Magnetohydrodynamic Boundary Layer Flow of a Viscoelastic Fluid Past a Nonlinear Stretching Sheet in the Presence of Viscous Dissipation Effect

Ahmad Banji Jafar,Imran Ullah,Sharidan Shafie

doi:10.3390/coatings9080490

Abstract

This paper numerically investigates the viscous dissipation effect on the boundary layer flow of an electrically-conducting viscoelastic fluid (Walter’s B liquid) past a nonlinear stretching sheet. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. The transformed equations are then solved using the Keller box method. A careful evaluation of the influence of the pertinent parameters on the velocity field and temperature distributions through various plots is done for the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. The computed coefficient of skin friction, the rate of heat transfer (Nusselt number), and the temperature at the wall are also presented in tabular form. It is revealed from this table that the magnitude of the heat transfer is reduced with the increase in the Eckert number E c , viscoelastic parameter K, and magnetic parameter M for the PST case by about 12%, 20%, and 29%, respectively. Similarly, the temperature at the wall for the PHF case also decreases with the increase in E c and M by about 8% and 24%, respectively. It is obvious that the application of the PST condition excels at keeping the viscoelastic fluid warmer than the PHF condition. This implies that applying the PHF condition is better for cooling the sheet faster. The temperature at the wall is unchanged with the changes in the pertinent parameters in the PST case, and it is ascertained that the present results are in close agreement with the previous published results.

Highlights

The existence of the closed-form solution, the simplicity of the mathematical expression, and the numerous applications, such as plastic sheet extrusion, drawing of plastic films, metallic plate cooling, and the glass blowing of the boundary layer flow past a stretching sheet, have received much attention in recent years
K, magnetic parameter M, Eckert number Ec, and Prandtl number Pr, on boundary flow of an electrically-conducting viscoelastic fluid past a nonlinear stretching sheet, results from the graphs for velocity and temperature profiles, as well as the numerical results of the skin friction coefficient and heat transfer rate for the prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are illustrated in tables
The surface temperature reduced with the increase in the Pr for the PHF case

Summary

Introduction

The existence of the closed-form solution, the simplicity of the mathematical expression, and the numerous applications, such as plastic sheet extrusion, drawing of plastic films, metallic plate cooling, and the glass blowing of the boundary layer flow past a stretching sheet, have received much attention in recent years. The desired final product of the production process largely depends on the rate at which the sheet cools. The rate of cooling is fundamentally influenced by the type of fluid adjacent to the boundary layer surface [1,2]. The rate at which the sheet is stretched and the rate at which it cools are the two major mechanisms that influence the mechanical properties of the desired product. The behaviors of the fluid flows and heat transfer induced by elongating or a moving sheet play a vital role in an industrial process [3]

Methods

Results

Conclusion