Determination of heat transfer coefficients of foods.Abstract Cooling and freezing of food by forced convection is one of the most significant applications of industrial refrigeration refrigeration, process for drawing heat from substances to lower their temperature, often for purposes of preservation. Refrigeration in its modern, portable form also depends on insulating materials that are thin yet effective. . In order for cooling and freezing operations to be cost-effective, it is necessary to optimally design the refrigeration equipment. This requires estimation of the cooling and freezing times of foods and the corresponding refrigeration loads. These estimates, in turn, depend upon the surface heat transfer coefficient The heat transfer coefficient is used in calculating the convection heat transfer between a moving fluid and a solid in thermodynamics. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). for the cooling or freezing operation. This paper describes a study which was initiated to resolve deficiencies in heat transfer coefficient data for food cooling and freezing processes by forced convection. Members of the food refrigeration industry were contacted to collect cooling and freezing curves as well as surface heat transfer data. A unique iterative it·er·a·tive adj. 1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness. 2. Grammar Frequentative. Noun 1. algorithm was developed to estimate the surface heat transfer coefficients of foods based upon their cooling and freezing curves. Making use of this algorithm, heat transfer coefficients for various food items were calculated from the cooling and freezing curves collected during the industrial survey. Nusselt, Prandtl and Reynolds numbers Reynolds number [for Osborne Reynolds], dimensionless quantity associated with the smoothness of flow of a fluid. It is an important quantity used in aerodynamics and hydraulics. were determined for the various food items, based upon their flowfield parameters, product dimensions and calculated heat transfer coefficients. Heat transfer coefficient correlations for various foods items were then developed, based upon these dimensionless parameters. These correlations are important in the design and operation of food cooling and freezing facilities and will be of immediate usefulness to engineers involved in the design and operation of such systems. Keywords: Heat transfer coefficient; food; refrigeration. 1. Introduction Preservation of food is one of the most significant applications of refrigeration. Cooling and freezing of food effectively reduce the activity of microorganisms and enzymes, thus retarding deterioration de·te·ri·o·ra·tion n. The process or condition of becoming worse. . Furthermore, crystallization Crystallization The formation of a solid from a solution, melt, vapor, or a different solid phase. Crystallization from solution is an important industrial operation because of the large number of materials marketed as crystalline particles. of water reduces the amount of liquid water in food items and inhibits microbial microbial pertaining to or emanating from a microbe. microbial digestion the breakdown of organic material, especially feedstuffs, by microbial organisms. growth (Heldman, 1975). Optimally designed refrigeration equipment is required to maximize the efficiency of food cooling and freezing operations. In addition, it is necessary that the refrigeration equipment fits the specific requirements of the particular cooling or freezing application. The design of food refrigeration equipment requires estimation of the cooling and freezing times of foods, as well as the corresponding refrigeration loads. The accuracy of these estimates, in turn, depends upon accurate estimates of the surface heat transfer coefficient for the forced convective cooling or freezing operation. a. Heat Transfer during Cooling and Freezing of Foods In many food-processing applications, including cooling and freezing, forced convective heat transfer Convective heat transfer is a mechanism of heat transfer occurring because of bulk motion (observable movement) of fluids. This can be contrasted with conductive heat transfer, which is the transfer of energy molecule by molecule through a solid or fluid, and radiative heat occurs between a fluid medium and the solid food item (Dincer, 1993). Knowledge of the surface heat