Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium

We have investigated the effects of large-scale surface non-uniformities on the boundary layer flow induced by a constant heat flux, vertically aligned, semi-infinite surface embedded in a porous medium. The amplitude of the waves of the surface were assumed to have the same order of magnitude as their wavelength as the Rayleigh number becomes large. Assuming the validity of the boundary layer approximation, it was found that the flow could only be determined by solving a pair of parabolic partial differential equations. Local hot spots were found to correspond almost exactly to points at which the slope of the function σ takes its maximum values. It was also found that the effect of an isolated hump on the surface persists a substantial distance down-stream of the hump.