A Numerical Investigation of Mixed Convection on a Horizontal Semi-Infinite Plate
The laminar mixed convection flow above a semi-infinite horizontal plate is studied for large Reynolds and Grashof numbers. To permit similarity solutions of the boundary-layer equations, the plate temperature, T w , is assumed to differ from the free-stream temperature, T ∞, according to the relation (T ∞ − T w ) ∝ x −1/2, where x is the distance from the leading edge. This corresponds to a plate that is strongly cooled near the leading edge while thermally insulated everywhere else. There are two branches of similarity solutions of the boundary-layer equations if the non-dimensional buoyancy parameter is larger than a critical value, which is negative and depends on the Prandtl number. Non-similar solutions connecting the self-similar solutions have also been found analytically. In the present work a finite-element package is used to solve the full NavierStokes and energy equations. The numerical results resemble the analysis in a certain regime of the buoyancy parameter. In other regimes, however, neither the self-similar solutions nor the connecting solutions are found numerically.
KeywordsMixed convection numerical solutions Navier-Stokes equations
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