Abstract
The main purpose of this chapter is to give a brief account of the mathematical methods of determining the temperature distribution with time and position in packaged foods while being heated and cooled. This is a prerequisite to establishing a process which will ensure the microbiological safety of the product and is also organoleptically acceptable. This requires an examination of the modes of heat transfer in different parts of the processing operation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The reader is encouraged to consult the very useful text on heat transfer and food products by Hallström et al. (1988). This is an excellent guide to the basic principles of heat transfer and its application to food processing.
References
Adams JA, Rogers DF (1973) Computer-aided heat transfer analysis. McGraw-Hill, New York
Akterian SG (1995) Numerical simulation of unsteady heat transfer in canned mushrooms in brine during sterilization processes. J Food Eng 25:45–53
Akterian SG (1996) Studying and controlling thermal sterilization of convection-heated canned foods using functions of sensitivity. J Food Eng 29(3/4):125–143
Akterian SG, Fikiin KA (1994) Numerical simulation of unsteady heat conduction in canned arbitrary shaped foods during sterilization processes. J Food Eng 21:343–354
Alhamdan A, Sastry SK (1990) Natural convection heat transfer between non-Newtonian fluids and an irregular-shaped particle. J Food Process Eng 13:113–124
Alhamdan A, Sastry SK, Blaisell JL (1990) Natural convection heat transfer between water and an irregular-shaped particle. Trans ASAE 33(2):620–624
Alles LAC, Cowell ND (1971) Heat penetration into rectangular food containers. Lebensm Wiss Technol 4(2):50–53
Anantheswaran RC, Rao MA (1985a) Heat transfer to model Newtonian liquid foods in cans during end-over-end rotation. J Food Eng 4(4):1–19
Anantheswaran RC, Rao MA (1985b) Heat transfer to model non-Newtonian liquid foods in cans during end-over-end rotation. J Food Eng 4(4):21–35
ANSYS (1968) ANSYS engineering analysis system. Swanson Analysis System, Houston, PA
Arpaci VS (1966) Conduction heat transfer. Addison-Wesley, New York
Atherton D, Overington WJG, Thorpe RH (1970) Processing studies on canned new potatoes. In: Potatoes for canning, AMDEC annual progress report 1970. Campden BRI, Chipping Campden Glos, UK
Awuah GB, Ramaswamy HS, Simpson BK (1993) Surface heat transfer coefficients associated with heating of food particles in CMC solution. J Food Process Eng 16(1):39–57
Ball CO, Olson FCW (1957) Sterilization in food technology—theory, practice and calculations. McGraw-Hill, New York
Ban H, Kaziwara Y (1941) Cooling of cans filled with water due to internal convection. Bull Jpn Soc Sci Fish 10:38–42 (in Japanese)
Banga JR, Alonso AA, Gallardo JM, Perez-Martin RI (1993) Mathematical modelling and simulation of the thermal processing of anisotropic and non-homogeneous conduction-heated canned foods: application to canned tuna. J Food Eng 18(4):369–387
Barakat HZ, Clark JA (1966) Analytical and experimental study of the transient laminar natural convection flows in partially filled liquid containers. In: Proceedings of the third international heat transfer conference (ASME), vol 2, pp. 152–162
van Beek G, Veerkamp CH (1982) A program for the calculation of the thermal properties of foodstuffs. Voedingsmiddelentechnologie 15:19–23
Bengtsson NE, Risman PO (1971) Dielectric properties of foods at 3 GHz as determined by cavity perturbation technique. 2. Measurement on food materials. J Microw Power 6:107–123
Bera F (1988) Break in the study of heat transfer by convection in cans. In: Progress in food preservation processes, vol 1. CERIA, Brussels, pp. 59–68
Bhowmik SR, Hayakawa K (1979) A new method for determining the apparent thermal diffusivity of thermally conductive food. J Food Sci 44(2):469–474
Bhowmik SR, Tandon S (1987) A method of thermal process evaluation of conduction heated foods in retortable pouches. J Food Sci 52(1):202–209
Bichier JG, Teixeira AA, Balaban MO, Heyliger TL (1995) Thermal process simulation of canned foods under mechanical agitation. J Food Process Eng 18(1):17–40
Bimbenet JJ, Michiels L (1974) Convective heat transfer in canning process. In: Proceedings of the IV International Congress of Food Science and Technology, vol IV, pp. 363–379
Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena. Wiley, New York
Blaisdell JL (1963) Natural convection heating of liquids undergoing sterilization in unagitated food containers. Ph.D. Thesis, Dept. of Agric. Eng., Michigan State Univ.
Burfoot D, Griffin WJ, James SJ (1988) Microwave pasteurization of prepared meals. J Food Eng 8(3):145–156
Burfoot D, Railton CJ, Foster AM, Reavell SR (1996) Modelling the pasteurisation of prepared meals with microwaves at 896 MHz. J Food Eng 30(1/2):117–133
Burmeister LC (1983) Convective heat transfer. Wiley, New York
Calay RK, Newborough M, Probert D, Calay PS (1995) Predictive equations for the dielectric properties of foods. Int J Food Sci Technol 29:699–713
Califano AN, Zaritzky NE (1993) A numerical method of simulating heat transfer in heterogeneous and irregularly shaped foodstuffs. J Food Process Eng 16(3):159–171
Carnahan B, Luther HA, Wilkes JO (1969) Applied numerical methods. Wiley, New York
Carslaw HR, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, Oxford
Castillo PF, Barreiro JA, Salas GR (1980) Prediction of nutrient retention in thermally processed heat conduction food packaged in retortable pouches. J Food Sci 45:1513–1516, 1528
Chang SY, Toledo RT (1990) Simultaneous determination of thermal diffusivity and heat-transfer coefficient during sterilization of carrot dices in a packed bed. J Food Sci 55(1):199–205
Chapman S, McKernan BJ (1963) Heat conduction in plastic food containers. Food Technol 17:1159–1162
Chau KV, Snyder GV (1988) Mathematical model for temperature distribution of thermally processed shrimp. Trans ASAE 31(2):608–612
Chen CR, Ramaswamy HS (2002a) Dynamic modelling of thermal processing using artificial neural networks. J Food Process Preserv 26:91–111
Chen CR, Ramaswamy HS (2002b) Modeling and optimization of constant retort temperature (CRT) thermal processing using neural networks and genetic algorithms. J Food Process Eng 25(4):351–379
Chen CR, Ramaswamy HS (2002c) Modeling and optimization of variable retort temperature (VRT) thermal processing using coupled neural networks and genetic algorithms. J Food Eng 53(3):209–220
Chiheb A, Debray E, Le Jean G, Piar G (1994) Linear model for predicting transient temperature during sterilization of a food product. J Food Sci 59(2):441–446
Choi Y, Okos MR (1986) Thermal properties of foods—review. In: Okos MR (ed) Physical and chemical properties of foods. ASAE, St Joseph, MI
Clary BL, Nelson GL (1970) Determining convective heat-transfer coefficients from ellipsoidal shapes. Trans ASAE 13(3):309–314
Clary BL, Nelson GL, Smith RE (1971) The application of geometry analysis technique in determining the heat transfer rates from biological materials. Trans ASAE 14(3):586–589
Cooper DLB (1937) The application of thermal data to the calculation of sterilizing times for canned fish. J Biol Bd Can 3(2):100–107
Coulson JM, Richardson JF (1985) Chemical engineering, vol 1, Fluid flow, heat transfer and mass transfer. Pergamon Press, Oxford
Cowell ND, Evans HL (1961) Studies in canning processes. Lag factors and slopes of tangents to heat penetration curves for canned foods heated by conduction. Food Technol 15:407–412
Cox PW, Bakalis S, Ismail H, Forester R, Parker DJ, Fryer PJ (2003) Visualization of three-dimensional flows in rotating cans using positron emission particle tracking (PEPT). J Food Eng 60(3):229–240
Croft DR, Lilley DG (1977) Heat transfer calculations using finite difference equations. Applied Science Publishers, London, UK
Cuesta FJ, Lamua M (1995) Asymptotic modelling of the transient regime in heat conduction in solids with general geometry. J Food Eng 24(3):295–320
Datta AK (1985) Numerical modelling of natural convection and conduction heat transfer in canned foods with application to on-line process control. Ph.D. Thesis, Univ. Florida
Datta AK, Liu J (1992) Thermal time distributions for microwave and conventional heating of food. Food Bioprod Process, Trans IChemE 70(C2):83–90
Datta AK, Teixeira AA (1987) Numerical modeling of natural convection heating in canned liquid foods. Trans Am Soc Mech Eng 30(5):1542–1551
Datta AK, Teixeira AA (1988) Numerically predicted transient temperature and velocity profiles during natural convection heating in canned liquid foods. J Food Sci 53(1):191–195
Datta AK, Teixeira AA, Chau KV (1984) Implication of analytical heat conduction equation in thermal processing of canned foods. ASAE Paper No. 84-6518. American Society of Agricultural Engineers, St Joseph, MI
De Baerdemaeker J, Singh RP, Segerlind LJ (1977) Modelling heat transfer in foods using the finite-element method. J Food Process Eng 1:37–50
Decareau RV (ed) (1985) Microwaves in the food processing industry. Academic, Orlando, FL
Decareau RV, Peterson RA (1986) Microwave processing and engineering. Ellis Horwood, Chichester, UK
Deniston MF (1984) Heat-transfer coefficients to liquids with food particles in axially rotating cans. MS Thesis, Univ. California, Davis
Deniston MF, Hassan BH, Merson RL (1987) Heat-transfer coefficients to liquids with food particles in axially rotating cans. J Food Sci 52:962–966
Dincer I, Varlik C, Gun H (1993) Heat transfer rate variation in a canned food during sterilization. Int Commun Heat Mass Transfer 20:301–309
Duquenoy A (1980) Heat transfer to canned liquids. In: Linko P et al (eds) Food process engineering, vol 1. Applied Science Publishers, London, UK, pp 483–489
Duquenoy A (1984) Heat transfer in cans: conduction and convection. In: McKenna BM (ed) Engineering and food, vol 1. Elsevier Applied Science Publishers, London, UK, pp 209–216
Ede AJ (1967) Advances in free convection. In: Advances in heat transfer, vol 4. Academic Press, New York, pp. 1–30
Eisner M (1988) Introduction to the technique of rotary sterilization. Author, Milwaukee, WI
Engelman MS, Sani RL (1983) Finite-element simulation of an in-package pasteurization process. Numer Heat Transfer 6:41–54
Erdogdu F, Balaban MO, Chau KV (1998a) Modeling of heat conduction in elliptical cross section: 1. Development and testing of the model. J Food Eng 38(2):223–239
Erdogdu F, Balaban MO, Chau KV (1998b) Modeling of heat conduction in elliptical cross section: 2. Adaptation to thermal processing of shrimp. J Food Eng 38(2):241–258
Erdogdu F, Balaban MO, Chau KV (2001) A numerical method for conduction heat transfer in oval shapes. In: Welti-Chanes J, Barbosa-Cánovas GV, Aguilera JM (eds) Engineering and food, ICEF8, vol 2. Technomic Pub. Co., Lancaster, PA, pp 1799–1803
Erdogdu F, Turhan M (2006) Analysis of dimensionless ratios of regular geometries for infinite geometry assumptions in conduction heat transfer problems. J Food Eng 77(4):818–824
Eszes F, Rajkó R (2004) Modelling heat penetration curves in thermal processes. In: Richardson P (ed) Improving the thermal processing of food. Woodhead Publishing Ltd., Cambridge, UK, pp 307–333
Evans HL (1958) Studies in canning processes: II. Effects of the variation in temperature of the thermal properties of foods. Food Technol 12(6):276–282
Evans HL, Board PW (1954) Studies in canning processes: I. Effect of headspace on heat penetration in products heating by conduction. Food Technol 8:258–263
Evans LB, Stefany NE (1966) An experimental study of transient heat transfer to liquids in cylindrical enclosures. Chem Eng Prog Symp Ser 62(64):209–215
Evans LB, Reid RC, Drake EM (1968) Transient natural convection in a vertical cylinder. AIChE J 14:251–259
Fagan MJ (1992) Finite element analysis—theory and practice. Longman Scientific and Technical, Harlow, UK
Fernandez CL, Rao MA, Rajavasireddy SP, Sastry SK (1988) Particulate heat transfer to canned snap beans in a steritort. J Food Process Preserv 10:183–198
Flambert CMF, Deltour J (1971) Calculation of the temperatures of foods in cylindrical cans heating by conduction. Ind Alim Agric 88(9):1279–1287 (in French)
Flambert CMF, Deltour J (1973a) Calculation of the lethality of conduction heat treatments applied to food in cylindrical cans. Ind Alim Agric 90(1):5–10 (in French)
Flambert CMF, Deltour J (1973b) Exact temperature and lethality calculation for sterilizing process. In: Leniger H (ed) 1st international congress on heat and mass transfer in food processing, Wageningen, The Netherlands
Fourier JBJ (1822) Théorie analytique de la chaleur, Paris, France (English translation by A. Freeman, 1955, New York: Dover Publications Inc.)
