Time varying rotating disk flow with heat transfer of a non-Newtonian fluid in porous medium

Ali Hazem,Mahmoud Menna,Mostafa Abdeen

doi:10.5937/kgjsci1436033h

Abstract

Time varying flow through a porous medium of an incompressible viscous non-Newtonian fluid due to a rotation of an infinite rotating disk is studied with heat transfer. Numerical solutions using finite differences are obtained for the nonlinear partial differential equations which govern the hydrodynamics and energy transfer. The effect of the porosity of the medium and the characteristics of the non-Newtonian fluid on the velocity and temperature distributions is considered.

Highlights

The steady flow due to an infinite rotating disk was handled by VON KARMAN in 1921 [1] who gave a formulation for the problem and introduced his famous transformations which reduced the governing partial differential equations to ordinary differential equations
In this study the time varying flow of a non-Newtonian fluid induced by a rotating disk with heat transfer in a porous medium was studied
The results indicate the restraining effect of the porosity on the flow velocities and the thickness of the boundary layer

Summary

INTRODUCTION

The steady flow due to an infinite rotating disk was handled by VON KARMAN in 1921 [1] who gave a formulation for the problem and introduced his famous transformations which reduced the governing partial differential equations to ordinary differential equations. The time varying laminar flow through a porous medium of an incompressible viscous non-Newtonian fluid due to the uniform rotation of an infinite disk is studied with heat transfer where the Darcy model is assumed [10,11,12]. The governing nonlinear partial differential equations are integrated numerically using the finite difference approximations The effect of the porosity of the medium and the characteristics of the non-Newtonian fluid on the flow and heat transfer distributions is discussed. Equations (13)-(15) represent coupled system of non-linear partial differential equations which are solved numerically under the initial and boundary conditions (9), Eq (16) can be obtained using the boundary conditions (12) using the finite difference approximations. Convergence of the scheme is assumed when all of the variables F, G, H, θ, ∂F/∂η, ∂G/∂η, and ∂θ/∂η for the last two approximations differs from unity by less than 10-6 for all values of η in 0

RESULTS AND DISCUSSION

CONCLUSION

References: