Comparison study of differential transform method with finite difference method for magnetoconvection in a vertical channel

Abstract

In this paper, coupled nonlinear equations governing the flow for magnetoconvection in a vertical channel for open and short circuits are solved. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical-analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced, and then applied for the aforementioned problems. The current results are then compared with those derived from the finite difference method (FDM) and perturbation method (PM) in order to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable results in predicting the solution of such problems. © 2013 Wiley Periodicals, Inc.