The connection between the distributed and lumped models for asymmetric cooling of long slabs by heat convection

The unsteady cooling of a long slab by symmetric heat convection is control led by a single Biot number Bi = (h) over barL/k applied at both surfaces. It is known that the thermal response of the long slab may be analyzed with a lumped model with a small error whenever Bi < 0.1. This paper deals with a plausible extension of the symmetric heat convection implicating an asym metric heat onvection controlled by two Biot numbers: Bi-1 = L<(h)over bar> (1)/k at the left surface and Bi-2 = L (h) over bar (2)/k at the right surf ace. The question that needs to be addressed is the following: under what c ircumstances can the unsteady cooling of a long slab by asymmetric heat con vection be treated with a lumped model? (C) 2001 Elsevier Science Ltd.