Abstract
In this letter, the shifted Legendre polynomials are employed for solving the natural heat convection heat transfer. The operational matrix of derivative for the shifted Legendre polynomial are derived. Then the shifted Legendre polynomials expansions along with this operational matrix are applied for solving the natural convection governing equations. The advantage of the proposed method is that the need for guessing and correcting the velocity and temperature slopes, f'' (0), and θ' (0) during the solution procedure is eliminated. Moreover, by using the given boundary conditions in the problem, a stable solution can be derived. The proposed method is evaluated by obtaining the similarity solutions of free convection along a vertical isothermal flat plate. The results obtained through this direct innovative solution show higher efficiency and performance in comparison with the conventional shooting method.