A note on the free convection boundary-layer flow over a vertical surface with spatial internal heat generation

Abstract

The model proposed by Postelnicu et al. [17, 18] for the natural convection boundary-layer flow on a vertical surface in a porous medium driven by spatially-dependent localised internal heating is discussed further. Their results for a prescribed wall temperature characterised by the parameter $\lambda$ are extended to a consideration of the singularity seen in the solution as $\lambda \rightarrow -\frac{1}{2}$ and to the asymptotic limit $\lambda \rightarrow \infty$, where convection resulting from the wall temperature becomes more important near the wall and showing a region of reversed flow/temperatures below ambient away from the wall. The case, not treated by Postelnicu et al., when there is a prescribed surface heat flux is also treated, finding that the solution became singular as $\lambda \rightarrow -\frac{1}{3}$, the nature of which is discussed. The large $\lambda$ limit is also obtained again finding that the dominant effect is the convection resulting from the wall heat transfer though here the temperature within the boundary layer remains above ambient.