transfer coefficient is required to accurately design equipment in which forced convection heat transfer is used to process foods. Newton's law Noun 1. Newton's law - one of three basic laws of classical mechanics law of motion, Newton's law of motion law of nature, law - a generalization that describes recurring facts or events in nature; "the laws of thermodynamics" of cooling defines the surface heat transfer coefficient, h, as follows: q = hA ([t.sub.s] - [t.sub.m]) (1) where q is the heat transfer rate, t is the surface temperature of the food, [t.sub.m] is the surrounding fluid temperature and A is the surface area of the food through which the heat transfer occurs. During a convective heat transfer process, energy is theoretically transferred by convection alone. However, in practice, conduction conduction, transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity. , radiation and mass transfer may also occur at the same time. In blast cooling/freezing operations, the conductive heat conductive heat n. Heat transmitted to the body by direct contact, as by an electric pad. transfer component is very small and can be neglected. The significance of the radiation heat transfer and evaporative cooling Evaporative cooling is a physical phenomenon in which evaporation of a liquid, typically into surrounding air, cools an object or a liquid in contact with it. Latent heat describes the amount of heat that is needed to evaporate the liquid; this heat comes from the liquid itself and due to mass transfer must be considered on an individual basis and their effects upon the surface heat transfer coefficient must be properly incorporated. Researchers often define an "effective" heat transfer coefficient, which includes the effects of convection and radiation heat transfer, as well as the energy transfer due to evaporation evaporation, change of a liquid into vapor at any temperature below its boiling point. For example, water, when placed in a shallow open container exposed to air, gradually disappears, evaporating at a rate that depends on the amount of surface exposed, the humidity of moisture from the surface of the food item (Lind, 1988). However, this paper focuses upon those cooling/freezing operations which are dominated by forced convective heat transfer and the resultant heat transfer coefficients do not account for conduction, radiation or latent heat latent heat, heat change associated with a change of state or phase (see states of matter). Latent heat, also called heat of transformation, is the heat given up or absorbed by a unit mass of a substance as it changes from a solid to a liquid, from a liquid to a gas, transfer. A detailed literature survey and discussion regarding heat transfer coefficients for foods is given by Arce and Sweat (1980). Since then, additional studies have been performed to measure or estimate the surface heat transfer coefficient during cooling, freezing or heating of food items (Alhamdan et al., 1990; Ansari, 1987; Chen et al., 1997; Daudin and Swain, 1990; Dincer, 1991, 1993, 1994a, 1994b, 1994c, 1995a, 1995b, 1995c, 1995d, 1996, 1997; Dincer et al., 1992; Dincer and Genceli, 1994, 1995a, 1995b; Dincer and Dost, 1996; Flores Flores, town, Guatemala Flores (flōrəs), town (1990 est. pop. 2,200), capital of Petén department, N Guatemala. Flores was built on an island in the southern part of Lake Petén Itzá and on the site of the and Mascheroni, 1988; Frederick and Comunian, 1994; Khairullah and Singh, 1991; Kondjoyan and Daudin, 1997; Mankad et al., 1997; Stewart et al., 1990; Vazquez and Calvelo, 1980, 1983; Verboven et al., 1997; Zuritz et al., 1990). However, collectively, these studies present surface heat transfer coefficient data and correlations for only a very limited number of food items and process conditions. Therefore, the objective of this study was to determine the surface heat transfer coefficients for a wide variety of foods during forced convective cooling and freezing processes. b. Determination of Heat Transfer Coefficients Techniques used to determine heat transfer coefficients generally fall into three categories: 1. Steady-state temperature measurement methods 2. Transient temperature measurement methods 3. Surface heat flux flux In metallurgy, any substance introduced in the smelting of ores to promote fluidity and to remove objectionable impurities in the form of slag. Limestone is commonly used for this purpose in smelting iron ores. measurement methods Of these three techniques, the most popular method is the transient temperature measurement technique, in which the heat transfer coefficient is determined by measuring product temperature with respect to time during a cooling or freezing process. All cooling processes exhibit similar behavior. After an initial "lag", the temperature at the thermal center of the food item decreases exponentially ex·po·nen·tial adj. 1. Of or relating to an exponent. 