MEASUREMENTS OF COOLING RATES OF FRUITS AND VEGETABLES Thesis éoe- {'Em Dogma of M. 5. MICHIGAN STATE UNIVERSITY Kamai E1 Din Hussein Motawi 1962 LI BR A R Y Michigan State Unchrsity MEASUREMENTS OF COOLING RATES OF FRUITS AND VEGETABLES BY Kamal Ei Din Hussein Hotawi AN ABSTRACT Submitted to the College of Agriculture Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Food Science Department l962 App raved fl ‘ ABSTRACT Cooling fruits and vegetables is, naturally. a matter of great concern to both the food producer and the food processor since, in general, to achieve top quality in the finished product. it is essential to maintain the high quality of the raw product. This is usually done through effective refrigeration from the time of harvest until the time of manufacture. The literature concerned with cooling performance makes little or no use of available mathematical and engineering information; therefore. this study of the measurements of cooling rates was pursued using the fundamental concepts of heat transfer, and applying the theoretical and empirical equations to the cooling of fruits and vegetables in an effort to establish the applicability of theory to practice in this important area of food technology. The experiments included tunnel cooling, in which cold air at 3|~32°F was the heat transfer medium for cooling different sizes or fruit one at a time at different air velocities; water cooling, in which some fruits and vegetables were cooled in running cold water at 32-33°F at different water flow rates; and a few heating tests in running hot water using a laboratory retort as a water bath. Measurements of cooling rates, particularly with air cooling. suggest strongly that the theoretical model assumed. together with the fundamental thermal properties such as thermal diffusivity. thermal conductivity, and surface heat transfer coefficient of the object. can be used to predict the cooling equation. Although the results obtained show that the changes in these values with respect to each other are in the predicted directions. more precise knowledge of the basic thermal properties of foods are needed before these relationships can be clearly established. ACKNOWLEDGMENTS Tne author is deeply indebted to Dr. R. C. Nicholas for his assistance in conducting this study, his aid and advice in analyzing the data, and his counsel in the preparation of the manuscript. The author also wishes to express his sincere appreciation for the assistance given him by Dr. I. J. Pflug to whom is due the original conception of the problem and the operational design for the hydro- cooling tests; Dr. C. L. Bedford who provided facilities and help with the air cooling equipment; and Hr. J. L. Blaisdeii who contributed much essential source material and valuable discussions. Appreciation Is also expressed to the Michigan Agricultural Experiment Station for financial support of the project and to the United Arab Republic Ministry of Education for the financial support which provided this opportunity for study. MEASUREMENTS OF COOLING RATES OF FRUITS AND VEGETABLES BY Kamal El Din Hussein Motawi A THESIS Submitted to the College of Agriculture Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Food Science Department i962 TABLE OF CONTENTS INTRODUCTION . . . . . REVIEW OF LITERATURE . . . . Cooling Methods . . . . . . Survey of Published Work STATUS 0? Cooling Studies . . TnEORY AND ANALYSIS 1')? COOL IIIG EXPERlMENTAL . . . . . . . . . RESULTS 0 O O O O O O 0 C O 0 DISCUSSION AND RECOMMENDATIONS . APPENDIX . . . . . . . LITERATURE CITED . . . . . . . I5 l7 2i 26 A2 .108 . S3 iNTRODUCTlON All fresh fruits and vegetables are alive and remain living throughout their entire period of salability or until processed. Being alive they respond to the environment in which they are held and have fairly definite limitations as to the conditions that they can tolerate. They remain alive by utilizing reserve energy stored during growth. The process of breaking down food into carbon dioxide and water with the release of energy and uptake of atmospheric oxygen is known as respiration. Respiration, the complex collection of enzymatic and other chemical activities is accompanied by quality changes and the eventual death of the commodity. These internal changes associated with life cannot be stopped but should be retarded if the fruit is to remain alive and quality is to be maintained at a high level for a prolonged period. Cooling the commodity prior to shipment is commonly termed precooling. The goal of precooling is to provide environmental conditions that will result in minimum deterioration and yet keep the perishable commodity alive and fresh. Within the temperature range usually encountered the rate of deterioration of fruits and vegetables is increased from two to four fold for each l8h9F(l0°C) rise in temperature. Not only do higher temperatures accelerate ripening and respiration but they also accelerate decay. The activities of the organisms causing decay are accelerated by temperature in the same general way as is respiration of the produce. thus temperature reduction has the dual function of reducing both respiration and microbial spoilage. Temperature reduction through refrigeration is the most important of the environmental factors subject to control, and it 2. is the most practical method of slowing deterioration. The significance of this dependence of the chemical reactions is related to the product storage life. The temperature differences between the commodity in the field and the cold storage are commonly h0-SO°F though often higher; this fact means that deterioration rates are 5- to 25-fold lower at refrigerated temperatures -- one hour at field temperatures can result in as much deterioration as one day at refrigerator temperatures. Very low temperature is not desirable for all products as some (principally those of tropical origin) are subject to chilling injury which results in a shortened storage life, failure to continue normal ripening, and increased'susceptibility to decay. This study is concerned, not with the final temperature of products already cooled, but with the possibility of predicting from available knowledge, the cooling curve of a particular product given the conditions under which it is to be cooled. REVIEW OF LITERATURE Ever since the cooling of fruits and vegetables became recognized as a desirable feature in their proper handling (and the sooner they are cooled, in