Scale analysis and integral approximation applied to heat and mass transfer in packed beds

In this paper, we apply two mathematical tools for the analysis of models describing heat and mass transfer in dispersed systems, namely scale analysis and integral approximation. The particular model investigated is a 1-D model describing the cooling of packed beds of fresh agricultural produce using the porous media approach. With scale analysis, one can determine relevant terms in the model and subsequently one can make justified approximations. Traditionally, in the porous media approach one assumes that temperature gradients in individual products are negligible, as expressed by the Biot number Bi < 0.1. By means of the integral approximation method, we have shown that the porous medium approach can be extended to the range Bi < 10 via the definition of an internal heat resistance. Via the integral approximation method, we have calculated the internal resistance for a variety of products having simple geometries. Scale analysis shows that for the problem investigated, there are two regimes, depending on whether solid and fluid phase are in so-called local thermal equilibrium.