Fujita H (1952) On a certain non-linear problem of thermal conduction in a can. Bull Jpn Soc Sci Fish 17:393–400 (in Japanese)
George RM (1990) A literature survey of the thermal diffusivity of food products. Technical Bulletin No. 73. Campden BRI, Chipping Campden, Glos, UK
George RM (1993) Making (micro)waves. Food Process 62(5):23–28
George RM, Campbell GM (1994) The use of metallic packaging to improve heating uniformity and process validation during microwave sterilization. In: Field R (ed) Food process engineering, IChemE symposium. Univ. Bath, UK, pp 219–225
Ghani AG, Farid MM, Chen XD, Richards P (1999a) Numerical simulation of natural convection heating of canned food by computational fluid dynamics. J Food Eng 41(1):55–64
Ghani AG, Farid MM, Chen XD, Richards P (1999b) An investigation of deactivation of bacteria in a canned liquid food during sterilization using computational fluid dynamics (CFD). J Food Eng 42(4):207–214
Ghani AG, Farid MM, Chen XD, Richards P (2002) Heat transfer in a 3-D pouch using computational fluid dynamics. J PHOENICS 12(3):293–305
Ghani AG, Farid MM, Chen XD, Richards P (2001a) Thermal sterilization of canned food in a 3-D pouch using computational fluid dynamics. J Food Eng 48(2):147–156
Ghani AGA, Farid MM, Chen XD, Watson C (2001b) Numerical simulation of transient twodimensional profiles of temperature and flow of liquid food in a can during sterilization. In: Welti-Chanes J, Barbosa-Cánovas GV, Aguilera JM (eds) Eighth international conference engineering and food, ICEF8, vol 2. Technomic, Lancaster, PA, pp 1832–1837
Gillespy TG (1951) Estimation of the sterilizing values of processes as applied to canned foods: I. Packs heating by conduction. J Sci Food Agric 2:107–125
Gillespy TG (1953) Estimation of the sterilizing values of processes as applied to canned foods: II. Packs heating by conduction: complex processing conditions and value of coming-up time of retort. J Sci Food Agric 4:553–565
Gouvaris AK, Scholefield J (1988) Comparisons of a computer evaluation with a standard evaluation of retort pouch thermal processing. Int J Food Sci Technol 23:601–606
Guerrei G (1993) Pasteurization of beverages: unsteady state heat transfer model and process analysis. Food Bioprod Process, Trans IChemE 71(C2):67–76
Hallström B, Skjöldebrand C, Trägärdh C (1988) Heat transfer and food products. Elsevier Applied Science, London
Hammitt FG, Chu PT (1962) Transient internal natural convection heating and cooling of closed, vertical, cylindrical vessels. Am Soc Mech Eng. Paper 62-WA-309, pp. 2–12
Hassan BH (1984) Heat-transfer coefficients from particles in liquid in axially rotating cans. Ph.D. Thesis, Univ. California, Davis
Hayakawa K (1964) Development of formulas for calculating the theoretical temperature history and sterilizing value in a cylindrical can of thermally conductive food during heating. Ph.D. Thesis, Rutgers State Univ., New Brunswick, NJ
Hayakawa K (1969) Estimating central temperatures of canned food during the initial heating and cooling period of heat process. Food Technol 23(11):1473–1477
Hayakawa K (1970) Experimental formulas for accurate estimation of transient temperature of food and their application to thermal process evaluation. Food Technol 24(12):1407–1418
Hayakawa K (1971) Estimating food temperatures during various processing or handling treatments. J Food Sci 36:378–385
Hayakawa K (1974) Response charts for estimating temperatures in cylindrical cans of solid food subjected to time variable processing temperatures. J Food Sci 39:1090–1098
Hayakawa K (1975) Roots of characteristic equations for heat conduction or mass diffusion in an infinite cylinder or sphere. Lebensm Wiss Technol 8:231–233
Hayakawa K, Ball CO (1968) A note on theoretical heating curve of a cylindrical can of thermally conductive food. Can Inst Food Sci Technol J 1(2):54–60
Hayakawa K, Ball CO (1969a) Charts for calculating average temperature of thermally conductive food in a cylindrical can during heat processing. Can Inst Food Sci Technol J 2(10):12–19
Hayakawa K, Ball CO (1969b) A note on theoretical cooling curves of a cylindrical can of thermally conductive food. Can Inst Food Sci Technol J 2(3):115–119
Hayakawa K, Ball CO (1971) Theoretical formulas for temperatures in cans of solid food and for evaluating various heat processes. J Food Sci 36(2):306–310
Hayakawa K, Giannoni-Succar EB (1996) Modified Duhamel’s theorem for variable. J Food Eng 27(2):409–422
Hayakawa K, Succar J (1983) A method for determining the apparent thermal diffusivity of spherical foods. Lebensm Wiss Technol 16:373–375
Hayakawa K, Villalobos G (1989) Formulas for estimating Smith et al. parameters to determine mass average temperature of irregular shaped bodies. J Food Process Eng 11:237–256
Hayakawa K, Giannoni-Succar EB, Huang F, Zhou L (1997) Use of empirical temperature response function for modified Duhamel’s theorem application. J Food Eng 34(3):331–353
Heldman DR, Singh RP (1980) Food process engineering. Section 3.4.6. Van Nostrand Reinhold/AVI, New York
Hendrickx M (1988) The application of transmission line matrix (TLM) modelling to food engineering. Doctoral Thesis, Univ. Leuven, Belgium
Hendrickx M, Silva C, Oliveira F, Tobback P (1993) Generalized semi-empirical formulas for optimal sterilization temperatures of conduction-heated foods with infinite surface heat-transfer coefficients. J Food Eng 19(2):141–158
Hicks EW (1951) On the evaluation of canning processes. Food Technol 5(4):132–142
