FOOD THERMOPHYSICAL PROPERTY MODELS by Bryan R. Becker, Ph.D., P.E. Associate Professor and Brian A. Fricke, Ph.D., E.I.T. Research Assistant Mechanical and Aerospace Engineering Department University of Missouri-Kansas City 5605 Troost Avenue Kansas City, MO 64110-2823 26 February 1999FOOD THERMOPHYSICAL PROPERTY MODELS Bryan R. Becker, Ph.D., P.E. and Brian A. Fricke, Ph.D., E.I.T. Mechanical and Aerospace Engineering Department University of Missouri-Kansas City 5605 Troost Avenue, Kansas City, MO 64110-2823 ABSTRACT The design engineer must predict the thermophysical properties of foods in order to design food storage and refrigeration equipment and estimate process times for refrigerating, freezing, heating or drying of foods. Since the thermophysical properties of foods are strongly dependent upon chemical composition and temperature, composition based models provide a means of estimating these properties. Numerous models of this type have been proposed and the designer of food processing equipment is thus faced with the challenge of selecting appropriate models from the plethora of those available. This paper describes selected food thermophysical property models and evaluates their performance by comparing their results to experimental thermophysical property data. The results given in this paper will be of value to the design engineer in the selection of appropriate food thermophysical property models. Introduction Knowledge of the thermophysical properties of foods is required to perform the various heat transfer calculations which are involved in the design of food storage and refrigeration equipment. The estimation of process times for refrigerating, freezing, heating or drying of foods also requires knowledge of food thermal properties. Due to the multitude of food items available, it is nearly impossible to experimentally determine and tabulate the thermal properties of foods for all possible conditions and compositions. Because the thermal properties of foods are strongly dependent upon chemical composition and temperature, the most viable option is to predict the thermophysical properties of foods using mathematical models which account for the effects of chemical composition and temperature. Composition data for foods are readily available in the literature [1-3]. This data consists of the mass fractions of the major components found in food items. Such components include water, protein, fat, carbohydrate, fiber and ash. Food thermal properties can be predicted by using this composition data in conjunction with temperature dependent mathematical models of the thermal properties of the individualcomponents. Choi and Okos [4] have developed mathematical models for predicting the thermal properties of food components as functions of temperature in the range of -40°C to 150°C. In addition, Choi and Okos developed models for predicting the thermal properties of water and ice. Thermophysical properties of foods which are often required for heat transfer calculations include ice fraction, specific heat and thermal conductivity. This paper provides a summary of prediction methods for estimating these thermophysical properties. In addition, the performance of the various thermophysical property models is evaluated by comparing their calculated results with experimentally determined thermophysical property data available from the literature. Ice Fraction In general, food items consist of water, dissolved solids and undissolved solids. During the freezing process, as some of the liquid water crystallizes, the solids dissolved in the remaining liquid water become increasingly more concentrated, thus lowering the freezing temperature. This unfrozen solution can be assumed to obey the freezing point depression equation given by Raoult's law [5]. Thus, based upon Raoult's law, Chen [6] proposed the following model for predicting the mass fraction of ice, xice , in a food item: If the molecular weight of the soluble solids, Ms , is unknown, then the following simple method may be used to estimate the ice fraction of a food item [7]: Because Equation 2 underestimates the ice fraction at temperatures near the initial freezing point and overestimates the ice fraction at lower temperatures, Tchigeov [8] proposed an empirical relationship to estimate the mass fraction of ice: tt) t - t (LMTRx = xffos2osice• (1) tt - 1) x - x ( = xfbwoice (2) ) 1 + t - t ( ln0.7138 + 11.105x = xfwoice (3)Specific Heat Unfrozen The specific heat of a food item, at temperatures above its initial freezing point, can be obtained from the mass average of the specific heats of the food components. Thus, the specific heat of an unfrozen food item, cu , may be determined as follows: If detailed composition data is not available, a simpler model for the specific heat of an unfrozen food item can be used [9]: Frozen Below the freezing point of the food item, the sensible heat due to temperature change and the latent heat due to the fusion of water must be considered. Because latent heat is not released at a constant temperature, but rather over a range of temperatures, an apparent specific heat can be used to account for both the sensible and latent heat effects. A common method to predict the apparent specific heat of food items is that of Schwartzberg [10]: The specific heat of the food item above its initial freezing point may be estimated with Equation 4 or Equation 5. Schwartzberg [11] expanded upon his earlier work and developed an alternative method for determining the apparent specific heat of a food item below the initial freezing point as follows: A slightly simpler apparent specific heat model, which is similar in form to that of Schwartzberg [10], was developed by Chen [9]. Chen's model is an expansion of Siebel's equation [12] for specific heat and has the following form: xc = ciiu∑ (4) x0.628 - x2.30 - 4.19 = c3ssu (5) ∆∆ c0.8 - tMTR x E+ c) x - x ( + c = c2w2oswobua (6) ) T - T () T - T ( L ) x - x ( + c = cofoobwofa (7) t MT Rx + x1.26 + 1.55 = c2s2ossa (8)Thermal Conductivity Early work in the modeling of the thermal conductivity of foods includes Eucken's adaption of Maxwell's equation [13]. This model is based upon the thermal conductivity of dilute dispersions