ilHHIIHHWHHIIH|WIIMIHH|IHIHHWIHIHIIIHIHII Wrens (~35 C) This is to certify that the thesis entitled HEAT TRANSFER PROPERTIES OF HOME MEAL REPLACEMENT PRODUCT/PACKAGE SYSTEMS presented by Mat thew A . Neumann has been accepted towards fulfillment of the requirements for M.S. _ Packaging degree 1n W Major professor January 26, 2001 [)ate 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State University PLACE IN RETURN Box to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE SEF‘ME 31309 3 4U U z "—i. MAR 2 2 ”38 6/01 cJCIRC/DatoDuo.p65-p.15 HEAT TRANSFER PROPERTIES OF HOME MEAL REPLACEMENT PRODUCT/PACKAGE SYSTEMS By Matthew A. Neumann A THESIS Submitted to Michigan State University In partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 2001 ABSTRACT HEAT TRANSFER PROPERTIES OF HOME MEAL REPLACEMENT PRODUCT/PACKAGE SYSTEM By Matthew A. Neumann This study examined the heat loss profile of four different commercially available frozen food dinners (2 sizes of lasagna, corn, and meatloaf) cooked in a conventional oven and microwave. By monitoring the heat loss profile (temperature vs. time) with thermocouples the R-values of several materials suitable for frozen food packaging (foil, paperboard, and PET) were calculated. The R-value of the materials were 0.607 ft2 - °F - hr/ BTU for PET, 0.441 for foil, and 0.490 for paper. Additionally, heat loss profiles were constructed for the cooling of the frozen dinners after heating. There was significant variation in the initial temperatures of the food products after heating. This suggests that there would be difficulty in theoretically modeling the heating and cooling rates. Additionally, while the individual locations tested for temperature versus time displayed irregular behavior, the average of these points when plotted as heat loss versus time data fitted a simple theoretical model very well. After cooking, the center temperature of the foods was generally lower than that of the surrounding mass. In some cases, the center temperature was much lower than the surrounding mass, which brought about a warming trend of the center mass. This research examines the behavior of water and commercially available food as it cools at room temperature in various packaging materials and sizes. ACKNOWLEDGEMENTS I am extremely gratefirl to all the support I have received working on this project as well as my degree in general. To my graduate committee, Dr. Gary Burgess, Dr. Bruce Harte, and Dr. Robert Ofoli: your knowledge, support, and patience was greatly appreciated. To Dr. Diana Twede, Dr. Robb Clarke, and Dr. Robert Lamoroux: your help with providing financial support through assistantships as well as providing me the flexibility to balance work, studies, and research has been a major contribution to my success. To all the graduate students and the PGA, specifically, Matthew Moon, Matthew Thomas, Erik Knudsen, Laura Bix, and Hussain Qurashi: no matter how many miles lie between us in our fixture, our friendships will not falter. Your support both academically and socially will not be forgotten. To my family, especially my parents: thank you for your encouragement and understanding. Finally, and most importantly, my wife, Colleen: despite my long hours of studying, researching, and working, you maintained your support, encouragement, patience and love. iii TABLE OF CONTENTS List of Tables ......................................................................................... v List of Figures ........................................................................................ vi Introduction ............................................................................................ 1 Literature Review ..................................................................................... 3 Materials and Methods ............................................................................... 7 Results and Discussion ............................................................................. 14 Conclusions .......................................................................................... 22 Bibliography ......................................................................................... 23 Appendices Appendix 1 .................................................................................. 24 Appendix 2 .................................................................................. 34 Appendix 3 .................................................................................. 59 iv Table LIST OF TABLES Cooking Times & Temperatures Ued Ti, 0, & Rz-values for Heat Loss Vs. Time Graphs Experimental R-Values of Packaging Materials Determined From Equation 6 Heat Capacity of Medium Microwave Lasagna Average Page 12 15 17 Figure 10. ll. 12. 13. 14. 15. 16. 17. 18. 19. 