Leading edge effects on free convection of a Darcian fluid about a semi- infinite vertical plate with uniform heat flux (Q1116846)

The method of matched asymptotic expansion, together with a deformed longitudinal coordinate, is applied to study the leading edge effect on free convection about a semi-infinite, uniform heat flux, vertical surface embedded in a porous medium. The leading edge effect manifests itself as inhomogeneous terms in the second- and third-order problems. Similarity solutions for the free convection porous-media flow are obtained up to the third-order approximation. It is shown that the leading edge effect increases the streamwise vertical velocity near the outer edge of the thermal boundary layer, resulting in a corresponding increase in heat flux. The leading edge and the entrainment effects are shown to increase the heat transfer rate almost equally. At \(Ra_ x=100\), the combined effects enhance the heat transfer rate by more than 10 \% as compared with those based on the boundary layer approximation. These effects increase as the Rayleigh number is decreased.