 27 m wide), so the view factor of the cow and open sidewall is not significantly increased with more wall opening. The results would likely change considerably if the row of cows was located closer to the sidewalls during the model simulations. The remaining explanations for the observed results are similar to those given for the discussion of open area effects. 139 Diffuse radiation through wall omnings. ANTRAN was also used to simulate the effect of the incoming diffuse radiation through sidewall openings. In this case, the reference barn was compared to an artificial situation where the sidewalls are covered and yet an equivalent interior air flow rate is maintained (possibly via me- chanical means). In these model results, the evaporation from the skin surface is essentially the same, as illustrated in Figure 6.2.5. This is expected since the velocity and properties of the air flowing past the row of cows in each case are the same. The small differences that are evident result from the absence or presence of diffuse radiation entering the sidewall for the covered and open sidewalls, respectively. 2,000 Hot & breezy Calm & muggy 1,500 Heat loss 1 .000 I Needed Respiration E Evaporation (skin) Heat transfer rate (W/cow) 500 . IRadiant EConvection 0 -500 Covered Open Covered Open Wall opening status Figure 6.2.5 The effect of radiation entering the open barn sidewall on modeled heat loss potential of a row of cows during mid-day of two extreme summertime weather conditions in Lansing, MI. 140 For both weather conditions, having a closed sidewall provides the modeled cows a slight advantage in terms of radiant heat transfer. On the hot and breezy day, there is somewhat less radiant heat load on the animals, whereas on a calm and muggy day, a small amount of heat is lost to the building’s shell that otherwise would be negated by the diffuse radiation entering the sidewall. Radiant and convective heat transfer from the cows depend on the hair coat surface temperature. With greater radiant heat load, the hair coat surface warms, and some of the benefits achieved by closing the sidewall are offset by the increased convection from cows with higher hair coat temperatures in the naturally ventilated barn. The net effect of eliminating the entry of diffuse radiation through the sidewalls when ventilation is maintained in the modeled barn is very small at best. Effect of insulation. This modeling trial examined the effect of fully insulating the roof of the barn. In the fully insulated barn, the interior roof surface temperature was assumed to be the same as air temperature. The effect of insulation on the row of cows is shown in Figure 6.2.6. Fully insulating the barn roof reduced the need for additional heat loss of each cow in the row by 150 and 75 W on the ‘hot & breezy’ day and ‘calm & muggy’ day, respectively. On the ‘hot & breezy’ day, the radiant heat load was modeled to be reduced by more than 200 Whom The net benefit derived from the insulation is less substantial, however, since what was a small sensible convective heat loss became an equivalent heat gain and a drop in evaporation from the skin occurred with a lower hair coat surface temperature. This particular case provides a good illustration of the strong interactions that exist between the heat transfer mechanisms and the potential for these 141 2,000 Hot & breezy Calm & muggy 1,500 Heat loss 1,000 I Needed Respiration fl Evaporation (skin) Radiant E Convection 01 O O Heat transfer rate (W/cow) Fully None Fully None insulation level Figure 6.2.6 Modeled heat loss potential of a row of cows within fully insulated and uninsulated barns during mid-day of two extreme summertime weather conditions in Lansing, MI. interactions to counteract each other. On the ‘calm & muggy’ day, a fully insulated roof provided an additional avenue for heat loss via radiant heat exchange with the roof due to its lower surface temperature. Again, the net result is a somewhat smaller benefit to the net heat load on the modeled animals. 