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The aim of this study is to present a reliable combination of thedifferential transformation method (DTM) and Pad\'e approximants to make, forthe first time, a semi-analytic analysis of the problem of free convectionboundary-layer flow over a vertical plate as produced by a body force about aflat plate in the direction of the generating body force. Boundary conditionsin an unbounded domain, i.e. boundary condition at infinity, pose a problem ingeneral for the numerical solution methods. Without using Pad\'e approximation,the semi-analytical solution obtained by the DTM cannot satisfy infinityboundary conditions. The obtained results are in good agreement with thoseprovided previously by the iterative numerical method. As a result, withouttaking or estimating missing boundary conditions, the DTM-Pad\'e methodprovides a simple, non-iterative and effective way for determining thesolutions of nonlinear free convection boundary layer problems possessing theboundary conditions at infinity.

A Semi Analytical Analysis of a Free Convection Boundary Layer Flow Over a Vertical Plate