Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature.

Samiulhaq Samiulhaq,Dumitru Vieru,Sohail Ahmad,Sharidan Shafie,Ilyas Khan,Derek Abbott

doi:10.1371/journal.pone.0088766

Abstract

Magnetic field influence on unsteady free convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.

Highlights

The natural convection heat transfer from a vertical plate to a fluid has applications in many industrial processes
Samiulhaq et al [7] discussed the influence of radiation and porosity on the unsteady magnetohydrodynamic (MHD) flow past an infinite vertical oscillating plate with uniform heat flux in a porous medium
Keeping in mind the importance of shear stress on the boundary, Fetecau et al [8] reinvestigated the problem of Samiulhaq et al [7] by considering shear stress on the boundary

Summary

Introduction

The natural convection heat transfer from a vertical plate to a fluid has applications in many industrial processes. We establish exact solutions for velocity and temperature corresponding to the natural convection flow of a second grade fluid near an infinite vertical plate with ramped wall temperature. Let us consider the unsteady MHD flow of an incompressible second grade fluid near an infinite vertical plate with ramped wall temperature. From velocity and temperature fields, the expressions for Nusselt number and skin friction can be determined They are measures of the heat transfer rate and shear stress at the boundary. Te solutions corresponding to the flow of a second grade fluid with ramped wall temperature or constant temperature on the boundary in the absence of magnetic or porous effects can be immediately obtained from the general solutions (21) and (26) by making M2?0 or K??, respectively.

Limitations of the Study and Future Recommendations

Conclusions