1) 2) 3) 7 - CONCLUSIONS The conclusions of this research are: The computer model ANTRAN, given the specific heat transfer characteristics of the animals, structural features and ambient summer weather conditions, calculates the thermal energy state of a continuous row of cows in a naturally ventilated barn with reasonable accuracy (modeled surface temperatures within 0.5 °C of those measured in an environmentally controlled chamber). Partitioning of the potential for heat loss amongst the prevailing heat transfer mechanisms is an essential component of the model. It enables the user to infer from model results how the heat losses due to the different heat transfer mechanisms respond to changes in model input. The impacts of varied weather conditions and certain primary barn design fea- tures on the heat exchange of dairy cattle in naturally ventilated barns were readily evaluated using the model. Specifically, when modeling a single row of cows within a barn: a) The deficit in heat loss when compared to heat production was greater for a ‘calm & muggy’ day compared to a ‘hot & breezy’ day due to the significantly lower evaporative heat loss available to the cows. 142 b) c) d) 143 Increasing sidewall open area provided noticeably increased evaporative heat loss from the cows’ outer body surface resulting in a lower net heat load. Convective heat transfer is increased with improved levels of ventila- tion, but the increases are proportionately smaller than the increases in gross ventilation rate. The effects of barn width, sidewall height and the entrance of diffuse radiation through open sidewalls on the net thermal energy balance of the row of cows were minimal. The model projected that heavily insulating a barn greatly reduced the radiant heat load of the roof on the cows for the ‘hot & breezy’ condi- tions. However, the benefits to the cows of insulating the roof were rrrinimal for the ‘calm & muggy’ day when the surplus of metabolic heat was greatest. Interactions between the convective and radiant heat transfer mecha- nisms were observed, with a negative change resulting from one mecha- nism often counteracting a positive response from the other. 8 - LIMITATIONS ON TRANSFERRING MODEL RESULTS TO PRACTICE Considerable care and discretion need to be taken when attempting to apply the results of this research directly to field situations. This section emphasizes some of the more important considerations and alerts the reader to some differences that might be eXpected in real field applications. The current version of the computer model ANTRAN was based on assumptions that are quite restrictive compared to the condi- tions that exist in real free stall barns. Especially important are the assumptions of steady-state conditions, two-dimensional mass and heat flows, absence of direct solar radiant heating of the animals, known animal characteristics, and only a single row of cattle. a) Steady-state conditions, although commonly assumed in modeling work, do not accurately represent the processes that are modeled here which all are, in reality, quite dynamic in nature. Acclimation activities were especially difficult to describe in a steady-state model. Appropriate application of this model requires the selection of a time period that is short enough to be descriptive of real conditions and yet long enough to stabilize the nature of the processes involved. Evaluation on an hourly basis is probably acceptable. b) Two-dimensional model heat and mass flows and the implications of using a two-dimensional model are presented in some detail in Chapter 4. Restrictions 144 e) d) e) 145 on allowable wind angle, building shape and cow positioning immediately preclude the direct application of the model to most practical situations. Direct solar heating is not accounted for in ANTRAN. Direct solar heating of the cow would occur in most barns when the sun is low on the horizon. This limits the use of ANTRAN to mid-day and evening hours. In some practical situations, the effects of the afternoon sun may be of great interest. Animal characteristics, both physical and physiological, are not well known and often vary considerably even among similar animals. Parameters that were used in this research to determine quantities such as hair coat resistance, respi- ratory ventilation rate, and the allowable temporary rise in body temperature were selected based on a very limited number of studies. A single row of cows and its consequences were alluded to earlier in Chapter 4. The primary limitation of this assumption is that it doesn’t allow evaluation of real multi-row barn situations. Situations that are thus not accounted for include comparisons of barns of varied stall arrangement or similar barns with differing cow stocking densities. 9 - RECOMMENDATIONS FOR FURTHER STUDY Less restrictive assumptions would expand application of the model ANTRAN. Included would be using a three-dimensional model of the cows within the ham or of the barn itself, incorporating routines to handle direct solar heating of the animals, evaluating the cows’ cumulative thermal status over greater portions of the day, providing a means of assessing multiple rows of animals, possibly utilizing Monte Carlo techniques for analyzing the radiant heat exchange and integrating feed intake and milk production models. Several of the current component models could be improved. The equations used to determine total ventilation rate, convective heat transfer and respiratory venti- lation rate, among others, are still quite crude. Input data to the model that more accurately represent the modeled animal, particularly at currently observed levels of production, would improve model accuracy. Areas for additional research include maximal sweating and respiratory ventilation rates, hair coat properties and feed consumption characteristics when under thermal Stl‘CSS. 146 APPENDICES APPEhHIDKIX TEMPERATURE HUMIDITY INDEX FOR DAIRY COWS Prank Wiersma (1990) Modified from Dr. Ag. Engineering - The University of Arizona, Tue-on Arizona T3! for Dairy Cowl. RELATIVE ”IDIYV nzasuasossaoesmnnuaou 15 10 nnunnnnn nuuauuuunn nmuuuuu1@@ nuanuuuPF& nnnuu.mfl n.nnu unnuawmwnn.un uuuuuau nun: nnn .QWEnuuuuumm%u umnunuusuun nun unnnnn unnnnnnn uuununuuuuuuunu. mann unnunnnnnn.anunuueuuauunnuu an nnnnuunnnnnnn..nnuuunuuuuuuuunuu nnnnnunnnnnnnnn.wuuuuuuuuuuuuunu N H II It It 02 OZ .3 .3 u u “ N0 STRES 3.2 as DJ 23.! 2‘ 4 8.0 20.1 20 1 272 211 ZIJ m ”A to ”I 3‘ t 31 7 32 3.0 an an MA I 3.. 3.1 8.1 37.2 31.! as I) 7. 8.4 O 0.. 4| 1 ‘1 7 ‘22 42.0 as 0.. u d 6 6.. a ‘l I 1 unuuuuuflnu unuunuuuuuwn nwmnnnfluuuuuanw an nurruunuuuuu .’ ..mmumummmmmmmmmuum III - (Dry-Bulb Temp. ' C)+(0.36 dew point Tanp., ' C)+d1.2 147 SAMPLE OUTPUT FROM THE COMPUTER MODEL ANTRAN APPENDIX B Title: More open 80% sidewall on hot day Output file: c:hotopen.out Input file: c:hotopen.dat Barn width: 27.0 m Roof pitch: 4.0:12 INDEX NODE DESCRIPTION Base, inlet wall Base, outlet wall Base of outlet Top of outlet Top, outlet wall Peak of roof Top, inlet wall Top of inlet Base of inlet \OOOQGM-Iin—t ** BARN DATA ** Wall height: 3.00 m Wall opening: 80.0 % Wall opening: 2.40 sq. m/m X-COORD Y-COORD .00 .00 27.00 .00 27.00 .30 27.00 2.70 27.00 3.00 13.50 7.50 .00 3.00 .00 2.70 .00 .30 ** LIVESTOCK DATA ** Livestock: dairy cattle Body mass: 635. kg Gestation: 120 days Body diameter: .70 m Model length: 2.18 m Basal Vent.: 100.0 Umin Coat thick: 1.4 mm Production: Heat Prod.: Surface area: Exposed area: Max. sweating: Coat Emis.: 148 SEGMENT Floor Base-out Outlet Supt-out Roof-out Roof-in Supt-in Inlet Base-in 30.0 kglday 1386. W 5.57 sq. m 4.80 sq. m .30 kglsq. m/hr .95 LENGTH 27 .00 .30 2.40 .30 14.23 14.23 .30 2.40 .30 149 ** ANIMAL ROW DATA ** ROW # X-COORD Y-COORD LEFT PT RIGHT PT TOP PT LOWER PT 1 9.00 1.00 8.65 9.35 1.35 .65 Floor area: 58.9 sq. m/animal ** AMBIENT AIR DATA ** Ambient Temp: 36.1 C Rel. humidity: 35.0 % Atm. Pressure: 101.3 kPa Dew point T.: 18.1 C Humid. ratio: .0131 kglkg Vapor Pres: 2.09 kPa Air density: 1.13 kglcu. m Enthalpy: 70.0 lekg T.I-I.I.: 83.8 Wind speed: 6.00 mls Opening Cd: .50 Vel. on An.: 1.30 mls Vent. Air T.: .0 C Day of year: 176 th day Longitude: 84.6 deg. Std meridian: 75.0 deg. Elevation: 70.2 deg. Direct SW: 848.0 W/sq. m Atmos. LW: 10.0 W/sq. m Ground albedo: .25 Added water: 0. % of capacity ** AIR FLOW DATA ** Wind angle: Vent. rate: Vel. on roof: Vent. Air RH: Local time: Latitude: Azimuth: Diffuse SW: Barn angle: ** SPECIAL FEATURES DATA ** 0.Deg. from Sq. 16. cu. mls 1.37 mls .0 % 13.0 mil. hr 42.8 deg. 13.8 deg. 142.0 W/sq. m .0 Deg. W of S 150 ** TEMPERATURE RESULTS ** Body Temp: 38.6 c qu. skin T.: 27.0 c Skin Temp.: 33.8 c Coat Surf. 11: 36.3 c ** HEAT TRANSFER RESULTS ** Rsp. latent Q: 88. W Total Resp. Q: 92. W Convective. Q: 9. W Radiant Q: -348. W Coat. Cond. Q: -338. W Latent skin Q: 873. W Total Q loss: 627. W Pct. of Meta.: 45.2 % Meta. surplus: 759. W Pct. of Meta: 45.2 % Sensible Q: -334. W Share total: -53.3 % Latent Q: 961. W Share total: 153.3 % Share of evaporative loss: Share of sensible loss: Respiration: 9.2 % Respiration: -l .0 96 Body surface: 90.8 % Convection: -2.7 % Radiant: 104.2 % ** MASS TRANSFER RESULTS ** Resp. Vent.: 84. Umin Resp. Evap.: .13 kg/hr Surf. Evap.: 1.30 kg/hr Surf. Evap.: .27 kg/sq. mlhr Reynolds #: .54E+05 Nusselt #: 210. Eff Thrm Cond: .04 WIm/C Conv HT Coef: 8.09 W/sq. mlC 151 ** TEMPERATURE RESULTS ** Body Temp.: 41.6 C qu. skin T.: 32.3 C Skin Temp.: 35.4 C Coat Surf. T.: 37.4 C ** HEAT TRANSFER RESULTS ** Rsp. latent Q: 339. W Total Resp. Q: . 352. W Convective. Q: 49. W Radiant Q: -317. W Coat. Cond. Q: -268. W Latent skin Q: 966. W Total Q loss: 1050. W Pct. of Meta: 75.7 % Meta. surplus: 336. W Pet. of Meta: 75.7 % Sensible Q: -255. W Share total: -24.3 % Latent Q: 1305. W Share total: 124.3 % Share of evaporative loss: Share of sensible loss: Respiration: 26.0 % Respiration: -5.3 % Body surface: 74.0 % Convection: -19.l % Radiant: 124.3 % ** MASS TRANSFER RESULTS ** Resp. Vent.: 322. lein Resp. Evap.: .51 kg/hr Surf. Evap.: 1.49 kg/hr Surf. Evap.: .31 kg/sq. m/hr Reynolds #: .54E+05 Nusselt #: 210. Eff Thn'n Cond: .04 Wlm/C Conv HT Coef: 8.09 W/sq. m/C BIBLIOGRAPHY BIBLIOGRAPHY ASAE. 1991. ASAE Standards 1991, 38th edition. American Society of Agricultural Engineers, 2950 Niles Rd., St. Joseph, MI. Selected standards. ASHRAE. 1989. ASHRAE Handbook, Fundamentals. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N .E., Atlanta, GA. Chs. 4. 22 and 27. Achenbach, E. 1977. 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