A Semi Analytical Analysis of a Free Convection Boundary Layer Flow Over a Vertical Plate
This provides a simpler, non-iterative solution method for researchers solving nonlinear boundary layer problems with boundary conditions at infinity.
The study applies a combination of differential transformation method (DTM) and Padé approximants to solve free convection boundary-layer flow over a vertical plate, achieving results that match previous numerical methods without needing to estimate missing boundary conditions.
The aim of this study is to present a reliable combination of the differential transformation method (DTM) and Padé approximants to make, for the first time, a semi-analytic analysis of the problem of free convection boundary-layer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. Without using Padé approximation, the semi-analytical solution obtained by the DTM cannot satisfy infinity boundary conditions. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the DTM-Padé method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.