20. Model of Exponential Heat Loss According to Newton’s Law of Cooling LIST OF FIGURES Meatloaf Tray Dimensions Heat Flow in a Body Having a Uniform Temperature Heat Flow in a Partially Heated Body Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Time For Water in PET A Time For Water in PET B Time For Water in PET C Time For Water in Paper A Time For Water in Paper B Time For Water in Paper C Time For Water in Foil A Time For Water in Foil B Time For Water in Foil C Time For Small Microwave Lasagna A Time For Small Microwave Lasagna B Time For Small Microwave Lasagna C Time For Medium Microwave Lasagna A Time For Medium Microwave Lasagna B Time For Medium Microwave Lasagna C Time For Microwave Corn A vi Page 21 21 25 26 27 28 29 30 31 32 33 38 39 40 41 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Heat Loss Vs. Time For Microwave Corn B Time For Microwave Corn C Time For Microwave Meatloaf A Time For Microwave Meatloaf B Time For Microwave Meatloaf C Time For Small Oven Lasagna A Time For Small Oven Lasagna B Time For Small Oven Lasagna C Time For Medium Oven Lasagna A Time For Medium Oven Lasagna B Time For Medium Oven Lasagna C Time For Oven Corn A Time For Oven Corn B Time For Oven Corn C Time For Oven Meatloaf A Time For Oven Meatloaf B Time For Oven Meatloaf C vii 42 43 45 46 47 48 49 50 51 52 53 54 55 56 57 58 INTRODUCTION With the decrease in time available for traditional home cooking along with an increase in single parent households, dual income households, and an aging population, people are using alternative means for meal preparation. (Larson, 1998) With this demand for faster and more convenient meal preparation comes the increase in use of home meal replacement food and packaging. Since the introduction of the frozen dinner in 1954, consumers were given the freedom to keep food for extended periods of time with little threat of deterioration or microbial growth. Upon demand, the food could then be prepared quickly using a conventional oven or more recently with a microwave oven. While the low preparation time offered by home meal replacement foods is important, it does little good to the consumer if the food/package system can not maintain the desired serving temperature. Multiple factors can effect the heat loss that occurs from the time the food has completed cooking until the food is ready to eat. The food parameters that effect heat loss include: water activity, density, contact area with the package surface, chemical composition, phase, and viscosity. Some parameters of the package include: insulating capacity of the material (R-value), density, volume, and surface area. Other factors that need to be considered are initial food temperature, external air temperature, and mode of heat loss at the interface between the food and package as well as the package and the environment. When heating a product with high water activity or low viscosity, the product is allowed greater circulation and thus sweeps the heat away from the outside edge of the package and is able to heat faster. Conversely as the product cools, heat is constantly swept to the outside edge for transfer into the surrounding atmosphere and the product would then cool faster. Substances with higher densities will generally conduct heat at a faster rate than those of a lower density, assuming all else equal. The objectives of this research were: 1. To detemrine the insulating ability (R-value) of different packaging tray sizes and materials. 2. To determine the relationship between heat loss and time for different sizes and types of frozen foods. 3. To derive thermodynamic data (heat capacity values) for the different foods tested. LITERATURE REVIEW THE 1st LAW OF THERMODYNAMICS The first law of thermodynamics states that in the absence of work, heat energy added to a substance results in a change in internal energy. For simple heating and cooling processes which do not involve phase changes, the internal energy is proportional to the temperature of the substance. In this way, as a food/packaging system is cooled, the internal energy of the system is transferred fi'om the food/package system to the atmosphere. By definition, a British Thermal Unit (BTU) is the amount of energy required to raise 1 lb. of water 1°F. For substances other than water, BTU = W * C * AT (1) W = the gross weight of the system, C = the heat capacity of the substance AT = the difference in final and initial temperatures of the system. If the amount of heat (BTU) removed from the system over a given time period can be determined, then the temperature drop AT over time can be determined. (Perry, 1984) MODES OF HEAT TRANSFER There are three mechanisms of heat energy from one body to another: conduction, convection, and radiation. (Holman, 1986) (Krieth, 1973) Conduction is the means by which heat energy is transferred from one body directly to another by means of immediate contact. In convection, heat energy is transferred from one body to a fluid medium, like air. In radiation, heat energy is emitted from a body by the emission of photons. Any combination of these three modes may be present in a system. (Perry, 1984) As foods cool, conduction and convection are the predominate modes of heat transfer and the contribution of radiation heat loss is negligible. R-VALUE OF AN INSULATING SYSTEM The R-value is a unit of measurement for the total thermal resistance of a system. It is used here to describe the ability of a package or container to resist the transfer of heat energy from the food inside at an elevated temperature to the surrounding air at a lower temperature. It combines all three modes of heat transfer and allows for a universal description of the net energy transfer from multiple sources and transfer modes.