Analytical and numerical approaches for Falkner–Skan flow of MHD Maxwell fluid using a non-Fourier heat flux model

Abstract

Purpose

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.

Design/methodology/approach

Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.

Findings

The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.

Research limitations/implications

An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.

Originality/value

Current problem even in case of Newtonian fluid has not been attempted previously.

Citation

Abbasbandy, S. and Mustafa, M. (2018), "Analytical and numerical approaches for Falkner–Skan flow of MHD Maxwell fluid using a non-Fourier heat flux model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 7, pp. 1539-1555. https://doi.org/10.1108/HFF-08-2017-0316