The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate is studied using the integral method. The closed-form solutions found are in good agreement with the available numerical results and also with the results obtained using a finite difference approximation and the expansion method. For large values of the flow resistance (due to the presence of the solid matrix), the asymptotic value for the heat transfer rate shows a Prandtl number dependency of 1/2 power, while the results for the intermediate values of the resistances show a 1/3 power dependency. The effect of the presence of the solid matrix on the heat transfer rate is shown through a regime diagram marking the boundaries of the regime of no significant alteration, the non-Darcian regime, and the Darcian regime.

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