2. Mathematics a. Containing, involving, or expressed as an exponent. b. (Cleland, 1990). A cooling curve A cooling curve is a line graph that represents the change of of matter, typically from either a gas to a solid or a liquid to a solid. Time is used in the x-axis while temperature is used for the y-axis. , shown in Figure 1, depicting this behavior can be obtained by plotting, on semi logarithmic logarithmic pertaining to logarithm. logarithmic relationship when the logs of two variables plotted against each other create a straight line. axes axes [L., Gr.] plural of axis. The straight lines which intersect at right angles and on which graphs are drawn. Usually the horizontal axis is the x-axis and the vertical one the y-axis. Called also axes of reference. , the fractional fractional size expressed as a relative part of a unit. fractional catabolic rate the percentage of an available pool of body component, e.g. protein, iron, which is replaced, transferred or lost per unit of time. unaccomplished un·ac·com·plished adj. 1. Not completed or done; unfinished. 2. Lacking special skills or abilities; unpolished, as in the social graces. temperature difference versus time. The fractional unaccomplished temperature difference, Y, is defined as follows: where [t.sub.m] is the cooling medium temperature, t is the product temperature and [t.sub.i] is the initial temperature of the product. [FIGURE 1 OMITTED] Y = [t.sub.m] - t / [t.sub.m] - [t.sub.i] = t - [t.sub.m] / [t.sub.i] - [t.sub.m] (2) This semi logarithmic temperature history curve consists of one initial curvilinear curvilinear a line appearing as a curve; nonlinear. curvilinear regression see curvilinear regression. portion, followed by one or more linear portions. Simple empirical formulae, which model this cooling behavior, have been proposed for estimating the cooling time (Law) such a lapse of time as ought, taking all the circumstances of the case in view, to produce a subsiding of passion previously provoked. - Wharton. See also: Cooling of foods and beverages. These models incorporate two factors, f and j, which represent the slope and intercept intercept in mathematical terms the points at which a curve cuts the two axes of a graph. , respectively, of the temperature history curve. As shown in Figure 1, the j factor is a measure of the "lag" between the onset of cooling and the exponential 1. (mathematics) exponential - A function which raises some given constant (the "base") to the power of its argument. I.e. f x = b^x If no base is specified, e, the base of natural logarthims, is assumed. 2. decrease in the temperature of the food. The f factor represents the time required to obtain a 90% reduction in the non-dimensional temperature difference. Graphically, the f factor corresponds to the time required for the linear portion of the temperature history curve to pass through one log cycle. The f factor is a function of the Biot number The Biot number (Bi) is a dimensionless number used in unsteady-state (or transient) heat transfer calculations. It is named after the French physicist Jean-Baptiste Biot (1774-1862), and relates the heat transfer resistance inside and at the surface of a body. while the j factor is a function of the Biot number and the location within the food item. The general form of the cooling time model is: where [theta Theta A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option. ] is the cooling time. In addition, the slope of the linear portion of the cooling curve, C, can be written in terms of the f factor: Y = [t.sub.m] - t/[t.sub.m] - [t.sub.i] = j exp exp abbr. 1. exponent 2. exponential (-2.303[theta]/f) (3) For simple geometrical shapes, such as infinite slabs, infinite circular cylinders and spheres, infinite series infinite series In mathematics, the sum of infinitely many