(Burgess, 1999) In terms of heat loss through a package the R-value can be described as the following: R-value = A * AT / Q (2) A = surface area of the container, AT = temperature difference between the food inside and the air outside Q = heat transfer rate in units of BTU/hr The English system R-value has the units: h — it2 — °F / Btu. The metric system R—value has the units: m2 — °C / Watts. (ASHRAE, 1985) (Holman, 1986) (Krieth, 1973) The R-value for a package should depend only on the construction of the package wall, specifically the thickness and material. The higher the R-value the better the package will insulate its contents. According to Equation 2, assuming the R—value is constant for a packaging material, an increase in the area or temperature difference will result in a higher rate of heat loss from the package and into the area surrounding the package. NEWTON’S LAW OF COOLING For any system at an initial temperature of T; placed in an atmosphere with temperature T, with T, > T., an application of the first law of thermodynamics coupled with the law of convection heat transfer says that: (Holman, 1986) (Krieth, 1973) (1/R)*A*[T(t)—T.]=-W*C*dT/dt (3) R = the system R-value, A = the container surface area, T(t) = temperature of the system at time t, Ta = temperature of the air surrounding the system (assumed constant) W = gross weight of the system C = the heat capacity of the system Rearrangement of this equation yields: dT/dt + B * T(t) = B * Ta (4) B=[A/(R*W*C)] Solving this differential equation yields: T(t) = T, + k * e'B‘ Where k is some constant to be determined by initial conditions. Forcing the initial temperature of the food immediately after heating to be T, at t=0 gives k = T; — T3. The theoretical change in temperature over time then is given by Newton’s Law of cooling T(t) = T. + ("ri — T.) 6‘“ (5) This is shown in Figure 1. Figure 1: Model of Exponential Heat Loss According to Newton’s Law of Cooling T, -i {-1 \ E \ System Temperature, T(t) E 8- \ E 0 I— T. Room Temperature. T. Tune. t ’ Graphs such as this can be constmcted for a food product held at a constant temperature provided that Ti, Ta, and B are known. T, and T3 are easily determined and B is a function of A, R, W, and C. A and W can be easily determined, but R and C can be more difficult. R can be estimated based on package construction, but C is dependent on many variables such as the water content, density, consistency etc... of the food. Filling a food package with water (heat capacity C = l BTU / lb. - °F) and fitting the heat loss vs. time to equation 5 allows one to calculate the R-value of the package. This can then be repeated for different packages which allows a comparison of R-values for those packages. It is important to note that equations 3, 4, and 5 apply only to systems which conduct heat internally much more rapidly than they lose heat to the air, which should be the case for cooling foods. This means that the internal temperature is a fiinction of time only, not position. Hence the assumption of a single temperature in equations 3, 4, and 5. MATERIALS AND METHODS A. Materials 1. Food / Packaging Materials: Commercial food products were used, according to procedure, in evaluating the heat loss profile of the given product/package system. a. 10.5 oz. (297g) Stouffers Lasagna With Meat Sauce in a 15.8-mil rectangular PET thermoforrn tray with a 0.488-mi1 PET heat sealed film covering. The tray had an internal volume of 24.0 in3. and the dimensions length = 4” to 4.75”, width = 3” to 3.75”, and depth = 1.75”. The range of length and width dimensions represent the difference between the dimensions at the top and bottom of the nestable tray. The surface area of the container was 40 in2 and the surface area of the lid was 14.77 inz. The suface area and volumes listed were estimated using the mean average of the dimensional ranges. In this study this product is referred to as “Small Lasagna.” This product was selected because it is available in multiple sizes and comparisons of size versus heat loss per unit of time can be established. Also, the food has a large surface contact area with the package as well as a low product surface area compared with particulate foods such as com. 21 oz. (595g) Stouffers Lasagna With Meat Sauce in a 20.3-mil rectangular PET thennoform tray with a 0.52-mi1 PET heat sealed film covering. The tray had an internal volume of 42.9 mi. and had the dimensions length = 5.44” to 6.13”, W = 4.13” toS”, and D = 1.63”. The range of length and width dimensions represents the difference between the dimensions at the top and bottom of the nestable tray. The surface area of the container was 60 in2 and the surface area of the lid was 26.38 inz. The suface area and volumes listed were estimated using the mean average of the dimensional ranges. This is referred to as “Medium Lasagna.” This product was selected because it is available in multiple sizes and comparisons of size versus heat loss per unit of time can be established. Also, the food has a large surface contact area with the package as well as a low product surface area compared with particulate foods such as com. This empty package was also used to calculate the R- value of a PET tray with a PET film covering. This package is referred to as “PET”. This package was selected because it represents a highly utilized microwaveable / ovenable convenience packaging material. 