Predictive equations for thermophysical properties and enthalpy during cooling and freezing of food materials Kostadin A. Fikiin * , Anguel G. Fikiin Refrigeration Science and Technology Division, Technical University of So®a, 95 Vassil Levski Blvd., 1000 So®a, Bulgaria Received 16 December 1996; accepted 20 December 1998 Abstract Good knowledge of thermophysical characteristics of a wide range of foodstus has a major importance for the accurate pre- diction of their unsteady-state temperature distribution, the process duration and energy consumption in cooling and freezing (heating and thawing). Such information is necessary to predict the microbiology and biochemistry of spoilage and to control the product safety and quality, as well as for the design, optimisation and ecient operation of refrigerating and thermal systems in the food and biotechnological industries. The purpose of this paper is to present reliable uni®ed equations for determination of the speci®c heat capacity, enthalpy, thermal conductivity, Kirchho function, etc. on the basis of generalised parameters (moisture content, actual and initial freezing temperatures). The relationship between the volumetric speci®c enthalpy and the Kirchho function is also derived. The proposed formulae have large areas of application. They cover practically all industrially processed food materials except those consisting mainly of fats. The equations may easily be used for both simple and rapid engineering calculations and for implementation in more sophisticated mathematical models and computer software, including the cases in which advanced enthalpy methods for numerical heat transfer simulations are involved. Ó 1999 Elsevier Science Ltd. All rights reserved. Keywords: Food refrigeration; Thermal properties; Enthalpy; Kirchho function; Heat transfer Journal of Food Engineering 40 (1999) 1±6 Nomenclature c Speci®c heat capacity (J kg 1 K 1 or kJ kg 1 K 1 in Eqs. (23)±(29)) E Kirchho function (W m 1 ) f Correction factor (as in Eq. (15)) H Enthalpy per unit mass (J kg 1 or kJ kg 1 in Eqs. (23)±(29)) H Enthalpy per unit volume (J m 3 or kJ m 3 in Eqs. (23)±(29)) I q Volumetric rate of the internal heat generations (W m 3 ) L Latent heat of water freezing/thawing (J kg 1 or kJ kg 1 in Eqs. (23)±(29)) t Temperature (°C) p Pressure (Pa) Greek letters e Porosity (m 3 gas m 3 m ) k Thermal conductivity (W m 1 K 1 ) q Substance density (kg m 3 ) s Time (s) u Relative moisture content of the food material (kg w kg 1 m ) x Relative quantity of the frozen water (ice fraction) (kg i kg 1 w ) Subscripts cr Cryoscopic (initial freezing) point d Dry substance fr Frozen (in freezing/thawing process) i Ice m Material p At constant pressure t At constant temperature un Unfrozen v At constant volume w Water e At given porosity x At constant ice content Acronyms FMs Food Materials SHC Speci®c Heat Capacity TC Thermal Conductivity TPs Thermophysical Properties * Corresponding author. Tel.: +359-2-884-816; fax: +359-2-884-816; e-mail: agf@vmei.acad.bg 0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 2 6 - 6