Transient Mixed Convection Flow of A Second-Grade Visco-Elastic Fluid over a Vertical Surface

A S S Shatnawi,A J J Chamkha,R A A Damseh,H M M Duwairi

doi:10.15388/na.2008.13.2.14577

Abstract

The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.

Highlights

Numerous applications of viscoelsatic fluids in several manufacturing processes have led to renewed interest among researchers to investigate viscoelsatic boundary layer flow over a stretching plastic sheet, Rajagopal et al [1, 2], Dandapat and Gupta [3], Rollins and Vajravelu [4], Anderson [5], Lawrence and Rao [6], Char [7] and Rao [8]
Hassanien reported results for elasticity or Deboch numbers up to 0.2 and concluded that the wall skin friction coefficient is increased whenever a fluid exhibits elasticity, a prediction which is undesirable from an industrial standpoint because it translates into a larger driving force or torque to withdraw the surface
Since in reality most of the fluids considered in industrial applications are more nonNewtonian in nature, especially of viscoelsatic type than viscous type, we extend the mixed convection heat transfer work to viscoelsatic fluids flow and heat transfer

Summary

Introduction

Numerous applications of viscoelsatic fluids in several manufacturing processes have led to renewed interest among researchers to investigate viscoelsatic boundary layer flow over a stretching plastic sheet, Rajagopal et al [1, 2], Dandapat and Gupta [3], Rollins and Vajravelu [4], Anderson [5], Lawrence and Rao [6], Char [7] and Rao [8]. The final equation was in the form of a forth-order non-linear ordinary differential equation that can not be solved analytically, or even numerically, due to the lack of sufficient boundary conditions. To circumvent this problem, Hassanien utilized perturbation technique [12] to reduce the governing equation into a system of two third-order differential equations which could be solved with the available boundary conditions. Say the range of applicability of Hassanien work is quite limited Another shortcoming of Hassanien work is in the use of the second grade model to represent viscoelsatic fluids. Numerical results for the velocity, and temperature profiles as well as the local coefficient of friction and local Nusselt number under the effect of viscoelsatic parameter, are presented

Problem formulation

D Dt dij

Boundary conditions on velocity

Results and discussion

Conclusions