10 oz. (283g) Boston Market Sweet Corn in Herb Sauce in a 21.85 mil rectangular PET thermoform tray with a 0.59 mil PET heat sealed film covering. The tray had an internal volume of 30.35 in3 . and had the dimensions L = 5.0625 to 5.75, W = 3.5 to 4.3125, and D = 1.4375”. The range of length and width dimensions represent the difi‘erence between the dimensions at the top and bottom of the nestable tray. The surface area of the container was 47.89 in2 and the surface area of the lid was 21.12 inz. The suface area and volumes listed were estimated using the mean average of the dimensional ranges. This is referred to as “Corn.” This product was selected because it represents food that has multiple contact surfaces with the packaging material and the food has a large overall surface area compared to non-particulate food. d. 9 oz. (255g) Boston Market Meatloaf With Gravy in a 16.34 mil semi- rectangular PET thermoform tray with a 0.54-mil PET heat sealed film covering. The tray had an internal volume of 34.84 in3. and dimensions as illustrated in figure 2, with a depth of 1.1875”. The surface area of the container was 52.20 in2 and the surface area of the lid was 29.34 inz. The volume was determined by filling the container with water and measuring the volume with a graduated cylinder. The surface area of the top and bottom of the package was estimated by dividing the volume by the depth. The surface area of the sides were estimating by multipling the circumference by the depth This is referred to as “Meatloaf.” This product was selected because it represents food that has a large contact surface with the packaging material and the food has a low overall product surface area compared to particulate food such as corn. Figure 2: Meatloaf Tray Dimensions e. l n I 6-5/8 l / \ 1 3-3/8” I 4-7/8” v 3.46 mil rectangular aluminum foil tray with 15.66 mil foil coated paperboard covering. The tray had an internal volume of 50.03 in3 and had the dimensions L = 5.875” to 6.5”, W = 3.875” to 4.75”, and D = 1.875”. The range of the length and width dimensions represent the difference between the dimensions at the top and bottom of the nestable tray. The surface area of the container was 66.06 in2 and the surface area of the lid was 26.68 inz. The surface area and volumes listed were estimated using the mean average of the dimensional ranges. This is referred to as “Foil.” This product was selected because it is an alternative to PET for ovenable food packaging. f. Empty 18.84 mil rectangular PET coated paper tray with 17.13 mil PET coated paper covering. The tray had an internal volume of 35.89 in3 and the dimensions L = 6” to 6.25”, W = 4.375” to 5”, and D = 1.25”. The range of the length and width dimensions represent the difference between the dimensions at the top and bottom of the nestable tray. The surface area of the container was 55.74 in2 and the surface area of the lid was 28.71 inz. The surface area and volumes listed were estimated by using the mean average of the dimensional ranges. This is referred to as “Paperboard.” This product was selected because it is an alternative to PET for ovenable food packaging. 2. Equipment a. Oven: GE model JBS27AY2AA — 4.5 cubic foot conventional oven was used for all samples referred to as “oven.” This oven was selected because it represents an oven “typically” used in a home environment. b. Microwave Oven: Goldstar model MA—963M — 0.7 cubic foot — 850 Watt microwave oven with automatic turntable. 3. Instrumentation a. Thermocouples: Omega precision fine wire thermocouples with glass insulation. Type: T. Thermocouple data was recorded with an Omega OM- 10 5000 datalogger with 40 channel capacity recording temperature readings every 30 seconds B. Methods: 1. Determining the R-value of packaging materials The package to be tested was positioned on a piece of ‘/2 inch thick plywood. The same piece of plywood was used for all studies to normalize the differences between countertops at different testing locations. The package was fitted with a thermocouple that would, when filled and sealed, rest with the sensor in the geometric center of the container. A second thermocouple was placed near the package to monitor room temperature but, placed far enough away fi'om the package as to avoid recording heat given off by the package. The package was then filled with hot (near boiling) water and sealed. The paperboard packages had to be lined with 0.5-mil PET film to prevent the water from melting the coating and leaking out. The datalogger was turned on and the temperature vs. time was recorded until such time that the internal temperature of the package was below 120°F. The data was then downloaded into a Microsoft Excel Spreadsheet and plotted as T(t) — T, vs. t. (See Appendix 1.) A best-fit to the theoretical result T(t) - T. = k 6‘” using standard regression software was then done and the correlation coefficient R2 value was determined. 11 The system R-value was then calculated using the fitted value for B as follows: R = A/ ([3 w C) (6) A = the system surface area B = the fitted value W = gross weight of the system C = the heat capacity of the system 2. Determining the heat/loss vs. time Three samples of each product were cooked according to directions in both microwave and oven. Cooking times as listed on the package label were given as range. An average of that range was used for the experimental cooking time. (Table 1.) Table 1: Cooking Times & Temperatures Used Heating Conditions Cooking Product Temperature / Package Experiment Method Power Setting Directions Time (min) Time (min) Small Lasagna 350 °F 45-50 47.5 Oven Medium Lasagna 350 °F 53-55 54 iCorn 350 °F 40 4O Meatloaf 350 °F 40 40 Small Lasagna HIGH 6-8 7 Medium Lasagna HIGH 12-15 13.5 Microwave 4-6 5 Corn HIGH (Stir after 3) (Stir after 3) Meatloaf HIGH 4.5 4.5 12 After cooking was completed, the product was placed on a piece of ‘/2 inch thick plywood. The same piece of plywood was used for all samples to normalize the differences between countertops at different testing locations. The package was fitted with three thermocouples and one thermocouple was placed near the package to monitor room temperature but placed far enough away from the package as to avoid recording heat given off by the package. For both sizes of lasagnas and the com the thermocouples were placed as follows. 