general, the better the quality) , means have been sought to increase the speed of cooling and to achieve more uniform cooling of the products. Cooling and precooling are accomplished through cold air or cold water as a transfer medium , by direct contact with ice or by evapor- ation of water from their surfaces as in leafy products (vacuum cooling). All these methods of cooling are, however, not applicable to all perishables. Since the rate at which produce cool is affected by the method of cooling, it is desirable to»describe briefy the common methods of cooling. COOLING METHODS l. Air Cooling A. Still-air cooling or Room cooling: one of the commonest methods in which one relies on the heat being carried from the product to the ice or refrigerated surfaces chiefly by natural convection. B. Faster methods of air cooling (Sainsbury, l95l; Guillou, l960). (l) Forced air cooling: The term 'forced-air cooling' is used here to designate the cooling of fruits or vegetables by use of a difference in air pressure to force air through stacked containers. Heat is believed to be carried away primarily by forced flow of air past the produce inside the containers rather than by flow past only the outside of the containers as in room cooling. It can be done in many ways and it is affected by many factors such as fan location and product-container arrangement. which result in differences in heat transfer rates (2) Ceiling-jet cooling (Guillou, I960). Its principle is that of providing air ducts on the ceiling of a cooling room and nozzles to direct the air jets vertically downward. Heat is removed from the product by air flowing Into the containers and around the individual articles. (3) Tunnel cooling (Sainsbury, l95l) in which air is caused to flow into stacked containers by placing them in a tunnel through which air is moved at high velocity. It gave excellent results at the experimental level, but on commercial use it turned out to be expensive because of difficulty in controlling air leakage which necessitated excessive refrigeration. II. Hydro-cooling Fruits and vegetables may be cooled very rapidly by bringing them in contact with moving cold water. It is the fastest method for all products except leafy vegetables (Guillou, l960). Finely chopped ice may be mixed with some products as they are packed. Direct contact with ice results in fast cooling, and, since the Ice turns to water at the ice product interface, this method could be thought of as an inefficient form of hydrocooling. Ill. Vagggm cooling Leafy vegetables are cooled on a large scale by pumping away the air around them until moisture evaporates rapidly from the leaf surfaces. 5. The heat necessary for vaporization comes from the produce itself, and at an absolute pressure of “.6 mm Hg (a usual final pressure in the pumping operation), the temperature of the produce approaches 32°F, the equilibrium temperature of the liquid and vapor phases at that pressure. The warmer the produce, the more heat must be removed to achieve the same final temperature; consequently, more weight (moisture) loss is exhibited by warm produce than by cold. Cooling is faster in the leafy portions of a head of lettuce than in the fleshy core (Berger, l96l). SURVEY OF PUBLISHED WORK Dewey (I950) showed the effect of air-blast precooling on the moisture content of stems of cherries and grapes. He studied sweet and sour cherries and Concord grapes held in wooden tills precooled in air blast at 32-3h0F with a relative humidity of 90 or 70%. In an air blast of about 770 fpm fruits were completely precooled in 30-50 minutes, whereas more than 7 hours were required for cooling both kinds of fruits in still air. The relative humidity of the air did not affect the cooling rate. The humidity of the air is of minor importance to moisture loss during precooling. The moisture loss from the stems of grapes were the same in moving and still air and in air of 70-90% humidity. In tests reported by Redit and Smith (I953) on the cooling of southern California peaches after loading into railway vans temperatures were lowered to 6l0F-650F (l6-I89C) in S-lh hours (depending on product location in the car) by portable precooling fans, or the fans fitted in the vans (ice was used in both cases), or by mechanical refrigeration. HydrOécoollng (steri-cooling) the peaches in water containing hypochlorlte, lowered their temperature to 45-550 (7-l3OC) in l2-IS minutes and they did not become appreciably warmer during periods of up to one hour on the packing house floor at hot summer air temperature. or after loading in pre-iced railway vans. None of these precooling methods cooled the fruit to the extent desirable to delay ripening and prevent decay. 7. C. E. Wright (I953) reported that quick cooling cuts fresh vege- table losses. At the fresh vegetable packing plant of Chase Co., Sanford, Florida, two hydro-cooling units are used to bring the temper- ature of the packed product to near freezing temperatures within half an hour. Allen and McKinon (l95h) reported that lO-l5 hours were required to cool the cherries near the outside of the package from a temperature of 65-70°F to 35°F in refrigerator cars when the circulating air temperature was maintained at 30-330F. The fruit in the center of the package was l0-l5o higher than that near the edges at the end of four hours and l-SOF higher at the end of l8 hours. A period of 2“ hours was considered necessary for complete cooling of the fruit at the center of the packages. Rates of cooling In both refrigerator cars and storage rooms were found to be 2.0 to 3.50F per hour for cherries in the center of the packages, and 3.0 to 6.0°F per hour for the fruit near the edges of the container over a period of 8-l0 hours. The average cooling rate at both center and edges of boxes over a period of l6-20 hours was slightly less than 2.00F per hour. And these cooling rates were obtained in moderate air circulation. It was found that air velocity affects cooling rates: when air velocity is increased cooling rates increase too. The same thing is true with regard to the tempera- ture (degrees F. drop/time) if the cooling medium is at constant temperature and cooling started at higher initial temperature. It was found also that cooling rates were not influenced by the maturity of the fruit. In hydro-cooling water is used as the cooling medium. The fruit may be immersed in a water bath or water may be flooded over and through the product either before or after packaging. The water is cooled by crushed ice or by refrigeration coils In the cooling tank system. Water temperature should be 32°F or slightly higher. Only seven minutes were required to reduce the temperature of Sing cherries from 65°F to 37° when immersed in the water bath ice melting at 32°F. Pentzer (l9h0) precooled California cantalopes. Air was the medium used for heat exchange from the commodity to the refrigerating surface. In this case cooling depends upon several well-recognized factors, the most important of which are: l. Volume, velocity and distribution of air 2. The difference in temperature between the commodity and the air used for cooling 3. The method of packing and stowlng as it affects air circulation A. Certain properties of the object to be cooled such as their size, shape, surfaces as they affect heat transfer, heat capacity, conductivity, and metabolic activity. Precooling tests were conducted in a considerable number of railway cars. The precooling rates with inside fan equipment reported by Pentzer are slightly higher than those obtained by Overholser and Moses (I928), but compare favorably with the rates obtained by Gaylord, Fawcett and Hienton (I935) in recent tests made on cantalopes with similar equipment. Cars precooled with truck-mounted mechanical refrigerating units had average cooling rates of h.l8°F and 4.l0°F per hour for 9-3/A and 8-l/2 hour periods, respectively. In non-precooled cars, in which the air movement was by natural circulation only, the cooling rates ranged in some cars from l.l°F per hour for a period of about l3 hours to 2.2h0F per hour for a period of A lie hours in other cars. 9. With all types of precooling in these tests cold air was blown over the top of the load, the direction of the air movement being from the top to the bottom of the load, towards the center of the car with portable car fans and towards the bunkers with the truck-mounted unit. The cooling rates in the middle and bottom layers were very similar, being slower in the bottom layers of product in all cars than in the top layer. Among the cars precooled with portable inside fans, the highest cooling rates obtained were h.9 to 5.I°F per hour; the fruit was fairly warm when precooling was started. The coolest car when loaded, averaging 63.h°F, had the lowest cooling rate of all the fan cooled cars, amounting to 2°F per hour for an 8-l/2 hour cooling period. The average cooling rate for the I9 cars cooled with portable car fans was 3.580F, indicating that under the conditions of these tests a reduction of 3.6°F per hour could be used as a guide in estimating the time required to precool cantalopes. Pentzer, Asbury and Barger (I945) studied the effects of various factors on precooling rates of California grapes and their refrigeration in transit. l. Type of equipment: In comparing the precooling rates obtained with various types of equipment, differences were found but none were so great that longer precooling would not have compensated for them. Even with the most efficient equipment time was the all-important factor. 2. Heavy and light chopping of ice: In tests made on the air circulation in refrigeration cars in transit, it was found that light chopped ice was better than heavy chopped ice. IO. 3. Type of load: There Is considerable evidence that crosswise loads are more difficult to cool because the ends of the boxes instead of the thinner and more open sides are exposed to the air channels. A. Type of package: It was found that type of package affects the cooling rate to a great extent. Therefore it was suggested that the grapes be cooled to some extent before they are packed. Lugs of grapes without lids were cooled in a small tunnel in which air at 28 to 32°F was circulated at velocities of #00 to 500 ppm. Thermo- couples were used to read temperatures of individual grapes in various parts of the lugs. In these tests it was found that l to l-l/Z hours were required to cool the grapes throughout the package to temperatures of ho to 45°F from initial temperatures of 75 to 80°F. They also showed that pads in the bottom of the lugs interferred to some extent with the circulation of air through the package and therefore retarded cooling. A more complete test was made in the small model tunnel cooler which was designed to cool lugs of grapes as they are conveyed In three tiers through it. Air entering the top of the tunnel was directed downward past the fruit. A centrifugal fan was used to give air velocity of about 600 fpm in the tunnel. Refrigeration was supplied by air from a cold-storage room. Air temperatures were not as low as desired but were probably representative of those that would be obtained under commercial conditions unless a greater amount of cooling surfaces was provided. The fruit cooled from about 70°F to 3A0F-h59F in an hour. The grapes In the bottom and center of the lugs cooled the least. It was suggested that small slots or holes in the back bottom of the package might have aided cooling by providing an outlet for the air ll. forced into it. The results indicated that it is possible to cool unlided lugs of grapes sufficiently in one hour to meet the precooling requirements for this commodity, but to do this commercially would require a large volume of air maintained at low temperature. Studies were reported by Gerhardt and Huklll (l9h5) on pre- cooling practice at two storage temperatures and their relation to the condition and appearance of Bing cherries. The rates of cooling of packed fruit at 3l°F and AAOF under otherwise identical conditions were reported to be the same. When an air blast of 375 fpm was used, cooling was l.9 times as fast as in still air, and cooling in ice water at 32°F (0°C) was IAS times as fast in still air at 3l°F. After A hours precooling fruit In an air blast at AAOF (7°C) had cooled as much as that in still air at 3l°F. Loss in weight of the cherries was reduced by rapid cooling in Ice water. Hydrocooling for 7 minutes at 32°F did not injure the appearance and condition of cherries. Bethell and Challman (I950) reported on a mechanical refrigeration system for California fruit which is to be sent to eastern markets. In the case of plums, the fruit is placed in the quick chill room on the day it is picked and is cooled to 32°F (0°C) in IS hours and then loaded into refrigerated railway vans, in which it Is held at the same temperature during transport. Rose and Corman (l936) studied the handling, pre cooling and tranSportation of Florida strawberries. They found that the wetting of strawberries affects their rate of cooling. There were four test lots of one quart each; two quarts were dry and two were wet. One lot of each pair was held in still air, and the other two lots were placed l2. in front of and about four feet away from a lh-inch electric fan running at such a speed that the rate of air movement over the berries averaged about 300 fpm. The temperature of the room where the tests were run was hl-AZOF most of the time. The temperatures were obtained by means of thermocouples. It was found that fan-blown berries cooled much more rapidly than those in still air, and that wet berries cooled somewhat faster than the dry ones. Therefore the wetting of strawberries hastens the rate at which they cool. Wetting the berries by means of washing caused slight damage to the product. Cooling is gradual and several hours to a day or twoimay be required to reduce the temperature of the load to that of the air in the car. The rate of cooling depends chiefly on the difference between the two temperatures, but It Is also affected by the quantity of the commodity to be cooled, the kind of container and the method of stacking or loading the packages In the car. When a crate of strawberries was placed in a cold storage room held at 32°F to 34°F, the most rapid cooling occurred during the first 8 hours, and the rate of cooling became gradually slower as the test was continued and the temperature of the room and the fruit approached each other, and the fruit was still about 20F warmer than the air in the room, even at the end of 2A hours. The rate of cooling a carload of strawberries was of course much slower than for a single crate. The results obtained under standard refrigeration with 3 per cent of salt at all icing stations showed clearly that the fruit in this car required considerable time to cool. In all parts of the load where temperatures were taken, it cooled most rapidly during the first l8 hours after loading was completed. The fruit at the bottom of the car required l3. approximately 22 hours to reach 30°F. The fruit at the top did not go below about 38°F during the entire transit period while it required l3-l/2 hours to reach 50°F and 39-l/2 hours to reach 38°F. This car was shipped March 2%, and the outside temperature when loading was completed was 69°F. The average temperature of the top fruit was 60.h°F and of the bottom fruit h7.5°F. Guillou (l960) reported that the performance of the precooling operation can be compared most conveniently in terms of half-cooling time. This is the time required for the temperature of the product to be reduced to one half of difference between product and cooling medium that existed at the beginning of the period considered. It is assumed that the cooling medium temperature Is relatively constant during the period. If the cooling medium fluctuates considerably, a cooling coefficient may be determined from average product and average cooling medium temperatures during the period. This coefficient is convertable to half-cooling time. Fara normal precooling operation using 33°F cooling medium, twice the half-cooling time will be required to reduce commodity temperature to hoor if the initial temperature is not higher than 6A0F. For initial temperaturesup to 96°F three times the half- cooling time should be allowed to produce a final commodity temperature of 40°F. Variations in cooling rates. Dewey (I950) and Guillou (I959) found the biggest variation in cooling rates and time of cooling occur as a result of the nature of commodity and density of the pack, type of package and method of loading. The time required for cooling varies with the temperature of the air blast to the heat load and also with the l4. rate at which air moves freely over the commodity being cooled. Best results will be attained when air movement in excess of 500 fpm between the packages is used and if goods are not wrapped in paper and are designed to permit reasonable air movement tnrough the container itself. In his study on fruit, Sainsbury (l96l) emphasized the importance of nearly uniform product temperature as possible during the storage period. When the necessary refrigeration capacity is provided to handle the heat that must be removed from the fruit, then the dimensions, nature of the container, and manner of stacking are the most important factors that influence cooling performance, which is reported in terms of Hhalf-cooling time.” Air passage through the packages and the distance from the center of a pile of packages to the surface where the heat is removed are the factors of most importance; half-cooling time in a package where convection is negligible varies almost with the square of the distance. The half-cooling time and approach temperature (temperature difference that remains between fruit and air after cooling) are definitely related. The approach temperature is approximately l°F for a 30 hour half-cooling time, 2° for a 60 hour half-cooling time, etc. He studied the effect the starting period (lag factor) had on the half- cooling time and it was found that the time required for the initial temperature to be reduced 50 percent at the center (the first half-cooling time 2.) is greater than the time for reduction from 50 percent to 25 percent 22 or from 25 percent to l2.5 percent 23, of initial value. So the time to reduce the temperature from 50 percent to 25 percent of its initial value usually is the true characteristic cooling time, or half- cooling time. The lag factor calculated was greater than I in all cases. l5. STATUS OF COOLING STUDIES In summary, studies of fruit cooling are, as a general rule, concerned with specific situations (for example, a special box in a particular location, stacked in a particular way) in which minor modifications are made (for example, the stacking arrangement). The reports of such work frequently make little or no reference to any fundamental aspects of heat transfer; often the temperature that is being measured is poorly defined (for example, ”average” temperatures have been reported without mention of what is being averaged). In the cases of Guillou (I960), Sainsbury (I9Sl), Gane (l937) and Thevener (l955) the simplification of Newtonian cooling ls unjustifiably made. Moreover, although the importance of rapid cooling is recognized, and although efforts are made to achieve rapid cooling, emphasis Is frequently on the (or some) final temperature reached by the fruit. No calculations are made showing probable quality savings as a function of cooling, nor has the economic balance between the more expensive rapid cooling and quality been worked out or estimated. There is, finally, some lack in uniformity in reporting results and experi- mental conditions. Since previous researchers' attention has not been directed to fundamental aspects of heat transfer, it is not possible to reproduce any of these experiments because the Important parameters governing heat transfer are often not even measurem or reported. Lack of these elements make any engineering design Impossible. A logical approach to the cooling problem is to consider those elements of heat transfer that enter the solution of the differential l6. equation governing the heat flow. These elements are shape of the product, initial temperature distribution in the product. temperature of the surroundings, thermal and other physical properties of the product, and boundary conditions between the product and the surroundings. Further, at the boundary one may imagine the problem to be one of measuring the surface transfer coefficient as a function of the cooling medium conditions (such as temperature and velocity) and of the product. The argument here is that the cooling situation is most completely and efficiently described in terms of these elements and that the solution to a particular problem might be achieved by analysis rather than experiment if fundamental parameters were known. The solution of the problem Is not simple. In this study, attention has been directed to individual fruits; it is recognized that the problem of going from individual fruits to boxes of fruit and from boxes of fruit to stacked arrangements of boxes may prove formidable (Blaisdell, I962). The objective of this study is to examine heat transfer in single fruits under a variety of conditions and to deduce from the observed cooling curves the constants involved in the theoretical equations. Many simplifying assumptions have been made, perhaps so many that the solutions will not prove helpful in actual design situations in a real storage. The solution of that problem is left for further study. The objective here is to describe the problems involved in relating observed cooling curves to theoretical curves. l7. THEORY ANO ANALYSIS OF COOLING CURVES The analysis in the present study is confined to the cooling of Spheres, the first simplifying assumption. The equation for the temperature, T, at any point, r, and any time, t, in a sphere of radius r., initially at a uniform temperature, To, placed in a constant temperature medium at Tc is: 2 gang T-Tc r, “- I sinMn-MnCosMn = h To - Tc r Mn 2 Mn - sin 2 M“ n-l sln (Mn 5 . (I) 'l where Mn are the roots of l-Mn Cot Mn 8 8... (la) 8 - Blot number - rlh/k h I surface heat transfer coefficient, Btu/hr-ft2-°F. ' k - thermal conductivity (of the sphere), Btu-ft/hr-ft2-°F. a - Fourier modulus A t/r2 A - thermal diffusity, k/Cw, ftZ/hr C.- specific heat of sphere, Btu/lb-°F. w - density of sphere, lb/ft3 (t, hr; r] and r, ft.) The temperature at the center of the sphere, where r = 0, is given by: 2 -H" a O O O O O O C C O O Q (2) r - T sin n" - M” Cos an c To - Tc Mn - sin Mn Cos "h (The derivation of this equation Is given In Schnider, I955). At a l8. time sufficiently long, all terms except the first are small and the cooling curve approaches asymptotically: Sin H' " H‘ COS Ml -lee :3 2 e e e e e - e e e a e e e(2.) M' - sin MI Cos M. which, by transferring to base i; and Stbstltuting for 8. boiuzes .H'2 A t . T ' TC SII‘I H. " H| COS HI ——.—-—-— 2 =2 *0 2.303rl e00000°(3’ TO - TC H. ’ Si" N. COS H1 The asymptote (equation 3) will plot as a straight line on semi- logarithmic coordinates. The slope of the line, % -M‘2A and sin "I - M Cos H' ). Ayrton and Perry the intercept j, at t a 0 is(2 ' .. ”I ' SI" H' COS "I (I878) have an excellent discussion treating the applied problem of calculating the fundamental constants h and k from the observed curves. Their treatment includes a discussion of four methods of handling the experimental data. I . From the values r', C, and w, the intercept of the asymptote, and slope (lif) one can calculate A and B, and ultimately. h and K as follows: I - From j get M' 2 - From Ml get B 3 - From f, r,, and u, get A - 2.303 rz/fafi h - From A, C, and w get k = ACw 5 - From k, B and r' get h - kB/rl (Curves for steps I and 2 and a table of some values of M' and B are given in the appendix). l9. The surface transfer coefficients calculated may be compared 112 s where D is a characteristic dimension of the immersed solid (0 - 2 rI directly with published values, or through the Nusselt number, Nu = for spheres), and k5 is the conductivity of the surroundings, so that kBD - 28k ksrl ks Nu = Two common methods of reporting cooling in fruit and vegetables, are given below: Sainsbury (l95l) log (T - Tc): -2f;03 t + log (To - Tc)' CR, or cooling rate, = the number of 0F the fruit temperature is reduced per hour per °F temperature difference between the fruit and cooling medium (air). Guillou (I960) log (T - Tc)= “19321th + (To - Tc) 2 = time to reduce the initial temperature difference between the object and its surroundings by one half, called the "half-cooling time.” The nomenclature (j and f) used in present study is that Ball and Olson. (I957). Since the fundamental constants Involved in the temperature equation (3) are to be derived from the experimental curves once the straight line asymptote to this curve is drawn, the two points (or other parameters) of a straight line become measures corresponding to the two undetermined coefficients in the second order differ- ential equation. The results in this study are reported as the slope and intercept (when t - 0) of the straight line heating curve drawn 20. on semioiogarithmic paper after the method of Bali and Olson {l957}. Their equation is: where j is called the lag factor and f the heating (or cooling) rate. The three methods (Sainsbury, Guillou, and Ball) may be compared. Table (l) Comparison of Cooling Curve Parameters NAME mnacerr SLOPE Sal b (1951) I ' CR "5 ury 2.303 CR - cooling rate Guillou (I960) l ~ '° 2'” Z I half-cooling time ._-..- - “h - w. .. — ' y .r— - I Sell (. .7) j Lag Factor f ’ a heating or ccslspg file “ma — m .aA'. — The final point to make is that both Sainsbury and Guillou assume an intercept of i. (Also Gane (l937) assumed j - l for air cooling and j a 2 for cooling in paraffin). This means that one of the two undetermined coefficients has been arbitrarily fixed. From a physical point of view it means that the entire resistance to heat transfer is in the surface layer. This situation corresponds to a very low Nusselt number as would be the case in most of the studies reviewed. At the other extreme, if the surface transfer coefficient is infinite, then j becomes 2 and H. is.II. Real fruit (provided it 2 is spherical) in real storage presumably lies somewhere in this region. 2|. EXPERIMENTAL ngperature measurements In heating, hydrocooling. and air cooling, temperature measure- ments were made by means of Zh-gage copper-Constantan thermocouples and a Brown recording potentiometer. All the tests were conducted by observing the temperature rise or reduction near the center‘ of individual products, except for peaches and plums for which the temperature was measured next to the pit. Each commodity was cut at the end of every run and examined to be sure the thermocouple was in or close to the center. Runs for which the thermocouple was more than I-l/2 mm. fromrthe center are not reported (peaches and plums excepted). lAccording to theory, the heating rates do not vary with location; the predicted reduction in lag factor at a distance I0% from the center (spheres) Is a maximum of 2% as calculated from the following equation: ' K . sin (n, r/r.) which is the correction to j for positions other than the center, where r) is the sphere radius and r is the distance of the thermo- couple rrom the center. The position error In any given location is a function of H and will be a maximumiwhen H. is a maximum, which in this work is pi. The point of thermocouple Insertion was sealed with wax to prevent the hot or cold water from getting into the fruit and to help hold the thermocouple in position. For air cooling the wax seal was also used so that the fruit remained dry and any possible erroneous reading caused by evaporation of juice from the opening where the thermocouple 22. was Inserted was avoided. One thermocouple was reserved in all tests to record the cooling or heating medium temperature. Frequency of reading and plotting varied with the rate of tempera- ture change in the product tested. For instance, in grapes readings were taken about every half minute and every six minutes for apples and other larger fruits. Air Cooling Experiment Room cooling or cooling tests were conducted on pears and Red Delicious apples. Fruit of approximately the same weight 'and shape were selected. Uniform Initial temperatures were achieved by holding the fruit at ordinary room temperatures overnight. The fruit was placed on a table in the cold room to cool. Air and fruit temperatures were recorded throughout the test period. Cooling rates were obtained and comared. Forced air cooling, (Tunnel cooling) For these series of tests a tunnel of 38-7/8 inches long and Il-3/h Inches diameter was constructed from metal ducts. A 9-watt electric fan with 9-3/h inch diameter blade to blow a draft of cold air past the fruit was fixed 7-l/2 inches from one end of the tunnel. This operation did not cause any appreciable rise In temperature of the air in the tunnel (less than 0.5°F). The tunnel was placed in the cold room In which all the air cooling tests were done. Apples and pears were cooled by this device. The fruits were suspended one at a time near the center of the tunnel 6-l/2 inches from the end of the tunnel opposite the fan. It was held from its stem by a piece of wire 23. attached to a hook fixed in the upper inside wall of the tunnel. Air velocity was controlled by varying the fan speed through a rheostat. The fruits were cooled at different air velocities, 300, 600 and 900 fpm. The fruits were selected as uniform in shape as possible and the initial temperatures were uniform and the same. In air cooling of apples and pears some were weighed before and after cooling to see if moisture was lost. The weighing after cooling was made in the cold room to avoid gaining moisture by condensation on the surface of the fruit. The maximum loss observed was 0.2%. Cooling room temperature and, therefore, the temperature of the air moving past the fruit, averaged 3l°F. with a range of 3-h°F. The fluctuation occurred every l0 minutes, but the variation was small compared with the difference between the commodity temperature and the average air temperature which was used for plotting. Air velocity was measured with an Alnor-thermo anemometer. With this equipment, a maximum air velocity of IOOO fpm. was possible. The air velocity was measured at four points, each l/h inch from the fruit in a plane perpendicular to the direction of air flow, one point on each side, one point above and one point below the fruit. The reported velocity Is the average of these values. A typical pattern was 900 and 9l0 fpm on the sides, 920 fpm. above and 870 below. Thirty fpm *was the maximum deviation of any of the four points measured from the reported average velocities. Hydrocooling and heating Hydrocooling and heating were conducted by using a laboratory retort as a water bath (see figure I). The water was recirculated from ZLi th //l C’“” '2 /’ . WATER LO / i L I I |.O l2 l.4 I6 l.8 2.0 OBSERVED LAG FACTOR,J Fig. 3. Comparison of observed and calculated lag factor for apples. 3“. TABLE 5: HYDROCOOLING NCINTOSH APPLES AND FEARS AT 3I°F AT DIFFERENT HATER FLOW RATESo Hater flow Cooling Lag Item Dimensionsa,cm. rate rate factor ft/min f,min j Apple I 2 3 7.0 6.3 3.6 22.5‘ 38.“ l.62 7.0 6.5 3.8 “0.0 37.2 I.7 7.0 6.5 3.8 53.5 36.0 I.79 Pears l 2 6.0 6.5 22.5 33.“ l.29 6.0 6.“ “0.0 3l.3 I.33 6.0 6.5 53.5 27.“ l.“l aSee Table 2, page 28, for description of dimensions. 35. ABLE 6: COHPARISON OF CALCULATED SURFACE TRANSFER COEFFICIENT FOR HcINTOSH APPLES COOLED AT DIFFERENT HATER FLOW RATES AT 3I°F 2 h, Btu/hr-OF-ft , r, = 3.5 CN. Flow rate ,0, ft / min Assumptiona 22.5 “0 53.5 I l0.“0 I2.29 l“.83 II l“.9 l6.