Free convection boundary layers on a vertical surface in a heat-generating porous medium

Abstract

The natural convection boundary-layer flow on a solid vertical surface with heat generated within the boundary layer at a rate proportional to (T - T ∞ ) p (p ≥ 1) is considered. The surface is held at the ambient temperature T ∞ except near the leading edge where it is held at a temperature above ambient. The behaviour of the flow as it develops from the leading edge is examined and is seen to become independent of the initial heat input; however, it does depend strongly on the exponent p. For 1 ≤ p ≤ 2, the local heating eventually dominates at large distances and there is a convective flow driven by this mechanism. For p ≥ 4, the local heating does not have a significant effect, the fluid temperature remains relatively small throughout and the heat transfer dies out through a wall jet flow. For 2 < p < 4, the local heating has a significant effect at relatively small distances, with a thermal runaway developing at a finite distance along the surface.