Abstract
The free convection boundary layer on an insulated wall formed by local internal heating through a modified form of Arrhenius kinetics is considered. It is shown to involve two dimensionless parameters, \(\epsilon \) the activation energy and \(q_0\) the rate of local heating. Numerical solutions to the initial-value problem are obtained showing that, for relatively weak internal heating (small \(q_0\)), a nontrivial flow arises at large times, whereas for larger local heating the solution becomes singular at a finite time. This behaviour is also seen to depend on the size of the initial input. The corresponding steady states, being the possible large time solutions to the initial-value problem, are also treated. These show the existence of a critical value \(q_{0,\mathrm{{crit}}}\) of \(q_0\), dependent on \(\epsilon \). These critical values determined numerically showing that there was a finite region of the \(\epsilon {\sim }q_0\) parameter plane over which steady states cannot be found. Asymptotic forms for both \(\epsilon \) and \(q_0\) being small and large are derived.
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Merkin, J.H. The Unsteady Free Convection Boundary-Layer Flow Near a Stagnation Point in a Heat Generating Porous Medium with Modified Arrhenius Kinetics. Transp Porous Med 113, 159–171 (2016). https://doi.org/10.1007/s11242-016-0687-x
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DOI: https://doi.org/10.1007/s11242-016-0687-x