0 Channel 1 was placed in the center of the product mass (center of length, width, and depth) labeled as “center”. 0 Channel 2 was placed at length = ‘A, width = ‘/2, and depth = ‘/2 labeled “side”. 0 Channel 3 was placed at length = %, width = ‘/2 and placed just barely below the surface of the food labeled “surface”. For the meatloaf, which came prepared as two separate ‘/2” patties the thermocouples were placed as follows. 0 Channel 1 and 2 were each placed in the center of a patty labeled patty 1 and patty 2 respectively. 0 Channel 3 was placed in the geometric center of the container which would coincide with the edge of one of the patties. The datalogger was then turned on and the temperature vs. time was recorded until such time that all thermocouples inside the package read below 120°F. The data was then downloaded into a Microsoft Excel Spreadsheet and plotted as AT (°F) vs. time (min). An exponential best-fit line with equation and R2 value was then constructed to determine B. (See Apendix 2) 13 RESULTS AND DISCUSSION Relationship between AT and Time According to Newton’s Law of Cooling (Equation 5) the relationship between AT, the difference between the food temperature and the room temperature, and time should be an exponential decay. The results of this study showed that when an average of the three thermocouples readings were taken the relationship holds true for water in the various trays. Appendix 1 gives the results of the experiment. Table 2 shows the Ti, B, & R2 value for the fit of these averages. An R2 of 1 indicates a perfect fit where the theoretical results predicts the experimental data exactly. The fact that all R2 in Table 2 are nearly 1 means that the fit is near perfect. 14 Table 2: T., B, & Rz-Values for Heat Loss Vs. Time Graphs Product Sample T. (0F) 13 R‘-value Small Oven Lasagna A 156.15 0.0052 0.9854 B 159.42 0.0054 0.9969 C 143.3 0.0039 0.9753 Small Microwave Lasagna A 165.05 0.0087 0.9983 B 153.29 0.0069 0.9420 C 144.08 0.005 0.9512 Medium Oven Lasagna A 124.71 0.0017 0.8466 B 131.04 0.0022 0.9165 C 133.93 0.0023 0.9075 Medium Microwave Lasagna A 171.44 0.0073 0.9786 B 171.14 0.0062 0.9985 C 166.95 0.0077 0.9982 Oven Corn A 125.87 0.0057 0.8988 B 135.16 0.0065 0.9946 C 149.24 0.0077 0.9981 Microwave Corn A 172.7 0.0111 0.9440 B 171.61 0.0098 0.9879 C 170.12 0.0118 0.9813 Oven Meatloaf A 173.86 0.0153 0.9676 B 178.57 0.0169 0.9646 C 172.45 0.0151 0.9629 Microwave Meatloaf A 176.41 0.018 0.9832 B 173.47 0.0159 0.9821 C 170.6 0.0174 0.9872 Initial Temperatures of Foods Despite cooking all products according to instructions and under near identical conditions, there was little regularity in initial temperatures at any of the thermocouple points in the food product. In many cases the difference between the highest initial temperature and the lowest initial temperature of the 3 samples, referred to as the range, were high ‘The initial temperature ranges are listed Appendix 3. 15 Only 3 thermocouple points (out of the 24 total points for all food) were within a 10°F range for all trials of the particular food. These data points and there respective ranges are listed below: 1. Surface of Oven Corn (91°F range) 2. Side of Microwave Corn (55°F range) 3. Patty 2 of Oven Meatloaf (32°F range) In contrast the 3 worst ranges were: 1. Side of Small Oven Lasagna (42.9°F range) 2. Surface of Small Microwave Lasagna (47.1°F range) 3. Center of Medium Microwave Lasagna (58.8°F range) None of the cooking methods consistently had a higher or lower range than another. From the total of all thermocouple readings, half of the microwave locations had a wider range of initial temperature and half had a narrower initial range than that of the oven. There was no regularity in temperature after heating between samples cooked in the oven versus samples cooked in a microwave. The difference between average initial temperature for all samples was greater than 10°F. The microwave samples tended to have a higher initial temperature for the medium lasagnas and corn. The meatloaf had a higher average initial temperature in all three locations for the samples cooked in the oven. The small lasagna had no definitive trend with two points being hotter for microwave and one point being higher for the oven. (Appendix 3) l6 R-value of Packaging Material Newton’s law of cooling allows us to find the R-value of a particular package (Equation 5,6). Using the values listed in the materials section (pages 7-10) and the B values from fitting the experimental data in Table 2 (page 15) to Newton’s law of cooling the R-values were determined. The values calculated are listed in Table 3. Example: Water in PET B R = A / (B w C) B = 0.0155 min" = 0.930 hr" A = 86.38 in2 = 0.5999 112 w = 567.99 g = 1.2511 lb C=lBTU/lb.