A Novel Analytical Solution of the Thermal Boundary-Layer over a Flat Plate with a Convective Surface Boundary Condition Using DTM-Padé

Abstract

In this paper, a novel analytical method (DTM-Pade) is proposed for solving nonlinear differential equations, especially for boundary-layer and natural convection problems. This method is based on combination of the differential transform method and the Pade approximant that we use for solve the thermal boundary-layer over a flat plate with a convective surface boundary condition. This technique is extended to give solutions for nonlinear differential equations whit boundary conditions at the infinity. In order to show the effectiveness of the DTM-Pade, the results obtained from the DTM-Pade is compared with available solutions obtained using Runge-Kutta-Fehlberg fourth-fifth order (RFK45) method to generate the numerical solution. Numerical comparisons between the DTM-Pade and the RFK45 reveal that the new technique introduced here is a promising tool for solving nonlinear differential equations whit infinity boundary conditions.