摘要：In this paper, an attempt has been made for the analytical solution of the unsteady mixed convection flow induced by the combined effects of the mechanically driven lid and the buoyancy force within rectangular enclosures. The couple of nonlinear equations describing the fluid behavior and temperature distribution within rectangular enclosures form a very complex system where the analytical solution is not available in the literature. To the best of the author's knowledge, this the first time such an attempt is presented. To drive the solutions of the coupled nonlinear boundary systems, an optimal homotopy asymptotic method was applied in the initial stage, then follow by the method of eigenfunction combined with orthogonality property. Explicit analytical solutions for both fluid velocity and temperature distribution are obtained. The results proved the effective technique for solving the couple nonlinear equations in a rectangular enclosure.
