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

Abstract

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