numbers, whose relationship can typically be expressed as a formula or a function. An infinite series that results in a finite sum is said to converge (see convergence). One that does not, diverges. solutions for cooling or freezing time may be derived from the one-dimensional transient heat equation (Carslaw and Jaeger jaeger (yā`gər), common name for several members of the family Stercorariidae, member of a family of hawklike sea birds closely related to the gull and the tern. The skua is also a member of this family. , 1980). After the initial "lag" period has passed, the second and higher terms of the infinite series solution are assumed to be negligible (Dincer and Dost, 1996). C = 2.303/f (4) The iterative technique developed in this paper for determining the heat transfer coefficients of irregularly shaped food items is based on the first-term solution for the dimensionless center temperature of a sphere, given as: Y = 2Bi sin [[mu].sub.1]/[[mu].sub.1] - sin [[mu].sub.1] cos [[mu].sub.1] exp (-[[mu].sup.2.sub.1]Fo) (5) where Bi is the Biot number: Bi = hd/k in which d is the shortest dimension of the food item and k is the thermal conductivity thermal conductivity A measure of the ability of a material to transfer heat. Given two surfaces on either side of the material with a temperature difference between them, the thermal conductivity is the heat energy transferred per unit time and per unit of the food item, and Fo is the Fourier number In physics and engineering, the Fourier number (Fo) or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes heat conduction. Conceptually, it is the ratio of the heat conduction rate to the rate of thermal energy storage. : Fo = [alpha][theta]/[d.sup.2] (7) where a is the thermal diffusivity In heat transfer analysis, thermal diffusivity (symbol:  ) is the ratio of thermal conductivity to volumetric heat capacity.By comparing Equations (3), (4), and (5), it can be seen that: cot [[mu].sub.1 = 1 - Bi/[[mu].sub.1] (8) -C[theta] = -[[mu].sup.2.sub.1]Fo (9) Since the Fourier number, Fo, of a cooling process can be readily determined, and, provided that the value of C can be determined from a cooling curve, the value of [[mu].sub.1] can be obtained by rearranging Equation (9): [[mu].sub.1] = [square root of (C[theta]/Fo)] (10) Then, the Biot number, Bi, can be obtained from Equation (8) and the surface heat transfer coefficient, h, may be obtained through algebraic 1. (language) ALGEBRAIC - An early system on MIT's Whirlwind. [CACM 2(5):16 (May 1959)]. 2. (theory) algebraic - In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements. manipulation of the definition of the Biot number, Equation (6). Since the analytical method described thus far is only applicable to spherical spher·i·cal adj. Having the shape of or approximating a sphere; globular. food items, an iterative technique was developed to handle irregular shaped food items. This iterative technique utilizes a shape factor, called the "equivalent heat transfer dimensionality," to extend the analytical method to irregularly shaped food items (Cleland and Earle, 1982; Lin et al., 1993, 1996a, 1996b). This "equivalent heat transfer dimensionality," E, compares the total heat transfer to the heat transfer through the shortest dimension. The "equivalent heat transfer dimensionality," E, is used to modify the analytical solution of heat conduction Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. in a sphere, Equation (5), as follows: Y = 2Bi sin [[mu].sub.1]/[[mu].sub.1] - sin [[mu].sub.1] cos [[mu].sub.1]exp(-[[mu].sup.2.sub.1] Fo E/3) (11) resulting in the following modification to Equation (10): [[mu].sub.1] = [square root of (C[theta]/Fo 3/E)] (12) Lin et al. (1993, 1996a, 1996b) present equations for determining the equivalent heat transfer dimensionality, E, as a function of Biot number and shape of the food item (short cylinder, squat cylinder, rectangular rod, ellipsoid, etc.). Values of E range from 1.0 to 3.0, with E = 3.0 being the equivalent heat transfer dimensionality of a sphere. Thus for a sphere, Equations (11) and (12) reduce to Equations (5) and (10). To determine the heat transfer coefficient of irregularly shaped food items, a value of [[mu].sub.1] is obtained via Equation (12) by assuming a value for the equivalent heat transfer dimensionality, E. Then, the Biot number can be calculated from Equation (8). From the Biot number, the equivalent heat transfer dimensionality can be obtained using the equations of Lin et al. (1993, 1996a, 1996b). The value of [[mu].sub.1] is then recalculated via Equation (12), using the updated value of equivalent heat transfer dimensionality. This process is repeated until the value of the Biot number converges. Finally, the heat transfer coefficient, h, may be determined through algebraic manipulation of the definition of the Biot number, Equation (6). c. Cooling and Freezing Curve Database Members of the food refrigeration industry were contacted to collect cooling and freezing curves as well as surface heat transfer data for various food items. These contacts included food refrigeration equipment manufacturers, designers of food refrigeration plants A refrigeration plant uses gas, liquid, and mechanical energy to move heat from one place to another. A liquid, such as ammonia, which has a low boiling temperature is allowed to pass into a space via tubing. , and food processors. An effort was made to collect information on as many food items as possible. A total of 777 cooling and freezing curves for various food items were collected from the industrial survey. These cooling and freezing curves were determined through the use of thermocouples imbedded imbedded, adj See embedded. within the food items. Cooling and freezing curves were collected for food items in the following categories: 1. Diary: cheese, cream and ice cream 2. Prepared Foods: entrees, croquettes, pasties past·ies pl.n. A pair of adhesive patches used to conceal a woman's nipples and worn principally by exotic dancers or striptease performers. [From paste1.] , pizza, sandwiches, soup 3. Poultry: whole and portions of chicken and turkey 4. Fruit/Vegetable 5. Fish/Seafood: various fish fillets, fish sticks, shrimp, scallops, squid 6. Bakery Products: raw dough, bread, rolls, cakes, pies and pastries 7. Meat: beef, lamb, pork and sausage sausage, food consisting of finely chopped meat mixed with seasonings and, often, other ingredients, all encased in a thin membrane. Although sausages were made by the ancient Greeks and Romans, they were usually plain and unspiced; in the Middle Ages people began to 8. Beverages 9. Miscellaneous The collected cooling and freezing curves were digitized and a database was developed which contains the digitized time-temperature data obtained from these curves. The temperatures were non-dimensionalized and the natural logarithms Natural logarithm Logarithm to the base e (approximately 2.7183). of these non-dimensional temperatures were taken. The slopes of the linear portion(s) of the logarithmic temperature versus time data were determined using the linear least-squares-fit technique. d. Calculated Heat Transfer Coefficients The slopes of the logarithmic cooling curves, in conjunction with the iterative algorithm described previously, were used to determine the heat transfer coefficients for the food items. A sample of the calculated heat transfer coefficients for pizza is presented in Table 1. Table 1 shows the calculated heat transfer coefficient along with food dimensions, mass, air temperature, air velocity with direction and packing description. e. Heat Transfer Coefficient Correlations For those food items having a significant amount of heat transfer coefficient data, non-dimensional analyses were performed to obtain simple heat transfer coefficient correlations which can be used to predict the heat transfer coefficients of those food items. The Nusselt number The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface that occurs in a 'real' situation, compared to the heat transferred if just conduction occurred. , Nu, a non-dimensional heat transfer coefficient, is defined as follows: Nu = hd/[k.sub.m] (13) where [k.sub.m] is the thermal conductivity of the cooling medium. Physical reasoning indicates a dependence of the heat transfer process on the flow field, and hence on the Reynolds number. The Reynolds number, Re, is defined as follows: Re = [[rho].sub.m]Ud/[[mu].sub.m] (14) where U is the free stream velocity of the cooling medium, [[rho.sub.m] is the density of the cooling medium and [[mu].sub.m] is the dynamic viscosity dynamic viscosity n. Symbol  A measure of the molecular frictional resistance of a fluid as calculated using Newton's law. of the cooling medium.
The relative rates of diffusion diffusion, in chemistry, the spontaneous migration of substances from regions where their concentration is high to regions where their concentration is low. Diffusion is important in many life processes. of heat and momentum are related by the Prandtl number The Prandtl number is a dimensionless number approximating the ratio of momentum diffusivity (viscosity) and thermal diffusivity. It is named after Ludwig Prandtl. It is defined as: Pr = [[mu].sub.m][c.sub.m]/[k.sub.m] (15) where cm is the specific heat capacity of the cooling medium. Previous experimental and analytical work has shown that an exponential function exponential function In mathematics, a function in which a constant base is raised to a variable power. Exponential functions are used to model changes in population size, in the spread of diseases, and in the growth of investments. is perhaps the simplest type of relation to use (Holman, 1990): Nu = c x [Re.sup.m] x [Pr.sup.n] (16) where c, m and n are constants to be determined from experimental data. Using the Data Analysis ToolPak available in Microsoft Excel (tool) Microsoft Excel - A spreadsheet program from Microsoft, part of their Microsoft Office suite of productivity tools for Microsoft Windows and Macintosh. Excel is probably the most widely used spreadsheet in the world. Latest version: Excel 97, as of 1997-01-14. , a non-linear fit was performed on Nusselt, Reynolds and Prandtl number data to obtain heat transfer coefficient correlations in the form given by Equation (16). The resulting Nusselt-Reynolds-Prandtl correlations for cake, chicken breast and pizza are summarized in Table 2 and plotted in Figures 2 through 4. Table 2 also gives the level of significance, F-statistic, and the coefficient of determination Coefficient of determination A measure of the goodness of fit of the relationship between the dependent and independent variables in a regression analysis; for instance, the percentage of variation in the return of an asset explained by the market portfolio return. Also known as R-square. , [r.sup.2], for the correlations. Generally, a significance level less than 0.05 indicates that the correlation represents the data significantly better than the mean. The coefficient of determination, [r.sup.2], indicates the proportion of variation in log(Nu x [Pr.sup.-0.3]) explained by the variation in log(Re). [FIGURES 2-4 OMITTED] 2. Conclusion This paper described a study which was initiated to resolve deficiencies in heat transfer coefficient data for food cooling and freezing processes by forced convection. An algorithm was developed to estimate the surface heat transfer coefficients of foods based upon their cooling and freezing curves. Making use of this algorithm, heat transfer coefficients for various food items were calculated from the cooling and freezing curves collected during the industrial survey. In addition, non-dimensional analysis was performed on the calculated heat transfer coefficient data to obtain Nusselt-Reynolds-Prandtl correlations. The data and correlations resulting from this project will be used by designers of cooling and freezing systems for foods and beverages. This information will make possible a more accurate determination of cooling and freezing times and corresponding refrigeration loads. Such information is important in the design and operation of cooling and freezing facilities and will be of immediate usefulness to engineers involved in the design and operation of such systems. Nomenclature nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc. binomial nomenclature A surface area Bi Biot number C cooling coefficient [c.sub.m] specific heat of the cooling medium d smallest dimension of the food item E equivalent heat transfer dimensionality f cooling time parameter Fo Fourier number h heat transfer coefficient j cooling time parameter k thermal conductivity [k.sub.m] thermal conductivity of the cooling medium Nu Nusselt number Pr Prandtl number q heat transfer rate Re Reynolds number t product temperature [t.sub.i] initial product temperature [t.sub.m] cooling medium temperature [t.sub.s] surface temperature of the food U free stream velocity of the cooling medium Y fractional unaccomplished temperature difference [alpha] thermal diffusivity of the food item [theta] cooling time [[mu].sub.1] characteristic parameter [[mu].sub.m] dynamic viscosity of the cooling medium [[rho].sub.m] density of the cooling medium References Alhamdan, A., S.K. 