Free convection induced by a horizontal wavy surface in a porous medium

The effect of stationary surface waves on the free convection induced by a horizontal uniformly heated surface in a porous medium is studied. Attention is focused on those cases where the waves have an 0 ( Ra −1/3 ) amplitude, where the Rayleigh number, Ra , is based on the wavelength of the waves and is assumed large. Within this amplitude regime the resulting nonsimilar boundary layer flow is described by a set of nonlinear parabolic partial differential equations whose solution is effected by means of the Keller box method. Extensive computations are presented for a wide range of wave amplitudes and phases, and some global heat transfer rates are given. For all amplitudes and phases a thin near-wall boundary layer develops within the basic boundary layer as the distance downstream increases; an asymptotic analysis is given which determines the structure of this layer. When the wave amplitude is greater than roughly 0.95 Ra −1/3 localised regions of reverse flow occur at the heated surface, the number of which depend on the amplitude and phase of the waves.