Abstract
The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T − T ∞)p, (p ≥ 1), where T is the fluid temperature and T ∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h s from the boundary. If h s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t −1) for t large. When h s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h s . For p > 2 there is a critical value h s,crit (dependent on the exponent p) of h s such that the solution still approaches a nontrivial steady state if h s < h s,crit. For h s > h s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.
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Merkin, J.H. Unsteady free convective boundary-layer flow near a stagnation point in a heat-generating porous medium. J Eng Math 79, 73–89 (2013). https://doi.org/10.1007/s10665-012-9560-2
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DOI: https://doi.org/10.1007/s10665-012-9560-2