Forced convection in a plane channel filled with a saturated bi-disperse porous medium, coupled with conduction in plane slabs bounding the channel, is investigated analytically on the basis of a two-velocity, two-temperature model. It is found that the effect of the finite thermal resistance due to the slabs is to reduce both the heat transfer to the porous medium and the degree of local thermal non-equilibrium. An increase in value of the Peclet number leads to a decrease in the rate of exponential decay in the downstream direction but does not affect the value of a suitably defined Nusselt number. The dependence of Nusselt number on Biot number associated with the boundary slabs, the interphase neat exchange parameter, the interphase thermal conductivity ratio, the interphase effective permeability ratio, and the macroscopic void fraction, is investigated. (C) 2004 Elsevier Ltd. All rights reserved.