Heat transfer in a stagnation point flow of a second grade fluid over a stretching surface with heat generation/absorption

Ali Hazem,Mostafa Abdeen,Mahmoud Menna

doi:10.5937/kgjsci1436041h

Abstract

The heat transfer in a steady planar stagnation point flow of an incompressible non-Newtonian second grade fluid impinging on a permeable stretching surface with heat generation or absorption is examined. The governing nonlinear momentum and energy equations are solved numerically using finite differences. The influence of the characteristics of the non-Newtonian fluid, the surface stretching velocity, the heat generation/ absorption coefficient, and Prandtl number on both the flow and heat transfer is reported.

Highlights

The flow of a viscous incompressible fluid near a planar stagnation point is a classical problem in fluid mechanics which was first handled by HIEMENZ (1911) who demonstrated that the governing Navier-Stokes partial differential equations can be transformed to an ordinary differential equation of third order using similarity transformation
More detailed solutions were later given by PRESTON (1946) while an approximate solution to the problem of uniform suction is obtained by ARIEL (1994)
The heat transfer in a steady planar stagnation point flow of an incompressible nonNewtonian second grade fluid impinging on a permeable stretching surface with heat generation/ absorption was studied

Summary

INTRODUCTION

The flow of a viscous incompressible fluid near a planar stagnation point is a classical problem in fluid mechanics which was first handled by HIEMENZ (1911) who demonstrated that the governing Navier-Stokes partial differential equations can be transformed to an ordinary differential equation of third order using similarity transformation. CRANE (1970) obtained a similarity solution in closed form for steady planar incompressible boundary layer flow caused by the stretching of a sheet which moves in its own plane with a velocity varying linearly with the distance from a fixed point. The heat transfer in a steady planar stagnation point flow of an incompressible non-Newtonian second grade fluid impinging on a permeable stretching surface is studied with heat generation or absorption. The numerical solution gives the flow and heat characteristics for the whole range of the non-Newtonian fluid parameter, the stretching velocity, the heat generation/absorption coefficient and the Prandtl number. A similarity solution exists if the wall and stream temperatures, T w and T∞ are constants–a realistic approximation in typical stagnation point heat transfer problems (WHITE, 1991). Convergence is assumed when the ratio of every one of f, f ′ , f ′′ , or f ′′′ for the last two approximations differed from unity by less than 10-5 at all values of η in 0

RESULTS AND DISCUSSION

CONCLUSIONS

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