Hiddink J (1975) Natural convection heating of liquids, with reference to sterilization of canned foods. Doctoral Thesis, Agric. Research Report No. 839. Agricultural University, Wageningen, Netherlands
Hiddink J, Schenk J, Bruin S (1976) Natural convection heating of liquids in closed containers. Appl Sci Res 32:217–235
Holdsworth SD, Overington WJG (1975) Calculation of the sterilizing value of food canning processes. Technical Bulletin No. 28. Campden BRI, Chipping Campden, Glos, UK
Hurwicz H, Tischer RG (1952) Heat processing of beef: I. A theoretical consideration of the distribution of temperature with time and in space during processing. Food Res 17:380–392
Ikegami Y (1977) Heat penetration in canned foods containing solids and liquid. Canners’ J 56(7):548–552
Ikegami Y (1978) Heat transfer and food surface temperature change with time. Canners’ J 57(7):593–596 (in Japanese)
Ingersoll LR, Zobel OJ, Ingersoll AC (1953) Heat conduction. Thames and Hudson, London
Iwata G (1940) Temperature–time relation for oval cans during heating. Bull Jpn Soc Sci Fish 9:117–120 (in Japanese)
Jakobsen F (1954) Notes on process evaluation. Food Res 19:66–79
Jaluria Y (1980) Natural convection heat and mass transfer. Pergamon Press, Oxford
Johns WR (1992a) Simulation of food processes with uncertain data. In: Hamm W, Holdsworth SD (eds) Food engineering in a computer climate. Institution of Chemical Engineers, Rugby, UK, pp 1–24
Johns WR (1992b) Simulation of food processes with uncertain data. Food Bioprod Process, Trans IChemE 70(C2):59–68
Jones DEA (1931) Heat penetration by convection. Food Technol (UK) 1:63–65
Jones DEA (1932) The cooling of foodstuffs. Food Technol (UK) 1:214–216
Jowitt R, Mynott AR (1974) Some factors affecting natural convective heat transfer to canned foods. Dechema Monographien 77:153–164
Kent M (1987) Electric and dielectric properties of food materials. Science and Technology Publishers, London
Kim KH, Teixeira AA (1997) Predicting internal temperature response to conduction-heating of odd-shaped solids. J Food Process Eng 20(1):51–63
Kumar A, Battacharya M (1991) Transient temperature and velocity profiles in a canned non-Newtonian liquid food during sterilization in a still-cook retort. Int J Heat Mass Transfer 34(4/5):1083–1096
Kumar A, Bhattacharya M, Blaylock J (1990) Numerical simulation of natural convection heating of canned thick viscous liquid food products. J Food Sci 55:1403–1411, 1420
Langstroth GO (1931) Thermal investigations on fish muscle. Control Can Biol Fish 6(NS):377–389
Lanoiseuille J-L, Canadau Y, Debray E (1995) Predicting internal temperature of canned foods during thermal processing using a linear recursive model. J Food Sci 60(4):833–835, 840
Larkin JW, Steffe JF (1982) Error analysis in estimating thermal diffusivity from heat penetration data. J Food Process Eng 6:135–158
Lekwauwa AN, Hayakawa K (1986) Computerized model for the prediction of thermal responses of packaged solid–liquid food mixture undergoing thermal processes. J Food Sci 51(4):1042–1049, 1056
Lenz MK, Lund DB (1977) The lethality–Fourier number method: experimental verification of a model for calculating temperature profiles and lethality in conduction-heating canned foods. J Food Sci 42(4):989–996, 1001
Lenz MK, Lund DB (1978) The lethality–Fourier number method. Heating rate variations and lethality confidence intervals for forced-convection heated foods in containers. J Food Process Eng 2(2):227–271
Leonhardt GF (1976a) Estimation of the central temperature of thermally conductive food in cylindrical and rectangular cans during heat processing. J Food Sci 41:685–690
Leonhardt GF (1976b) Estimation of the average temperature of thermally conductive food in cylindrical and rectangular cans during heat processing. J Food Sci 41:691–695
Lewis MJ (1987) Physical properties of food processing system. Ellis Horwood, Chichester, UK
Luikov AV (1968) Analytical heat diffusion theory. Academic, New York
Lund DB, Norback JP (1983) Heat transfer and selected topics. In: Saguy I (ed) Computer-aided techniques in food technology. Marcel Dekker, New York, pp 137–148
Maesmans G, Hendrickx M, DeCordt S, Fransis A, Tobback P (1992) Fluid-to-particle heat-transfer coefficient determination of heterogeneous foods: a review. J Food Process Preserv 16:29–69
Magnus W, Oberhettinger F, Soni RP (1966) Formulas and theorems for the special functions of mathematical physics. Springer, Berlin
Manson JE, Zahradnik JW, Stumbo CR (1970) Evaluation of lethality and nutrient retentions of conduction-heating food in rectangular containers. Food Technol 24(11):1297–1301
Manson JE, Stumbo CR, Zhradnik JW (1974) Evaluation of thermal processes for conduction heating foods in pear-shaped containers. J Food Sci 39:276–281
Márquez CA, De Michelis A, Salvadori VO, Mascheroni RH (1998) Application of transfer functions to the thermal processing of particulate foods enclosed in a liquid medium. J Food Eng 38(2):189–205
Masilov VA, Medvedev OK (1967) Physical constants for tomato products. Pisch Tekhnol 4:78–79 (in Russian)
McGinnis DS (1986) Prediction of transient conduction heat transfer in foods packaged in flexible retort pouches. Can Inst Food Sci Technol J 19(4):148–157
Merson RL, Stoforos NG (1990) Motion of spherical particles in axially rotating cans. Effect of liquid-particle heat transfer. In: Spiess WEL, Schubert H (eds) Engineering and food, vol 2. Elsevier Applied Science, London, pp 60–69
Merson RL, Leonard SJ, Meija E, Heil J (1981) Temperature distributions and liquid-side heat-transfer coefficients in model liquid foods in cans undergoing flame sterilization heating. J Food Process Eng 4:85–97
Merson RL, Singh RP, Carroad PA (1978) An evaluation of Ball’s formula method of thermal process calculations. Food Technol 32(3):66–76
Metaxas AC, Meredith RJ (1983) Industrial microwave heating. Peregrinus, London
Mickley HS, Sherwood TK, Reed CE (1957) Applied mathematics in chemical engineering, 2nd edn. McGraw-Hill, New York
Miglioli L, Massini R, Padrelli T, Cassara A (1983) Mechanism of heat transfer by natural convection: heating of water inside a cylindrical container. Ind Conserve 58:158–163 (in Italian)
Miles CA, van Beek G, Veerkamp CH (1983) Calculation of the thermophysical properties of foods. In: Jowitt R et al (eds) Physical properties of foods. Applied Science Publishers, London, pp 269–312
Minkowycz WJ, Sparrow EM, Schneider GE, Fletcher RH (1988) Handbook of numerical heat transfer. Wiley, New York
Mirespassi TJ (1965) Heat transfer tables for time-variable boundary temperatures in slabs. Br Chem Eng 10(11):764–769
Mohamed IO (2003) Computer simulation of food sterilization using an alternating direction implicit finite difference method. J Food Eng 60(3):301–306
Mudgett RE (1986a) Electrical properties of foods. In: Rao MA, Rizvi SSH (eds) Engineering properties of foods. Marcel Dekker, New York, pp 329–390
Mudgett RE (1986b) Microwave properties of heating characteristics of foods. Food Technol 40:84–93
Nahor HB, Scheerlinck N, Verniest R, De Baerdemaeker J, Nicolai BM (2001) Optimal experimental design for the parameter estimation of conduction heated foods. J Food Eng 48(2):109–119
Naveh D (1982) Analysis of transient conduction heat transfer in thermal processing of foods using the finite-element method. Ph.D. Thesis, Univ. of Minnesota, Minneapolis
Naveh D, Kopelman IJ (1980) Effects of some processing parameters on heat transfer coefficients in a rotating autoclave. J Food Process Preserv 4(4):67–77
Naveh D, Kopelman IJ, Pflug IJ (1983a) The finite element method in thermal processing of foods. J Food Sci 48:1086–1093
Naveh D, Kopelman IJ, Zechman L, Pflug IJ (1983b) Transient cooling of conduction heating products during sterilization: temperature histories. J Food Process Preserv 7:259–273
Newman M, Holdsworth SD (1989) Methods of thermal process calculation for food particles. Technical Memorandum No. 321 (revised). Campden BRI, Chipping Campden, Glos, UK
Nicolai BM, De Baerdemaeker J (1992) Simulation of heat transfer in foods with stochastic initial and boundary conditions. Food Bioprod Process, Trans IChemE 70(Part C):78–82
Nicolai BM, De Baerdemaeker J (1996) Sensitivity analysis with respect to the surface heat-transfer coefficient as applied to thermal process calculations. J Food Eng 28(1):21–33
Nicolaï BM, De Baerdemaeker J (1997) Finite element perturbation analysis of non-linear heat conduction problems with random field parameters. Int J Numer Methods Heat Fluid Flow 7(5):525–544
Nicolai BM, Verboven P, Sheerlinck N (2001) Modelling and simulation of thermal processes. In: Richardson P (ed) Thermal technologies in food processing. Woodhead Publishing, Cambridge, pp 92–112
Nicolaï BM, Verboven P, Scheerlinck N, De Baerdemaeker J (1998) Numerical analysis of the propagation of random parameter fluctuations in time and space during thermal processes. J Food Eng 38:259–278
Nicolai BM, Van Den Broek P, Skellekens M, De Roek G, Martens T, De Baerdemaeker J (1995) Finite element analysis of heat conduction in lasagne during thermal processing. Int J Food Sci Technol 30(3):347–363
Noh BS, Heil JR, Patino H (1986) Heat transfer study on flame pasteurization of liquids in aluminum cans. J Food Sci 51(3):715–719
Norohna J, Hendrickx M, Van Loey A, Tobback P (1995) New semi-empirical approach to handle time-variable boundary conditions during sterilization of non-conductive heating foods. J Food Eng 24(2):249–268
Ohlsson T, Bengtsson NE (1975) Dielectric food data for microwave sterilization processing. J Microw Power 10:93–108
Okada M (1940a) Cooling of canned foods. Bull Jpn Soc Sci Fish 9:64–68 (in Japanese)
Okada M (1940b) Natural convection in can-shaped space, referred to the laws of similitude. Bull Jpn Soc Sci Fish 8:325–327 (in Japanese)
Okada M (1940c) Cooling of rectangular cans of food. Bull Jpn Soc Sci Fish 9:208–213 (in Japanese)
Okos MR (ed) (1986) Physical and chemical properties of food. American Society of Agricultural Engineers, St Joseph, MI
Olivares M, Guzman JA, Solar I (1986) Thermal diffusivity of non-homogeneous food. J Food Process Preserv 10:57–67
Olson FCW (1947) Recent Japanese researches on canning technology. Food Technol 1:553–555
Olson FCW, Jackson JM (1942) Heating curves: theory and practical applications. Ind Eng Chem 34(3):337–341
Olson FCW, Schultz OT (1942) Temperature in solids during heating and cooling. Ind Eng Chem 34(7):874–877
Ozisik MN (1980) Heat conduction. International Text Book Co., Scranton, PA
Palazoglu K (2006) Influence of convection heat-transfer coefficient on the heating rate of materials with different thermal diffusivities. J Food Eng 73(3):290–296
Patkai G, Kormendy I, Erdelyi M (1990) Outline of a system for the selection of the optimum sterilization process for canned foods: Part II. The determination of heat-transfer coefficients and conductivities in some industrial equipments for canned products. Acta Alim 19(4):305–320
