Non-similar boundary layer analysis of mixed convection about a horizontal heated surface in a fluid-saturated porous medium

An analysis has been performed for the study of the buoyancy effects in the parallel and stagnation forced flows in a porous medium adjacent to a heated surface with wall temperature being a power function of distance, i.e., $\text{T}{}_{\mathrm{<mtext>W</mtext>}}\text{≈}\text{x}{}^{\mathrm{\lambda }}$. Local non-similarity methods were used to obtain approximate solutions for the problem. Numerical solutions were carried out to the third level of truncation for parallel aiding flow over a heated horizontal surface with $\text{0 ≤ λ ≤ 2}$ for a wide range of buoyancy parameters. For wall temperature with λ < 0.5, it is found that the differences between the first and the third level of truncations are very small. The difference is more marked for λ > 0.5, and it accentuates as the value of the buoyancy parameter or λ is increased.