This paper presents a theoretical study of fully developed forced convection in a channel partially filled with a porous matrix. The matrix is attached at the channel wall and extends inward, toward the centerline. Two channel configurations are investigated, namely, parallel plates and circular pipe. For each channel configuration, both the case of constant wall heat flux and constant wall temperature were studied. The main novel feature of this study is that it takes into account the flow inside the porous region and determines the effect of this flow on the heat exchange between the wall and the fluid in the channel. The Brinkman flow model which has been proven appropriate for flows in sparsely packed porous media and for flows near solid boundaries was used to model the flow inside the porous region. Important results of engineering interest were obtained and are reported in this paper. These results thoroughly document the dependence of the Nusselt number on several parameters of the problem. Of particular importance is the finding that the dependence of Nu on the thickness of the porous layer is not monotonic. A critical thickness exists at which the value of Nu reaches a minimum.

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