Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy-Brinkman-Forchheimer model

Abstract

Purpose

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

Design/methodology/approach

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

Findings

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

Originality/value

The obtained results are new and presented for the first time in the literature.

Citation

Zhang, L., Bhatti, M.M. and Michaelides, E.E. (2021), "Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy-Brinkman-Forchheimer model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 8, pp. 2623-2639. https://doi.org/10.1108/HFF-09-2020-0566