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Heat and Mass Transfer Coefficients In engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration gradient as driving force:[1] at the Surface of a Pork Hindquarter hindquarter the rump and legs, i.e. the loin, pelvis, pelvic limb and associated musculature. asymmetric hindquarter see asymmetric hind quarter syndrome. . Journal of Food Engineering 32(2): 225-240. Lin, Z., A.C. Cleland, G.F. Serrallach, and D.J. Cleland. 1993. Prediction of Chilling Times for Objects of Regular Multi-Dimensional Shapes Using a General Geometric Factor. Refrigeration Science and Technology 1993-3: 259-267. Lin, Z., A.C. Cleland, D.J. Cleland, and G.F. Serrallach. 1996a. A Simple Method for Prediction of Chilling Times for Objects of Two-Dimensional Irregular Shape. International Journal of Refrigeration 19(2): 95-106. Lin, Z., A.C. Cleland, D.J. Cleland, and G.F. Serrallach. 1996b. A Simple Method for Prediction of Chilling Times: Extension to Three-Dimensional Irregular Shapes. International Journal of Refrigeration 19(2): 107-114. Lind, I. 1988. Surface Heat Transfer in Thawing by Forced Air Convection. Journal of Food Engineering 7: 19-39. Mankad, S., K.M. Nixon, and P.J. Fryer. 1997. Measurements of Particle-Liquid Heat Transfer in Systems of Varied Solids Fraction. Journal of Food Engineering 31(1): 9-33. Microsoft Corporation (company) Microsoft Corporation - The biggest supplier of operating systems and other software for IBM PC compatibles. Software products include MS-DOS, Microsoft Windows, Windows NT, Microsoft Access, LAN Manager, MS Client, SQL Server, Open Data Base Connectivity (ODBC), MS Mail, . 2001. Excel 2002. Redmond, WA. Stewart, W.E., B.R. Becker, M.E. Greer, and L.A. Stickler stick·ler n. 1. One who insists on something unyieldingly: a stickler for neatness. 2. Something puzzling or difficult. . 1990. An Experimental Method of Approximating Effective Heat Transfer Coefficients for Food Products. ASHRAE Transactions 96(2): 142-147. Vazquez, A., and A. Calvelo. 1980. Gas Particle Heat Transfer Coefficient in Fluidized Pea Beds. Journal of Food Process Engineering 4(1): 53-70. Vazquez, A., and A. Calvelo. 1983. Gas-Particle Heat Transfer Coefficient for the Fluidization Fluidization The processing technique employing a suspension or fluidization of small solid particles in a vertically rising stream of fluid—usually gas—so that fluid and solid come into intimate contact. of Different Shaped Foods. Journal of Food Science 48(1): 114-118. Verboven, P., B.M. Nicolai, N. Scheerlink, and J. De Baerdemaeker. 1997. The Local Surface Heat Transfer Coefficient in Thermal Food Process Calculations: A CFD CFD - Computational Fluid Dynamics Approach. Journal of Food Engineering 33(1): 15-35. Zuritz, C.A., S.C. McCoy, and S.K. Sastry. 1990. Convective Heat Transfer Coefficients for Irregular Particles Immersed im·merse tr.v. im·mersed, im·mers·ing, im·mers·es 1. To cover completely in a liquid; submerge. 2. To baptize by submerging in water. 3. in Non-Newtonian Fluid During Tube Flow. Journal of Food Engineering 11 (2): 159-174 Brian A. Fricke, Ph.D., Deep Bandyopadhyay, Arun K. Ranjan, Mark F. McClernon, Ph.D., P.E., Bryan R. Becket beck·et n. Nautical A device, such as a looped rope, hook and eye, strap, or grommet, used to hold or fasten loose ropes, spars, or oars in position. [Origin unknown.] Noun 1. , Ph.D., P.E. Civil and Mechanical Engineering Division University of Missouri--Kansas City 5100 Rockhill Road Kansas City Kansas City, two adjacent cities of the same name, one (1990 pop. 149,767), seat of Wyandotte co., NE Kansas (inc. 1859), the other (1990 pop. 435,146), Clay, Jackson, and Platte counties, NW Mo. (inc. 1850). , MO 64110-2499 U.S.A.
Table 1. Calculated Heat Transfer Coefficients for Pizza.
