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

TL;DR

This paper introduces a semi-analytical approach combining the differential transformation method and Padé approximants to effectively solve free convection boundary layer flow problems over a vertical plate, especially handling boundary conditions at infinity.

Contribution

It presents a novel, non-iterative semi-analytical method that accurately solves nonlinear free convection boundary layer problems with boundary conditions at infinity.

Findings

Method agrees well with previous numerical results.

Provides a simple and effective solution approach.

Handles boundary conditions at infinity without iteration.

Abstract

The aim of this study is to present a reliable combination of the differential transformation method (DTM) and Pad\'e 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 Pad\'e 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-Pad\'e 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.