Paulus K, Ojo A (1974) Heat transfer during flame sterilization. In: Proceedings of the IVth congress food science and technology, vol 4, pp. 443–448
Peralta Rodriguez RD (1982) Heat transfer to simulated canned liquid foods undergoing sterilization. Ph.D. Thesis, Univ. California, Davis
Peralta Rodriguez RD (1987a) Heat transfer in flame sterilization of liquid food simulants. Technical Bulletin No. 62. Campden BRI, Chipping Campden, Glos, UK
Peralta Rodriguez RD (1987b) Microcomputer routines for calculations of Bessel functions and roots of characteristic equations for heat or mass diffusion in bodies with cylindrical geometries. Lebensm Wiss Technol 20:309–310
Peralta Rodriguez RD, Merson RL (1982) Heat transfer and chemical kinetics during flame sterilization. Food Proc Eng, AIChE Symp Ser 218(78):58–67
Peralta Rodriguez RD, Merson RL (1983) Experimental verification of a heat transfer model for simulated liquid foods undergoing flame sterilization. J Food Sci 48:726–733
Perez-Martin RI, Banga JR, Gallard JM (1990) Simulation of thermal processes in tuna can manufacture. In: Spiess WEL, Schubert H (eds) Engineering and food. Elsevier Applied Science, London, pp 848–856
Perry JH, Green M (eds) (1984) Perry’s chemical engineers’ handbook, 6th edn. McGraw-Hill, New York
Peterson WR, Adams JP (1983) Water velocity effect on heat penetration parameters during institutional size retort pouch processing. J Food Sci 49:28–31
Plazl I, Lakner M, Koloini T (2006) Modelling of temperature distributions in canned tomato based dip during industrial pasteurization. J Food Eng 75(3):400–406
Pornchaloempong P, Balaban MO, Chau KV (2001) Simulation of conduction heating in conical shapes. In: Welti-Chanes J, Barbosa-Cánovas GV, Aguilera JM (eds) Engineering and food, ICEF8, vol 1. Technomic Pub. Co., Lancaster, PA, pp 671–675
Pornchaloempong P, Balaban MO, Teixeira AA, Chau KV (2003) Numerical simulation of conduction heating in conically shaped bodies. J Food Process Eng 25:539–555
Price RB, Bhowmik SR (1994) Heat transfer in canned foods undergoing agitation. J Food Eng 23(4):621–629
Puri VM, Anantheswaran RC (1993) The finite-element method in food processing: a review. J Food Eng 19(3):247–274
Quast DG, Siozawa YY (1974) Heat transfer rates during heating of axially rotated cans. In: Proceedings of the IVth international congress food science and technology, vol 4, pp. 458–468
Quarini J, Scott G (1997) Transient natural convection in enclosures filled with non-Newtonian fluids. In: Jowitt R (ed) Engineering and food, ICEF7 Part 2, K. Sheffield Academic Press, Sheffield, UK, pp 49–53
Ramaswamy HS, Lo KV, Tung MA (1982) Simplified equations for transient temperatures in conduction foods with convective heat transfer at the surface. J Food Sci 47(6):2042–2065
Ramaswamy HS, Tung MA, Stark R (1983) A method to measure surface heat transfer from steam/air mixtures in batch retorts. J Food Sci 48:900–904
Rao MA, Anantheswaran RC (1988) Convective heat transfer in fluid foods in cans. Adv Food Res 32:39–84
Richardson PS, Holdsworth SD (1989) Mathematical modelling and control of sterilization processes. In: Field RW, Howell JA (eds) Process engineering in the food industry. Elsevier Applied Science, London, pp 169–187
Riedel L (1947) The theory of the heat sterilization of canned foods. Mitt. Kältetech. Inst. Karlsruhe, No. 1, 3–40 (in German)
Rowley AT (2001) Radio frequency heating. In: Richardson P (ed) Thermal technologies in food processing. Woodhead Publishing Ltd., Cambridge, UK, pp 163–177
Ruckenstein E (1971) Transport equations in transfer co-ordinates. Chem Eng Sci 26:1795–1802
Rumsey TR (1984) Modeling heat transfer in cans containing liquid and particulates. AMSE Paper No. 84-6515. American Society of Mechanical Engineers, St Joseph, MI
Ryynänen S (1995) The electromagnetic properties of food materials. J Food Eng 26(4):409–429
Sablani SS, Ramaswamy HS (1993) Fluid/particle heat-transfer coefficients in cans during end-over-end processing. Lebensm Wiss Technol 26(6):498–501
Sablani SS, Ramaswamy HS (1996) Particle heat-transfer coefficients under various retort operation conditions with end-over-end rotation. J Food Process Eng 19(4):403–424
Sablani SS, Ramaswamy HS (1997) Heat transfer to particles in cans with end-over-end rotation: influence of particle size and concentration (%v/v). J Food Process Eng 20(4):265–283
Sablani SS, Ramaswamy HS, Sreekanth S, Prasher SO (1997) Neural network modeling of heat transfer to liquid particle mixtures in cans subjected to end-over-end processing. Food Res Int 30(2):105–116
Sablani SS, Ramaswamy HS (1998) Multi-particle mixing behavior and its role in heat transfer during end-over-end agitation of cans. J Food Eng 38(2):141–152
Salvadori VO, Mascheroni RH, Sanz PD, Dominguez Alsonso M (1994a) Application of the z-transfer functions to multidimensional heat transfer problems. Latin Am Appl Res 24:137–147
Salvadori VO, Sanz PD, Dominguez Alsonso M, Mascheroni RH (1994b) Application of z-transfer functions to heat and mass transfer problems; their calculation by numerical methods. J Food Eng 23(3):293–307
Sastry SK (1984) Convective heat-transfer coefficients for canned mushrooms processed in still retorts. ASME Paper No. 84-6517. American Society of Mechanical Engineers, St Joseph, MI
Sastry SK, Beelman RB, Speroni JJ (1985) A three-dimensional finite element model for thermally induced changes in foods: application to degradation of agaritine in canned mushrooms. J Food Sci 50:1293–1299, 1326
