The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets

Abstract

a b s t r a c tIn this study, by means of homotopy perturbation method (HPM) an approximate analytical solution of the magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous stretching sheet is obtained. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. HPM produces analytical expressions for the solution of nonlinear differential equations. The obtained analytic solution is in the form of an infinite power series. In this work, the analytical solution obtained by using only two terms from HPM solution. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems. Also it is shown that this method coincides with homotopy analysis method (HAM) for the studied problem.

Heat transfer and MHD flow of non-newtonian Maxwell fluid through a parallel plate channel: analytical and numerical solution

“…Hayat et al (2006) was among the first who studied the MHD flow of an upper convected Maxwell (UCM) fluid over a porous stretching sheet using homotopy analysis method (HAM). Raftari and Yildirim (2010) proposed a novel analytical model (homotopy perturbation method (HPM) to analyze the same problem investigated by (Hayat et al, 2006). Switching from the non-rotating flow to rotating one was made by Sajid et al (2011).…”

“…They concluded that the rotation parameter can help in controlling the thickness of boundary layer. Compared to the analytical techniques used by (Hayat et al, 2006;Raftari and Yildirim, 2010), Abel et al (2012) proposed a numerical scheme, fourth order RungeKutta method, to examine the MHD flow for UCM Maxwell over a stretching sheet. These studies were focused on the noslip boundary condition imposed along the flat plate.…”

Magnetohydrodynamic flow of linear visco-elastic fluid model above a shrinking/stretching sheet: A series solution

“…The literature on the topic is quite extensive and, hence, cannot be described here in detail. However, some most recent works of eminent researchers regarding the UCM uid may be mentioned [8][9][10][11][12][13][14][15][16][17][18][19].…”

Simulations for Maxwell fluid flow past a convectively heated exponentially stretching sheet with nanoparticles

“…Hayat et al 5 obtained homotopy based series solution for stagnation-point flow of Maxwell fluid towards a stretching sheet. After these pioneering works, researchers have widely discussed two-and three-dimensional flows of Maxwell fluids in different geometries (see Aliakbar et al, 6 Raftari and Yildirim, 7 Hayat et al, 8,9 Mukhopadhyay, 10 Abel et al, 11 Hayat et al, 12 Shateyi 13 and Mushtaq et al 14 ).…”