This paper proposes appropriate conjugate parameters, dimensionless coordinates and temperatures to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flows adjacent to vertical and horizontal flat plates. The obtained finite-difference solutions are uniformly valid over the entire thermo-fluid-dynamic field for fluids of any Prandtl number between 0.001 and infinity. The variations of the local heat transfer rates as well as the interface temperatures and frictions along the plates are shown explicitly. Typical velocity and temperature profiles in the boundary layers are presented. Very comprehensive and accurate correlations of the local Nusselt numbers are also presented and are compared with the reported correlation equations for the vertical case.
