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 controlled by a single Biot number Bi = hL/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 asymmetric heat convection controlled by two Biot numbers: Bi1 = Lh1/k at the left surface and Bi2 = Lh2/k at the right surface. The question that needs to be addressed is the following: under what circumstances can the unsteady cooling of a long slab by asymmetric heat convection be treated with a lumped model?