“ I8.3 III l“8 I95 224 aAssumption I - observed j and f are correct ll - A = .00685-Btu-ft/hr-oF-ft2 and observed f \ Ill - Kramers (quoted In Zenz and Cthmer, l960). in water at l22°F (velocity of 53.5 ft/min) are given in Table 7; surface heat transfer coefficients calculated by the same three methods as above are shown In Table 8. For calculation II, the conductivity of the apple was adjusted to account for the higher conductivity of water at the temperatures prevailing during heating. At the constant flow rate, heating rates increased with increasing size and lag factors decreased. The cooling characteristics of different sizes of cucumbers cooled in water at 33°F. and flow rate of 8“ lb/min. are given in Table 9; with the Increasing size, cooling rates Increased and lag factors decreased. The heating characteristics for grapes, plums and peaches heated in water at I30°F and at different flow rates are summarized in Table I0. Note that at a given flow rate, the heating rates increase with fruit size, and lag factors decrease; as flow rate Increases, then, for a given fruit, heating rates decrease and lag factors increase. The results of hydrocoollng and heating tests of both cucumbers and peaches are shown In Table II. Although the heating rates are higher on heating than on cooling, the difference is not as large as might be expected by the change in thermal diffusivity at the higher temperature. (This change In heating rate was observed for apples.) 37. TABLE 7: HEATING DIFFERENT SIZES OF NCINTOSH APPLES AT I22°F AND HATER FLOW RATE OF 53.5 FT/NIN Heating rate, Lag ri Dimensionsa,cm. f,min factor, j (1) 3.6 2.9 (2) 5.8 20.5 1.61 (3) 3-7 (I) 7.0 3.5 (2) 6.2 26.5 1.50 (3) 3.8 (I) 7.5 3.75 (2) 6.5 34.5 1.38 (3) 3.7 aSee Table 2, page 28, for description of dimension. 38. TABLE 8: COMPARISON OF HEAT TRANSFER COEFFICIENT (n), Btu/hr-OF-ftz FDR DIFFERENT SIZES 0F NCINTOSH APPLES AT HATER FLOW RATE OF 53.5 FT/HIN Assumption. r, cm I II III 2.9 I6.“ IO.I “2 3.5 1u.3 ’ 6.05 69 3.75 9.8 “.05 27 aAssumption I - observed j and f are correct II - A - 0.00762 Btu-ft/hr-oF-ftz and observed f. III - Kramers (quoted in Zenz and 0thmer. I960) 39- TABLE 9: COOLING DIFFERENT SIZES 0F CUCUMBERS AT BATH TEMPERATLRE 0F 33°F AND WATER FLOH RATE OF 8“ LB/NIN Diameter Length Cooling Lag factor cm cm rate, f, j min 3.0 8.6 9.2 I.“2 3.2 IO.I II.“ l.33 3.5 II.2 l“.“ l.23 5.0 l3.5 22.8 I.07 TABLE l0: HEATING GRAPES, PLUHS AND PEACHES AT DIFFERENT HATER FLOH RATES AT l30°F “0. Water flow rate Grapes Plums Peaches Ib/min figmin gj f, min i_ f, min j 50 3.6 l.“0 I6.0 l.30 23.5 l.IO IOO 3.2 I.5“ I5.0 I.“7 22.5 l.IS l50 3.0 l.6“ I“.5 l.60 2I.0 l.20 200 2.8 I.75 I“.0 l.86 2l.0 l.20 “I. TABLE II: HEATING AND COOLING CUCUMBER AND PEACHES UNDER IDENTICAL CONDITIONS AT FLOW RATE OF 8“ LB/HIN Cucumber Peaches Heating; Cooling_ Heating Cooling Diameter or Weight 3.2 cm 3.2 cm l25 9 l2“ 9 Length, cm I0.0 l0.0 Initial temp. °F 76 76 78 77 Bath temp. °F 120 32 120 . 33 Initial temp. difference, °F ““ ““ “2 ““ f, min II.0 II.25 l9 22 lag factor, j l.36 l.3“ I.58 l.33 “2. DISCUSSION AND RECOMMENDATIONS Tne data presented in Table 2 do verify Dewey's (I950) and Guillou‘s results (I959) that the shortest characteristic cooling time is associated with the higher air velocities and that the slowest cool- ing is associated with the lowest air velocity. Here f is proportional to the characteristic cooling time, as shown in Table I. This trend can also be seen from the cooling curves presented in Figure 2 which shows the change of f and j values for three apples of the same size from the same variety, with the change of air velocity. The lag factor j, which characterizes the beginning stage of cooling, was arbitrarily fixed in the Sainsbury (I95I) and Guillou (I960) studies to be I. The results obtained from the experimental data in the present study show that this assumption is not justified, since the values obtained for j were more than I. Moreover, although j approaches l as h approaches zero, there is no a priori reason for fixing the value at I for all circumstances. At the other extreme, for which j approaches 2 as h approaches infinity, one finds that Cane (I937) assumed j a 2 even though from a plot of his published data the curve has a j measurably less than 2. The real problem is that the slope (whether called cooling rate, or half-cooling time) is a functIOn of both h and k; they are not independently determinable from the slope of the curve. This dependence means that k, over which one has no control in a particular instance, and which probably varies within rather narrow limits for a given variety of fruit and probably not much more for all fruits, has not “3. been measured when half-cooling time has been measured, and that half-cooling time is not a constant for a particular fruit, but a constant only for the very special set of cooling conditions under which it was measured. Study of the data presented in Table “ of the comparison of surface heat transfer coefficients, h, for different sizes of apples at different air velocities does indicate that h increases with increasing air velocity in all cases. This trend is In the direction predicted by Kramers' equation. Kramers' equation also predicts a decrease in h with an increase In size for a constant air velocity. The data varifies this trend In all but three Instances. In calculation I of the observed h, in which it was assumed that the observed f and j were true, the range of values obtained for A was rather large although the apples were from the same variety. It seems unlikely that specific heat and density would vary enough from apple to apple to give this calculated range In A's. Probably one has here a measure of the over-all experimental variation. But, even so, the change In observed n values for the tested apples are generally in the predicted direction both assumptions l and II as shown In Table “. In the other methods of calculation for h different values were obtained, but the difference was not so great. These differences may be due to the values of some constants as specific heat; in this study unassecITr heat ofCL89 Btu/lb-°F was taken from Short and Bartlett (l9““) for apples of 83.7% moisture. and since the moisture content and specific best for the appies test»: in this stray «or» no: determined the true values any be different frcr: those used in the ““. calculations. In calculation I values for h compare reasonably with those calculated by the other three different methods. But it is hard to say which is more correct since there is no agreement on a particular method as to which gives the correct answer and can be used as a standard. All methods are based on the principle of heat transfer, but they differ in the assumptions made, so the values obtained by these calculations are different but not widely so. Figure 3 shows a comparison of the observed