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Similarity Solutions and Finite Element Method for Unsteady Free-convection Flow with Constant Heat Flux

Moncef Aouadi

Abstract


The group-theoretical and the finite element methods are applied to present an analysis of the problem of unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid. The flat sheet is subjected to a constant heat flux giving rise to a buoyancy force. The nonlinear coupled partial differential equations and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the finite element method. Effect of Prandtl number on the temperature and velocity of the boundary layer are studied and plotted in curves. A comparison with results given in literature proves
the good performance of the finite element method.

Keywords


Free convection flow, group-theoretic method, finite element method

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