Schultz OT, Olson FCW (1938) Thermal processing of canned foods in tin containers: I. Variation of heating rate with can size for products heating by convection. Food Res 3:647–651
Segerlind LJ (1984) Applied finite element analysis. Wiley, New York
Sheen S, Tong C-H, Fu Y, Lund DB (1993) Lethality of thermal processes for food in anomalous-shaped plastic containers. J Food Eng 20(3):199–213
Shiga I (1970) Temperatures in canned foods during processing. Food Preserv Q 30(3):56–58
Shin S, Bhowmik SR (1990) Computer simulation to evaluate thermal processing of food in cylindrical plastic cans. J Food Eng 12(2):117–131
Shin S, Bhowmik SR (1993) Determination of thermophysical properties of plastic cans used for thermal sterilization of foods. Lebensm Wiss Technol 26(5):476–479
Silva CLM, Hendrickx M, Oliveira F, Tobback P (1992) Optimum sterilization temperatures for conduction heating food considering finite surface heat transfer coefficients. J Food Sci 57(3):743–748
Silva CLM, Oliveira FAR, Hendrickx M (1994) Quality optimization of conduction heating foods sterilized in different packages. Int J Food Sci Technol 29:515–530
Simpson R, Almonacid S, Teixeira A (2003) Bigelow’s general method revisited: development of a new calculation technique. J Food Sci 68(4):1324–1333
Simpson R, Almonacid S, Mitchell M (2004) Mathematical model development, experimental validations and process optimization: retortable pouches packed with seafood in cone frustum shape. J Food Eng 63(2):153–162
Simpson R, Aris I, Torres JA (1989) Sterilization of conduction heated foods in oval-shaped containers. J Food Sci 54(5):1327–1331, 1363
Singh RP (1982) Thermal diffusivity in thermal processing. Food Technol 36(2):87–91
Singh RP, Segerlind LJ (1974) The finite element method in food engineering. ASAE Paper No. 74-6015. American Society of Agricultural Engineers, St Joseph, MI
Skinner RH (1979) The linear second-order system as an empirical model of can-centre temperature history. In: Proceedings of the international meeting food microbiology and technology, Parma, Italy, pp. 309–322
Smith GD (1974) Numerical solution of partial differential equations. Oxford University Press, London
Smith RE (1966) Analysis of transient heat transfer from anomalous shapes with heterogeneous properties. Ph.D. Thesis, Oklahoma State Univ., Stillwater
Smith RE, Nelson GL, Henrickson RL (1967) Analyses on transient heat transfer from anomalous shapes. Trans ASAE 10(2):236–245
Smith RE, Nelson GL, Henrickson RL (1968) Applications of geometry analysis of anomalous shapes to problems in transient heat transfer. Trans ASAE 11(2):296–303
Soule CL, Merson RL (1985) Heat-transfer coefficients to Newtonian liquids in axially rotated cans. J Food Process Eng 8(1):33–46
Stevens PM (1972) Lethality calculations, including effects of product movement, for convection heating and for broken-heating foods in still-cook retorts. Ph.D. Thesis, Univ. Massachusetts, Amherst
Stoforos NG (1988) Heat transfer in axially rotating canned liquid/particulate food systems. Ph.D. Thesis, Dept. Agric. Eng., Univ. California, Davis
Stoforos NG, Merson RL (1990) Estimating heat-transfer coefficients in liquid/particulate canned foods using only liquid temperature data. J Food Sci 55(2):478–483
Stoforos NG, Merson RL (1991) Measurements of heat-transfer coefficients in rotating liquid/particle systems. Biotechnol Prog 7:267–271
Stoforos NG, Merson RL (1992) Physical property and rotational speed effects on heat transfer in axially rotating liquid/particle canned foods. J Food Sci 57(3):749–754
Stoforos NG, Merson RL (1995) A solution to the equations governing heat transfer in agitating liquid/particle canned foods. J Food Process Eng 18(2):165–186
Stoforos NG, Noronha J, Hendrickx M, Tobback P (1997) Inverse superposition for calculating food product temperatures during in-container thermal processing. J Food Sci 62(2):219–224, 248
Taggert R, Farrow FD (1941) Heat penetration into canned foods. Part 1. Food 16:325–330
Taggert R, Farrow FD (1942) Heat penetration into canned foods. Part 2. Food 17:13–17
Tan C-S, Ling AC (1988) Effect of non-uniform heat transfer through can surfaces on process lethality of conduction heating foods. Can Inst Food Sci J 21(4):378–385
Tani S (1938a) Heat conduction in canned foods. Bull Jpn Soc Sci Fish 8:79–83 (in Japanese)
Tani S (1938b) Natural convection in can-shaped space. Bull Jpn Soc Sci Fish 8:76–78 (in Japanese)
Tatom JW, Carlson WO (1966) Transient turbulent free convection in closed containers. In: Proceedings of the 3rd international heat transfer conference (ASME), vol 2, pp. 163–171
Tattiyakul J, Rao MA, Datta AK (2001) Simulation of heat transfer to a canned corn starch dispersion subjected to axial rotation. Chem Eng Process 40:391–399
Tattiyakul J, Rao MA, Datta AK (2002a) Heat transfer to a canned starch dispersion under intermittent agitation. J Food Eng 54(4):321–329
Tattiyakul J, Rao MA, Datta AK (2002b) Heat transfer to three canned fluids of different thermo-rheological behaviour under intermittent agitation. Food Bioprod Process, Trans IChemE 80(C1):20–27
Teixeira AA, Dixon JR, Zahradnik JW, Zinsmeister GE (1969) Computer determination of spore survival distributions in the thermal processing of conduction-heated foods. Food Technol 23(3):352–354
