Natural convective boundary-layer flow in a heat generating porous medium with a constant surface heat flux

The natural convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T−T∞)p(T−T∞)p, where TT is the local temperature and T∞T∞ is the ambient temperature, is considered when there is a constant surface heat flux. For small xx, where xx measures the distance along the surface, the flow and heat transfer are determined by the surface heat flux, with the local heating becoming more significant as xx increases. Two different situations arise, depending on the exponent pp, as to how the flow develops from the leading edge. For p<2p<2 the flow evolves to large distances with the local heating being the dominant effect for large xx. For p>2p>2 a singularity develops in the solution at a finite value xsxs of xx, with xsxs being dependent on pp, leading to a thermal runaway. The nature of this singularity is discussed as well as the special case when p=2p=2.