-°F R = 0.5999 fiz / [0.930 hr" * 1.2511 lb. * (1 BTU / lb. — °F) R=0.516ft2—°F—hr/BTU Table 3: Experimental R-Values of Packaging Materials Determined From Equation 6 R-Values of Packaging Materials“ Sample PET Paper Foil A 0.672 0.5143 0.398 B 0.516 0.4553 0.416 C 0.634 0.4992 0.509 AVG 0.607 0.490 0.441 STD DEV 0.081 0.031 0.060 *(fiI—T-hrflBTU It is clear from the chart that the PET tray is the superior package in terms of maintaining food temperature. Foil is the worst food insulator and paper is in between. 17 Heat Capacity of a Selected Food Using the average R-value calculated for the PET tray (0.607 ft2 — °F — hr / BTU) the heat capacity of the Medium lasagna was calculated. See Table 4. Rearranging equation 6 to solve for C instead of R yields: C=A/(B*R*W) (7) Example: Medium Microwave Lasagna A A = 86.38 in2 = 0.5999 ft2 [3 = 0.0201 min" = 01.21 hr" R=0.607 fi2—°F—hr/BTU W = 557.12g = 1.221b c = 0.5999 112 / [1.21 hr“ * (0.607 112 — °1= — hr / BTU) * 1.22 lb] C = 0.6650 BTU / lb - °F Table 4: Heat Capacity of Medium Microwave Lasagna Average. Heat Capacity of Medium Microwave Lasagna“ A 066501 B 0.9348 C 0.7817 AVG 0.7938 STD DEV 0.1353 *Units = BTU / (lb-°F) Since the heat capacity of the Medium Microwave Lasagna is less than 1 BTU / lb-°F, less energy is needed to increase the temperature of Lasagna than is needed for the same weight of water. This result agrees with the theoretical prediction that higher density matter transfers heat more efficiently than lower density matter. It also agrees with heat 18 capacity values obtained by other means and listed in published references.(Frozen Food Roundtable, 1981) In the instances where multiple types of food are present in a single package, the heat capacity (C) for each individual item will be independent of each other causing different initial temperatures (Ti) for each food when heating is completed. In instances where C varies greatly, consumers will potentially have a low quality perception of the cooked foods. For example, if two foods, Food-A and Food-B are placed in a single package and Food-A has a lower C than Food-B, Food-A has the potential to overcook if the cooking directions target the optimum serving temperature for Food B. Likewise, F ood-B has the potential to be undercooked if the cooking directions target the optimum serving temperature for Food-A. Internal Temperature Behavior of Samples In at least one sample of every product/cooking method, with the exception of the Oven Meatloaf, the behavior of the center temperature varied from the theoretical behavior expected from a cooling product. In Newton’s Law of Cooling, it is assumed that, after a body of mass is heated and placed in an atmosphere at a lower temperature, a unidirectional heat flow away from the mass into the surrounding atmosphere will occur (figure 3). In several samples an increase in temperature at the center was noted afier heating of the product was completed. This irregularity is caused by a large temperature difference between the center of the food mass and the surrounding food mass. This large temperature difference created a second thermal gradient directed towards the center of the food mass (the slowest heating point). This second thermal gradient caused 19 the center mass to continue to increase in temperature, or at least plateau until such time that the temperature difference was low enough to negate the second gradient. (Figure 4) The reason for this irregular behavior is due to the thickness of the food products. With thick samples, such as the lasagnas, and corn (all greater than 1” thick), the surrounding mass (Figure 4) prevents the heat energy from reaching the center mass. Since the center mass does not receive the same amount of energy as the surrounding mass the center mass will have a lower initial temperature than the surrounding mass. In thick samples, the difference between the initial temperature of the center mass and surrounding mass is large enough to establish the second heat gradient. This rationale explains why the meatloaf patties, which ranged from V2” to 3%” thick, did not exhibit the irregular behavior. This finding negates the assumption behind equations 3,4, and 5 which were used to find R-values and heat capacities (C). The values obtained for these quantities are therefore suspect from a theoretical point of view. The fact that they agree with expected values however says that they have experimental merit. Specifically, the C values represent averages over position within the food when the food is subjected to convection cooling. Likewise, R should also be taken as an “insitu” value. When water cooled in the individual packages the center-heating phenomena did not occur. The contents began cooling as predicted by the model. (Figure 1,3, Appendix 1) The major reason for this difference, compared to foods, is that with water being a fluid, it is allowed to circulate thus creating heat gradients within the package so small they are negligible. 