Teixeira AA, Tucker GS, Balaban MO, Bichier J (1992) Innovations in conduction-heating models for on-line retort control of canned foods with any j-value. In: Singh R, Wirakartakusumah MA (eds) Advances in food engineering. CRC Press, Boca Raton, FL, pp 293–308
Teixeira Neto RO (1982) Heat transfer rates to liquid foods during flame-sterilization. J Food Sci 47:476–481
Thijssen HAC, Kochen LHPJM (1980) Short-cut method for the calculation of sterilizing conditions for packed foods yielding optimum quality retention at variable temperature of heating and cooling medium. In: Food process engineering, vol 1. Applied Science Publishers, London, pp 122–136
Thijssen HAC, Kerkhoff PJAM, Liefkens AAA (1978) Short-cut method for the calculation of sterilization conditions yielding optimum quality retention for conduction-type heating of packaged foods. J Food Sci 43(4):1096–1101
Thompson GE (1919) Temperature-time relations in canned foods during sterilization. J Ind Eng Chem 11:657–664
Thompson GE (1922) Heat flow in a finite cylinder having variable surface geometry. Phys Rev (2nd Series) 20:601–606
Thorne S (1989) Computer prediction of temperatures in solid foods during heating or cooling. In: Thorne S (ed) Developments in food preservation. Applied Science Publishers, London, pp 305–324
Thorpe RH, Atherton D (1969) Processing studies on canned new potatoes. In: Woodman J (ed) Potatoes for canning, AMDEC annual progress report 1969. Campden BRI, Chipping, Glos, UK
Tucker G, Badley E (1990) CTemp: Centre temperature prediction program for heat sterilization processes (user’s guide). Campden BRI, Chipping Campden, Glos, UK
Tucker G, Clark P (1989) Computer modelling for the control of sterilization processes. Technical Memorandum No. 529. Campden BRI, Chipping Campden, Glos, UK
Tucker G, Clark P (1990) Modelling the cooling phase of heat sterilization processes using heat-transfer coefficients. Int J Food Sci Technol 25(6):668–681
Tucker GS, Holdsworth SD (1991a) Optimization of quality factors for foods thermally processed in rectangular containers. Technical Memorandum No. 627. Campden BRI, Chipping, Glos, UK
Tucker GS, Holdsworth SD (1991b) Mathematical modelling of sterilization and cooking process for heat preserved foods—application of a new heat transfer model. Food Bioprod Process, Trans IChemE 69(Cl):5–12
Tucker GS, Kassim HO, Johns WR, Best RJ (1992) Zone modelling: Part I—application to thermal processing of homogeneous material in simpsl geometry, Technical Memo. No. 654. Campden and Chorleywood Food Research Association, Chipping Campden, UK
Tung MA, Morello GF, Ramaswamy HS (1989) Food properties, heat transfer conditions and sterilization considerations in retort processes. In: Singh RP, Medina AG (eds) Food properties and computer-aided engineering of food processing systems. Kluwer Academic Publishers, New York, pp 49–71
Turhan M, Erdogdu F (2003) Error associated with assuming a finite regular geometry as an infinite one for modeling of transient heat and mass transfer processes. J Food Eng 59(2/3):291–296
Turhan M, Erdogdu F (2004) Errors based on location and volume average changes in infinite geometry assumptions in heat and mass transfer processes. J Food Eng 64(2):199–206
Uno J, Hayakawa K (1979) Nonsymmetric heat conduction in an infinite slab. J Food Sci 44(2):396–403
Uno J, Hayakawa K (1980) A method for estimating thermal diffusivity of heat conduction food in a cylindrical can. J Food Sci 45:692–695
Varma MN, Kannan A (2006) CFD studies on natural convection heating of canned foods in conical and cylindrical containers. J Food Sci 45:692–695
Verboven P, De Baerdemaeker J, Nicolaï BM (2004) Using computational fluid dynamics to optimise thermal processes. In: Richardson P (ed) Improving the thermal processing of foods. Woodhead Publishing, Cambridge, UK, pp 82–102
Videv K (1972) Mathematical model of the sterilization process of canned foods during convection heating. Doctoral Thesis, Institute of Food and Flavour Industries, Plovdiv, Bulgaria (in Bulgarian)
Wadsworth JI, Spardaro JJ (1970) Transient temperature distribution in whole sweet potato roots during immersion heating. Food Technol 24(8):913–928
Wang PY, Draudt HN, Heldman DR (1972) Temperature histories of conduction-heating foods exposed to step changes in ambient temperatures. Trans ASAE 15(6):1165–1167
Wang Y, Lau MH, Tang G, Mao R (2004) Kinetics of chemical marker M-1 formation in whey protein gels for developing sterilization processes based on dielectric heating. J Food Eng 64(1):111–118
Welt BA, Teixeira AA, Chau KV, Balaban MO, Hintenlang DE (1997) Explicit finite difference methods of heat transfer simulation and thermal process design. J Food Sci 62(2):230–236
Williamson ED, Adams LH (1919) Temperature distribution in solids during heating and cooling. Phys Rev (2nd series) 14(2):99–114
Yang WH, Rao MA (1998) Transient natural convection heat transfer to starch dispersion in a cylindrical container: numerical solution and result. J Food Eng 36(4):395–415
Zechman LG (1983) Natural convection heating of liquids in metal containers. MS Thesis, Univ. Minnesota, Minneapolis
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Holdsworth, S.D., Simpson, R. (2016). Heat Transfer. In: Thermal Processing of Packaged Foods. Food Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-319-24904-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-24904-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24902-5
Online ISBN: 978-3-319-24904-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)