Free convective boundary-layer flow in a heat-generating porous medium: Similarity solutions

The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T - T infinity)(p), where T is the local temperature and T-infinity is the ambient temperature, is considered when there are power-law variations in either the wall temperature or the wall heat flux which enables the equations to be reduced to similarity form. When the wall temperature is prescribed, solutions are found for p <= 2 and p >= p(c) (p(c) = 10.673) with a saddle-node bifurcation at p = p(c) and two solution branches for p > p(c). When the wall heat flux is prescribed, solutions are found only for p < 2. The special case p = 2 is considered and the limiting forms as p -> 2 and p -> infinity are obtained and compared with the solutions obtained from solving the similarity equations numerically.