j's and calculated j's (assumption II) which are obtained by using the assumed values of A, k, h, and working back through H], to get j. The observed and calculated j's compare best at higher air velocities, but less well at the lower air velocities. For pears as far as f and j values are concerned, all that is noted about apples can be said about pears; however, for calculating h and k one needs to solve the heat transfer equation for the boundary conditions of a pear which, so far as the author knows, have not been described. Study of Table 5 for the cooling rates of apples cooled by running cold water shows that it is rather obvious that cooling rates are smaller than those for the same size apples even at the highest air velocity used which means that hydrocooling is fairly rapid when com- pared with the data presented in Table 2 for air cooling. It is obvious also (Table 6) that surface heat transfer coefficients for the hydrocooled apples are higher than those in air cooling. This result is characteristic of objects cooled by direct contact with a liquid which makes It the most rapid method for cooling such types of fruit. “S. A comparison of surface heat transfer coefficients for hydrocooled apples, observed and calculated by the different methods. compared reasonably except by Kramers' equation which predicts very high values. There are a number of possible explanations for these very high predicted values. First, one can certainly question Kramers' equation since It is a smoothed (from many experiments) equation forced to give the best fit for air and water. Second, as j approaches 2, H' approaches pi and the Blot number changes very rapidly; that is, experimental incertainty increases at high j values. Tables 7 and 8 show the change in heating rates for different sizes of McIntosh apples when heated in running hot water, and a comparison of surface heat transfer coefficients. These results compare reasonably with those obtained In hydrocooling the same size apples (Table 6); the difference due primarily to the high conductivity of water and secondar- ily to variety difference (density). Kramers' equation still gives high values for h, but not as high as In hydrocooling. It should be noted also that a different weighted k value for water between 75-I22°F was used in calculation for h in heating tests. In hydrocooling cucumbers, cooling rates were determined for different sizes of cucumber (see Table 9). The changes are In the same general direction as for apples and peers, decreasing j and increasing f with increased fruit size. Probably the heat transfer constants (h and k) could be best determined by assuming that the cucumber is a cylinder. However, the same question arises as to what “6. values to take for specific heat, density, moisture content, radius and length. When grapes, plums and peaches were heated in hot water at l30°r. heating rates varied with the size of the product and water flow rate as was expected (see Table l0). Table II shows that heating and cooling rates of cucumbers of the same size under nearly identical conditions are almost the same although one would expect heating rates, f, to be somewhat smaller because the conductivities are surely not the same. It was noted that the texture of cucumbers did not seem to be affected on heating. 0n the other hand, heating and cooling rates of peaches of the same weight,were not the same. In heating f was smaller than f in cooling, as might be expected. However, It was noticed that the peaches were badly softened on heating. This difference between heating and cooling rates of peaches may be due to a change in the thermal properties of peach tissues as a result of heating. All the data, with the important exception of hydrocooled apples, strongly suggest that the theoretical model has a relationship close enough to real fruit to be of some value in predicting cooling rates (given, for example, k and h). It seems obvious now that the key test of this relationship between model and fruit rests on the measurement of k (and therefore, c and w) and r for each particular test fruit. I That these fundamental considerations have escaped the attention of researchers for over 30 years seems a little incredible. It is contended here that the experimental, analytical, and theoretical approach outlined in this thesis have merit In cooling “7. studies. It is recommended that this work be pursued as follows: With apples (or, perhaps, oranges) one should measure weight, specific heat, density, moisture content and cooling rates and from these determine k and h under the test conditions. These data should settle the question of correspondence between theory and reality as well as give some measure of experimental variation. If the above shows agreement, continue with other “Spherical" fruits and find k and h under various test conditions. Find k for various fruits and vegetables and determine variation In k among fruits of the same lot. Try some experiments with Irregular fruits such as pears and try to find if a shape factor correction can be used to the spherical case a “8. APPENDIX l. Definition of symbols used in this study II. Table I - Lag factor in spheres iii. Figure A - Lag factor, j, as the coefficient of the first term of the series expansion for heat transfer in spheres. iv. Figure B - Solution of l-Ml Cot M' - B “9. DEFINITION OF SYMBOLS USED IN THIS STUDY Thermal diffusivity, k/Cw, ftZ/hr Blot number - r'h/k Specific heat (of sphere), Btu/lb°F Diameter, cm Reciprocal of the slope of the heat penetration curve, whether for cooling or heating, with Iog.0(T-Tc) or Ioglo(Th-T) plotted against time. Flow rate fpm In air cooling, fpm or lb/min In hydrocooling Surface heat transfer coefficient, Btu/hr-ft2-0F T"T The lag factor of the heat penetration curve, equal to ° c in T -T Th‘To o c Tn'Té cooling and in heating. Thermal conductivity, Btu-ft/hr-ftZ-OF Distance from center of a sphere, cm Radius of sphere, cm Temperature of the heating bath, °F Temperature of the cooling bath, °F Initial (uniform) temperature, °F Intercept on the time equals zero axis of the asymptote to the heat penetration curve Temperature °F at time t Time, minutes Density of sphere, lb/ft3 Half-cooling time or characteristic cooling time Viscosity A PARTIAL TABLE OF LAG FACTORS IN SPHERES sin ”I - chos H, M. - sin H. cos H' Lag factor, j - 2 Blot number, Bi - I - HI cot H' rad. 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