20 Figure 3: Heat Flow in a Body Having a Uniform Temperature : 1111111 : MHHHHHJ’ Fiugr e:4 He aotFl win aPartiallyHeatedBo ody $3mPL1ng1M11f11L1 : fljllH—E E *111111f : HHHHHI’ T2>Tl T2>T3 21 CONCLUSIONS This study provided a basis for comparing and selecting appropriate food/package systems. Specifically this study provided a method for determining R-values of packaging materials as well as heat capacities of foods using Newton’s Law of Cooling. It was concluded that the R-value of PET is higher than that of Foil and Paper and therefore is a superior insulator of food products. Generally speaking, the initial center temperature of the selected foods was lower than that of the surface and remained lower for the entire cooling process. Although the individual points within a meal did not always follow the predicted behavior according to Newton’s Law of Cooling, when an average of the points were taken the behavior closely resembled the theoretical predictions. While results of individual average cooling behavior followed theoretical outcome closely, the initial temperatures of identical food/package systems prepared under identical conditions contained high variability. Furthermore, initial temperatures of microwave and conventional oven were dissimilar with respect to all points tested. Therefore, modeling of required cooking time for desired heat level may not be completely dependable. 22 BIBLIOGRAPHY 1. ASHRAE Handbook Fundamentals. 1985. American Society of Heating, Refiigeration, and Air-Conditioning Engineers, INC. Atlanta, GA. 2. Burgess, Gary 1999. Practical Thermal Resistance and Ice Requirement Calculations for Insulating Packages. Packaging Technology and Science. 12. pp. 75-80 3. Frozen Food Roundtable, Code of Recommended Practices for the handling and Merchandising of Frozen Foods. September, 1981. Washington, DC. 20007 4. Holman, JP. 1986. Heat Transfer. 6'h Edition. McGraw-Hill Book Co. 5. Krieth, F. 1973. Principles of Heat Transfer. 3rd Edition. Intext Press. 6. Larson, Ronald B. 1998. The Home Meal Replacenment Opportunity: A Marketing Perspective. Working Paper. The Retail Food Industry Center. University of Minnesota, St. Paul, MN 7. Perry’s Chemical Engineers’ Handbook. 1984. Edited by R. Perry, D. Green, and J. Maloney, McGraw-Hill, Inc. 23 Appendix 1 Heat Loss vs. Time Data to Determine R-Value of Packaging Materials Note: The following images in this thesis were originally published in color. In the following graphs, for the best-fit lines, Y = temperature and X = time. 24 380... 3.09 .5an ll an._. 8.60 9:0... Eoom I 95... .935 o on .55 65:. on cm on ow on .bll.’ ”fwfitihlhrhvfihrihlkl..i51i .1 < hum 5 Luna; .5» «E: .m> moo.— uaoz ”m 0.59“. ON or ov on on cow ONF OS. 09 one com (:10) dwar 25 i=5 2:: ow om ov on ON 0 F o 9:6... 8.09 .593 I 9:8. 2.8 9:8. Eoom I 9:0... .235 o (:10) dwer m 9mm :_ L335 3. 25... .w> 33 “no: 6 0.59". 26 Es. 2:: on on cm on ov on ON 0 P 3E8. 3.09 doaxm II 9:0 .9 0:00 9:0 L. Boom I 9:0 L. .203 o 0 9mm 5 .395 :0» 0E2. .m> 08.. uocz Us. 0.59".— ON ow om ow 00 F cm? 0: cm? ow F com oNN (:10) dwar 27 .55. 2:: cm on ow on cm 0 v 9.th 9.09 .596 I1 9:0... 2.0m. 9:0 .9 E03. I nE0h 20.0.5 9 < Leann. :. L203 .8 08.... .0> 000; «00... 6 239.". om ov cm on 8—. owe o: 08 cm— com (:10) dul’l 28 .52. 2:: om ov on ON O F 3E0... 8.09 .3an II 9:0... $.00 9:0... Eoom. I 9:0: .202. o m Logan. :. L803 :8 0E... .0> 000.. ~00... no 0.59". ON O? cm OO 00: ON: O: OO: (:10) dwer 29 9:0... 2.09 doaxm I. 9:0 .. 8.00 9:0 .. Eoom. I 9:0 .. .203 o OO .55. 2:: on O0 OM ON 11111150 . 1": 01.: 1521.111... ii t.\r.in.|1..l 1 ...... 0 000a. :. L803 :8 0.5.: .0> 000.. 000... 5.. 0.59“. O— ON O? OO ow OOF ON: OS. OOF ow: OON (do) data; 30 3E0: 0:09 289$ 11 9:0 .. 0:00 9:0 ... Eoom I 9:0 .. 0.0.5 o .55. 2:: cm on ov on ON O F 404101 . - I'I'U «144:1 . ..‘V' ((11 4 . 4.1:: «t4 . 14:: v... '51.Erz.t.h'iv. J a! Er...l.lri§l.11:t.lul A 9A). . .. ivri liliflci. . < :0". c. .0003 L0: 2:: .0> 000.. 000... "E. 0.55.". OO F ON _. OE. OOF OO F OON ONN (do) dune; 31 .55. 2:: 9:0: 0:03 doaxm 11 9:0: 0:00 9:0: Eoom. I 9:0: ..0:0>> o m ..ou. 0. :30; 3: 05.... .0> 000.. :00... HN: 0.52". ON ov O0 O0 OO : ON: 9: O0: O0: OON ONN (:10) dwer 32 3E0: 0:00: doaxm. II 9:0 ... 0:00 080: Eoom I 9:0: 2000.5 0 ca .55. 2:: 9: cm on ov on f . .1041)?! - 19.0.. luv-J. 1:10.. . 0 =0". 0. :30; 3: 08.... .0> 0no... :00... ”n: 0.52". ON O: OO: ON: O: OO: O0 : OON ONN (:10) dwal 33 Apendix 2 Heat loss vs. Time Data of F ood/Package Systems Note: The following images in this thesis were originally published in color. In the following graphs, for the best-fit lines, Y = temperature and X = time. 34 .EE. 2:: mv ov mm On ON ON m : O : n O 000.93.59.01 .. . .. 3.000.6568... ......0............i..........:_......_.... 0E0: Eco”. x m. 000.03.. x .w 9:0 : 000.50 m. 9:0 : 00.0 I H 9:0: .0200 o < 000000.. 00320.2 ..050 .0: 0E.: .0> 000.. «00... ”v: 0.50.“. 35 .:_E. 2:: on o: O0 O0 Ov on ON O : O 000.93 doaxml .. .: .. t. 1......ir. 9:0: Eoom x . . . . . . . . . 000.03.. x 9:0 : 000.50 9:0: 00.0 I 95:02.00 0 (:10) due]. 0 05000.. 00320:... ..0E0 .0: 08.: .0> 000.. 000: ”0: 0.50.". 36 .55. 2:: O0 om O0 O0 ON O : 9:0 : E03... x 0m0.0>< x 9:0 ... 000.50 9:0 : 00.0 I 9:0 : 00:00 0 0 05000.. 0>0320=2 ..0E0 .0: 0E.: .0> 000.. 000... "o: 0.50.". ON O0 O0 O0 OO: ON: O0: Hammer 37 .55. 2:: OO O0 on O0 O0 O0 O0 ON O : 000.03.. .590. I :m. 0 O>< 0:00 a 9:0 : Eoom. x 15.111.110.53405 3.1.1.58! n . it: 0i}? .41.)... . .. 000.05. A 9:0 : 00050 0E0: 00.0 I 9:0 : .0500 o < 000000.. 00320.! E2005 .0: 0.5: .0> 000.. :00... K: 0.50.“. ON O0 O0 O0 OO: ON: O0: O0: O0 : OON ONN (:10) dwar 38 .55. 05: o: 00 O0 O0 :: 0 o>< 20:. Sen. 1 000.021. :0an I :m 0 0>< 0:00 a 9:0 : Eoom. 2 000.020. x 9:0 : 000.50 0E0: 00.0 0 9:0 : .0500 o 0 000000.. 0>0320=z 50.00! .0: 2...: O0 ON .0> 000.. :00... ”a: 050.“. O: O0 O0 OO : ON: O0: O0 : ow : OON ONN (:10) duct 39 A55. 