Authors: J H Merkin
Publish Date: 2016/04/16
Volume: 113, Issue: 1, Pages: 159-171
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 initialvalue 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 initialvalue problem are also treated These show the existence of a critical value q 0mathrmcrit 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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