A NUMERICAL METHOD FOR SIMULATING HEAT TRANSFER IN HETEROGENEOUS and IRREGULARLY SHAPED FOODSTUFFS¹

Abstract

Heat conduction during cooking of foodstuffs with heterogeneous thermal properties was simulated, mainly for irregularly shaped geometries. A code employing boundary-fitted grids was implemented in a numerically conservative form (control volume formulation). This technique consists of finding a numerical coordinate transformation which fits a regular grid to the domain of integration. With the grid as data, coefficients for a transformed differential equation are then obtained.The proposed model was experimentally verified on irregularly shaped pieces of beef containing a nonuniform distribution of fat. Relative errors between predicted and measured temperatures were less than 2 %.The effects of heat transfer coeflcient and temperature of the cooking medium on the temperature distribution during the process were analyzed. The influence of different fat patterns was also considered. 'The authors are members of the Carrera del Investigador Cientifko y Tecnol6gico. Conicet, Argentina.

Transport phenomena in food engineering: basic concepts and advances

“…With this intention, Manson, Stumbo, and Zahradnik (1974) used a finite difference model to predict the temperatures in conduction heating of pear-shaped objects, and Simpson, Aris, and Torres (1989) applied a finite difference approximation to the differential equation for transient heat conduction in three dimensions to evaluate thermal processing of foods in oval-shaped containers. The method of finite difference has been used by other researchers to simulate heat conduction in irregularly shaped foods (Califano & Zaritzky, 1993;Sheen, Tong, Fu, & Lund, 1993;Akterian & Fikiin, 1994;Kim & Teixeira, 1997). More recently, Erdogdu, Balaban, and Chau (2003) reported results using a volume element based approach to finite difference model for heat transfer in elliptical cross sections by using power curves; an important contribution of this work was the use of different boundary conditions at the surface and non-homogeneous thermo physical properties inside the food.…”

Simulation of Freezing or Thawing Heat Conduction in Irregular Two-Dimensional Domains by a Boundary-Fitted Grid Method

“…However, the transition to a more universal reference frame allows orthogonal grids that are either uniform or nonuniform in one or both directions to be constructed for more complex domains in physical space (21). An algebraic analog of Eqn [3] was obtained by application of the control-volume formulation and an explicit discretization scheme with respect to time (20). The calculation domain was divided into a number of nonoverlapping discrete control volumes such that there is one control volume surrounding each grid point.…”

“…In the present work, boundaryfitted grids were generated by solving Laplace's equations for the fitted coordinates, namely (20):…”

Geometry modelling of food materials from magnetic resonance imaging

“…The main reasons may arise in complexity for correctly describing the true shape, solving the problem by appropriate numerical methods and computational requirements for simulating processes. Heating or cooling (Gustafson et al, 1979), cooking (Califano and Zaritzky, 1993), freezing and thawing (Califano and Zaritzky, 1997), deep-fat frying (Ngadi et al, 1997) and drying (Neményi et al, 2000) were simulated using 2D irregular geometries for different food materials. Considering 3D geometries, thermal processing (Sastry et al, 1985) and cooking (Purlis and Salvadori, 2005; were also studied.…”