Solving of boundary-layer equations with transpiration effects, governance on a vertical permeable cylinder using modified differential transform method

The suction and injection effects on the free convection boundary-layer flow over a vertical cylinder are studied. The main stream velocity and wall temperature are proportional to the axial distance along the surface of the cylinder. Both analytic and numerical solutions of the arising mathematical problem are obtained. An analytic solution is derived by a new analytical method (DTM-Padé) and numerical solutions have been performed by using a fourth-order Runge-Kutta and shooting methods. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method (DTM) solutions are only valid for small values of the independent variable but the obtained results by DTM-Padé are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences.