Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike

An analysis is made for steady free convection about a vertical flat plate embedded in a saturated porous medium at high Rayleigh numbers. Within the framework of boundary layer approximations, similarity solutions are obtained for a class of problems where wall temperature varies as xλ, i.e., a power function of distance from the origin where wall temperature begins to deviate from that of the surrounding fluids. Analytical expressions are obtained for boundary layer thickness, local and overall surface heat flux, and local and average heat transfer coefficients. Application to convective heat transfer about an isothermal dike intruded in an aquifer is discussed.