A new approximate analytical technique for dual solutions of nonlinear differential equations arising in mixed convection heat transfer in a porous medium

Abstract

Purpose

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.

Design/methodology/approach

Homotopy–Padé method.

Findings

The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.

Research limitations/implications

The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.

Social implications

Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.

Originality/value

In this study, the authors are using two modified methods.

Citation

Abbasbandy, S., Shivanian, E., Vajravelu, K. and Kumar, S. (2017), "A new approximate analytical technique for dual solutions of nonlinear differential equations arising in mixed convection heat transfer in a porous medium", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 2, pp. 486-503. https://doi.org/10.1108/HFF-11-2015-0479