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Résumé :
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We investigate the steady, two-dimensional, free convection flow caused by a sinusoidally heated and cooled infinite vertical surface that delimits a semi-infinite porous media. An analytical solution which is valid for small values of the Rayleigh number, Ra, is obtained using a regular perturbation method. A finite-difference technique is used to numerically solve the problem for 0 = Ra = 150 and for small values of Ra, the results are in very good agreement with the analytical solutions and the streamlines are in the form of a row of counter rotating cells which are situated close to the vertical surface. As the Rayleigh number increases, above a value of about 40, then the cellular flow separates from the plate. At very large values of Ra, a scaling analysis has been performed and the results suggest that the vertical velocity and the local Nusselt number on the plate support better the boundary-layer scalings, than does the mean vertical velocity and the mean Nusselt number along the plate. In the situation in which the flow separates, i.e. for Ra = 40, the smallest possible solution domain must be chosen, by using the symmetry of the problem, otherwise it has not been possible to obtain a convergent numerical solution.
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