2::. ow on O? on ON O F ..... €80... 0m0.0>< 0:00 anh E03. 050... 0m0.0>< 9:0... 000.26 9:0... 00% I 080.. 0.50 o 0 05000.. 30398.5. E300...— ..o. 05.... .0> 000.. .00: ”2 0.59". (do) dune; 40 .55. as: on O? on ON O _‘ .0m0.0> 000.. .00... 6N 0.50.". O¢ O0 ow OOP ONF (:IO) dweL 41 .55. 2:: cm on 9. on ON €80... 0m06>$ .coaxm II. 0E0... :63. x 0E0... 0m0.0>< x 080... 000.5w 9:8 020 9:0... .0600 o m :60 05266.: 6. 0E; .0> 000.. .00... "..N 0.52“. 00.. ON. O3. Ow. om. OON ONN (:10) (“l-'9]. 42 .55. 05: Ow mm on ..N ON m P O F $00.03.. ..69m. II 9:09 Eoom x 0m0.0>< x 9:09 80.5w 9:09 005 I 950.. .0200 o o :60 90396.5. .6. 08.9 .0> 000... .00... ”NN 0.52.... ON Ow cm on OO. ON. O: one (do) dweJ. 43 on .000.0><. .603 ..|.. 950.. Eoom x 0m0.0>< ...». .0500 0508000 N 2.0.. ._ . Em. . .55. 05.. mN ON 0. O. 1“... ... 5‘43??? ..\...w. ; ......Ec . ... .... 4.. A , < .0260! 90.66.! 6. 0E. .. .0> 000.. .00: "nu 050.". (do) dWGJ. :<:)u | 9:0. :68. x 0m0.0>< x .250 2.6.5000 N 3.0. .. :50. . ov .55. 05... mm on mN ON 0. O. ..Vl ... {.0 . 0;!434 . . o0oo:-:.'Ill .n . .... 1.0.11). . ... o o o t - 0:”,(73uox , at... m .0260: 30320.5. .0. 0E... .0> 000.. .00... ...N 0.50.“. ON ov O0 O0 OO . ON. O3 O0. O0 . OON ONN (50) dwu 45 .55. 05.. O0 0N ON 0 . O . $00.03.. .6an I 9:0... Eoom x 0m0.0>< x .0200 2.6.800 N as. . 3.0. .- 0 .0260... 05266.: 6. 08.... .0> 000.. .00... "mm 060.“. ON O0 O0 O0 OO . ON. ov. O0. O0 . OON ONN (so) dum 46 .55. 05.. OO . 00 O0 on O0 00 00 O0 ON O . O .0006}... .630 I QEOI—u soom X .. .waiprY -.1.....r.4>s.r\r§7......1.,. a; ,. 00.0.03. x 9:0... 000.50 (:10) due; 9:0... 0.0.0 I 950.. 6:60 o < 05000.. :30 ..0E0 6. 0E.» .0> 000.. .00... .0N 0.50.". 47 .55. 05.. Ox. O0 on 00 on ON O . 300.03.. 209.0 I 9:0 .. 208.. x 0m0.0>< x 9:0 .. 000.50 9:0 9 00.0 I 020. .0200 o 0 020000.. :0>O ..020 6. 0E... .0> 000.. .00... in 0.50.“. ON O0 O0 O0 OO. ON . 00. O0 . O0 . OON ONN (:IO) due; 48 .55. 05.. on O0 00 O? on ON O . .0006}... 009.0 I 9:0 . 200m. x 0m0.0>< x 020.. 000.50 9:0 .. 00.0 I 9:0 .. .0200 o 0 000000.. :0>O =0E0 .6. 0E... .0> 000.. .00... "an 0.60.". (so) dune; 49 9:0 .. Eoom 0m0.0>< 9:0 . 000.50 9:0. 00.0 020... .0200 Oh .55. 05.. O0 00 O0 00 ON < 000000.. :0>O 5.0.00.2 6. 0E... .0> 000. .00: "an 0.50.". O. ON 0.. O0 O0 ON. O0. O0. O0. (:IO) dwu 50 .000.0><. 209.0 I 9:0. 200m. 0m0.0>< QEGP moat :w Q50.020 020.. .0200 X .X ASE. 2::. o. 00 on o0 on ON 0. 0 ON 00 O0 O0 OO. ON. ... . .V x, mumwfw... . , ... .... 5HWK. .. .... ......0........ ..H O0. 0 000000.. :30 05.00: 6. 02.... .0> 000.. .00... an 0.50.“. (5") due; 51 .000.0><. 209.0 I 0E0. .600 0. 000.024. 9:0 .. 000.50 9:0 .. 00.0 I 9:0 .. .0200 o O0 .55. 05.. on O0 on 00 00 ON O . «4.4.(5)..I.?43..B. 30:353. ...)..z)..)...\‘ .. 5.1.1.} . .11 » . . . . . frirtii... . . 3.3 ya} 0 000000.. :30 23.005. 6. 02.... .0> 000.. .00... ".n 0.50.". (do) dune; 52 .55. 05.. O0 0N ON 0 . O. 0 O .000.0><. :0qu I 9:0 .. 200m. 0. I. a wmm.o>< x w 9:0 .. 000.50 ..w .50. 00.0 _. 1:100:30: .... . , .. {€521.13 9:0 .. .0200 o < :60 :0>O .0. 0E... .0> 000.. .00... Hum 050.“. 53 .000.0><. :0an I 9:0 .. 2001 000.03.. 9:0 .. 000.50 050. 00.0 9:0 . .0200 X X .55. 05.. O0 00 O0 0N ON 0 . l&w.ifi§.kf...1?1)t.{wflln .. .....0,,.... .......»0..\.. .0 250....(5; - Fm . .. .. 40 1 ., wow.-. .4 0 F60 :0>O 6. 0E... .0> 000.. .00... "an 0.50.". O. .. 0 . ...... . . I .71 4x .. ...: 5.? (Fifi! .13. ... . 0 ON O0 O0 O0 O0. (:10) dune; .55. 05.. 00 on 0N ON 0. O. .000.0><. 009.0 I 020.. E000 x 000.03.. x 00.0. 000.50 00.0... 00.0 I 9:0 9 .0200 o 0 0.60 00.5 .0. 00.... .0> 000.. .00... .00 050.". ON O0 O0 O0 OO. ON. O0. O0. O0. OON (so) due; 55 800.030.. 009.0 I 00.0... 200m. 000.030. .0200 0.002000 N 0.0.. . 0.00 X X 0 O0 .55. 05.. 00 O0 0N ON 0. O. . 2 ,, ...... .(.....I .1. ......1. < 50:00.... 00>o .6. 0.0.... .0> 000.. .00... "mm 050.". ON. 00. O0 . O0 . OON ONN (50) due; 56 .55. 05.. O0 00 O0 0N ON 0 . O. .000.0><. 009.0 I 900... 200m. 0.. 000.0>< x .0200 00.02000 N 0.0.. ._ . .500 0 m .0220... 00>o .6. 00.. .. .0> 000.. .00... "an 050.“. ON O0 O0 O0 O0 . ON . O0 . O0 . O0 . OON ONN (:10) dwa; S7 .....0. 0.0.... 00 O0 0N ON 0. O. .000.0><. 009.0 I 9:0 .. 0.000 x 000.0>< x .0200 0.000.000 N 0.00 . 500 CI 0 .0200: 00>o .0. 00.. .. .0> 0004 .00... ...” 050.". ON O0 O0 O0 OO. ON. O0. O0. O0. OON (:IO) dwaJ. 58 0000.005 5.0.- 0...- 0.0.- 0.0. 0.00 0.0 5.00 0.00 0.05 0.0. ..ON ...0. 0>m>>o.0__>_ .0> 00>m 000.0>K 0.0. N0 0N. ..m 0.0. 5.00 5.5. N.5N 5.0. 0.0. va N00 0 cam 0.5 0.. N0 5.0. 0.0 m.m. 5.0 0.0. 0.0. 0.0 ..0N 5.0. >wD Ohm 0.50. 0.0. 0N0. 0.00. ...m. 0.00. 0.00. 0.00. 5.00 0.00. ..mm. ..Nv. O>< % 0N0. 0.00. 50. N05. 5.00. mdN. 0.0. 0.00. 0.0. 0.00. 0.00. ..ON. 0 W 0.00. 0N0. 0.00. .00. 0.00. 0.00 0.00. 0.00. 0.00 0.0. 5.05. 0.50. m 0N0. me. 0N9. 5.00. 0.0. 5.0. ..5m. 5.0m. 0.0 mem. 0.05. 0.00. < ..0. 0N0 0.0N 5.0. 0.0 0.00 .000 ..0N 0.00 ..50 m... 0.00 00:0”. ..O. 0.0. ..0. N0 0N 0.0. NdN 0N. ”mm 0.0m ..0 N5. >mo 0.5m 0.05. 0.00. 0.05. 0.05. 0.00. 0.00. 0.05. 0N0. N00. 0.05. N00. 0.0. 0>< W. 5.00. 0,00. 0.00. 5.N5. om. N..0. 0.00. 0.00. 0.00. N00. 0.00. NNw 0 .w.. 0.0. 0.00. 5.5. 0.05. 0.0. 0.00. 0N0. 0.5. 5.00. 0N0. 0.55. 0.00. m m .0.Nw. 0.0. 00ml. 0.00. 0.00. 0N0. 5.00. 0.05. 0.00. 0.00. 0.0. 0.0.. < M .0200 N500. .....00 000.50 00.0 .0200 000.50 00.0 .0200 000.50 00.0 .0200 0000.000 50200.2 0.00 am. 05.00.). 00 000.. __00.0 m05..|0.00E09 00.0 _0...0_ 00000. .0 000.0000 05.0.0050. .002. 0 500000.. 59 utmmmnmwm 7 @1an