A series solution of the boundary value problem arising in the application of fluid mechanics

Abstract

Purpose

This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM).

Design/methodology/approach

The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs.

Findings

It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number.

Originality/value

To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

Citation

Khan, Y. (2018), "A series solution of the boundary value problem arising in the application of fluid mechanics", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 10, pp. 2480-2490. https://doi.org/10.1108/HFF-11-2017-0474