Effects of Upstream Geometry on Natural Convection of a Darcian Fluid About a Semi-Infinite Inclined Heated Surface

The method of matched asymptotic expansions is applied to the problem of steady natural convection of a Darcian fluid about a semi-infinite inclined heated surface with a power law variation of wall temperature, i.e., Tˆ_waxˆ^λ for xˆ≥0 where 0≤λ<1. The leading edge of the inclined surface intercepts at an angle, Λ₀, with another impermeable unheated surface extending upstream. The effects of the inclination angle α₀ (0 ≤ α₀ < < π/2) of the heated surface as well as the upstream geometry at xˆ<0 (as specified by Λ₀) on heat transfer and fluid flow characteristics near the heated surface are investigated. At a given inclination angle α₀, it is found that heat transfer from an upward-facing heated inclined surface is larger than that of a downward-facing heated surface, and that decreasing the intercepting angle (Λ₀) tends to lower the heat transfer rate. These effects become increasingly pronounced as the Rayleigh number is decreased.