Application of the differential transformation method to the solutions of the free convection problem

This paper employs the differential transformation method to investigate the velocity and temperature distributions associated with a free convection boundary-layer flow over a vertical plate. A group of transformations are used to reduce the free convection problem to three sets of initial value problems, which are then solved by means of the differential transformation method. The proposed method yields close-form solutions of a coupled system of nonlinear ordinary differential equations, which can then be calculated numerically. Numerical results for the dimensionless velocity and temperature profiles of the free convection boundary-layer flow are presented graphically for various values of Prandtl number. It is shown that the current results are in good agreement with those provided previously by other numerical methods. Therefore, it is concluded that the method presented in this study provides a simple, non-iterative, and effective scheme for determining the solutions of a coupled system of nonlinear free convection boundary-layer problems.