Heat
Transfer Length,
Description Coefficient, m
W/([m.sup.2]
x K)
Pizza 12.8 0.24
Pizza, Box of 6 pieces, 4 2.9 0.178
oz./piece
Pizza with Topping, 12
inch Diameter, On 12.7
Cardboard
Pizza, Canadian Bacon, 12 11.5
inch Diameter
Pizza, Ham and Pineapple, 7.6
16 inch Diameter
Pizza, Sausage and Cheese, 12.1
Round, No Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 13.7 0.406
Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 17.4 0.406
Packaging
Pizza, Sausage Special
Deluxe, Round with 5.3
Cardboard Backing and
Clear Shrink Wrap
Pizza, Sausage Special
Deluxe, Round with no 16.3
Backing, Unwrapped
Sheet Pizza 9.1
Pizza, Vegetable, 12 inch 14.5
Diameter
Pizza Crust with Uncooked 17.3
Ingredients on Top
Diameter, Height,
Description m or m
Width, m
Pizza 0.022
Pizza, Box of 6 pieces, 4 0.203 0.019
oz./piece
Pizza with Topping, 12
inch Diameter, On 0.413 0.013
Cardboard
Pizza, Canadian Bacon, 12 0.305 0.02
inch Diameter
Pizza, Ham and Pineapple, 0.406 0.02
16 inch Diameter
Pizza, Sausage and Cheese, 0.178 0.029
Round, No Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 0.305 0.032
Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 0.305 0.032
Packaging
Pizza, Sausage Special
Deluxe, Round with 0.305 0.022
Cardboard Backing and
Clear Shrink Wrap
Pizza, Sausage Special
Deluxe, Round with no 0.318 0.019
Backing, Unwrapped
Sheet Pizza 0.394 0.013
Pizza, Vegetable, 12 inch 0.305 0.02
Diameter
Pizza Crust with Uncooked 0.152 0.013
Ingredients on Top
Mass, Air
Description gm Temperature,
[degrees]C
Pizza 392 -30
Pizza, Box of 6 pieces, 4 680 -34.4
oz./piece
Pizza with Topping, 12
inch Diameter, On 1077 -34.4
Cardboard
Pizza, Canadian Bacon, 12 1077 -34.4
inch Diameter
Pizza, Ham and Pineapple, 1497 -34.4
16 inch Diameter
Pizza, Sausage and Cheese, 211 -26
Round, No Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 1549 -28.9
Packaging
Pizza, Sausage and Cheese,
Rectangular, Sliced, No 1548 -34.4
Packaging
Pizza, Sausage Special
Deluxe, Round with 504 -27.5
Cardboard Backing and
Clear Shrink Wrap
Pizza, Sausage Special
Deluxe, Round with no 753 -28.9
Backing, Unwrapped
Sheet Pizza 680 -34.4
Pizza, Vegetable, 12 inch 624 -34.4
Diameter
Pizza Crust with Uncooked 170 -34.4
Ingredients on Top
Air Air Flow
Description Velocity, Direction
m/s
Pizza 3 along
height
Pizza, Box of 6 pieces, 4 3 along
oz./piece width
Pizza with Topping, 12
inch Diameter, On 3
Cardboard
Pizza, Canadian Bacon, 12 3
inch Diameter
Pizza, Ham and Pineapple, 3
16 inch Diameter
Pizza, Sausage and Cheese, 3.8 along
Round, No Packaging diameter
Pizza, Sausage and Cheese, along
Rectangular, Sliced, No 3.8 width
Packaging
Pizza, Sausage and Cheese, along
Rectangular, Sliced, No 3.8 width
Packaging
Pizza, Sausage Special
Deluxe, Round with 3.3 along
Cardboard Backing and diameter
Clear Shrink Wrap
Pizza, Sausage Special along
Deluxe, Round with no 3.3 diameter
Backing, Unwrapped
Sheet Pizza 3
Pizza, Vegetable, 12 inch 3
Diameter
Pizza Crust with Uncooked 3 along
Ingredients on Top diameter
Table 2. Nusselt-Reynolds-Prandtl Correlations for Selected Food Items.
Number
Food Type Reynolds Number of Data
Range Points
Cake 4000<Re<80000 29
Chicken Breast 1000<Re<11000 22
Pizza 3000<Re<12000 12
Level of Coefficient of
Food Type Significance Determination,
(F-statistic) [r.sup.2]
Cake 5.34E-12 0.833
Chicken Breast 0.00115 0.418
Pizza 0.00814 0.520
Food Type Nu-Re-Pr Correlation
Cake Nu = 0.00156 x [Re.sup.0.960] x [Pr.sup.O.3]
Chicken Breast Nu = 0.0378 x [Re.sup.0.837] x [Pr.sup.0.3]
Pizza Nu = 0.00517 x [Re.sup.0.891] x [Pr.sup.0.3]
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