Finite difference solution of heat and mass transfer problems related to precooling of food

Abstract

The present work aims at finding an optimized finite difference scheme for the solution of problems involving pure heat transfer and simultaneous heat and mass transfer from the surface of solids exposed to a cooling environment. Regular shaped bodies in the form of infinite slab, infinite cylinder and sphere were considered and a generalized mathematical model was written in dimensionless form. A sample problem was chosen from the literature to develop an optimized scheme of solutions. A fully explicit finite difference scheme, an implicit finite difference scheme and different combination schemes with varying values of weighing factor have been thoroughly studied. The weighing factor was varied from 0 (fully explicit scheme) to 1 (fully implicit scheme) in steps of 0.1 (implicit–explicit schemes with different weighing averages). The characteristic dimension (half thickness or radius) was divided into a number of divisions; n=4, 8, 10, 20, 30, 40, 50 and 60 respectively. All the possible options of dimensionless time (the Fourier number) increments were taken one by one to give the best convergence and truncation error criteria. The simplest explicit finite difference scheme with n=10 and Fourier number increments one sixth of the square of the space division size was found to be highly reliable and accurate.