Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

Diksha Gupta,Bani Singh,Lokendra Kumar

doi:10.1155/2014/362351

Abstract

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements.

Highlights

In the last few decades, the interest for non-Newtonian fluids has considerably increased due to their connection with applied sciences
The present paper investigates the unsteady mixed convection flow and heat transfer of an incompressible micropolar fluid over a vertical shrinking sheet with time-dependent suction at the sheet
The present study has addressed theoretically and numerically the unsteady mixed convection flow and heat transfer of an incompressible micropolar fluid over a porous shrinking sheet in the presence of viscous dissipation

Summary

Introduction

In the last few decades, the interest for non-Newtonian fluids has considerably increased due to their connection with applied sciences The motion of these fluids plays essential role in theory and in many industrial processes. In the micropolar fluid theory, two new variables to the velocity are added which were not presented in the Navier-Stokes model. These variables are microrotations that represent spin and microinertia tensors which describe the distribution of atoms and molecules inside the microscopic fluid particles. Later Eringen [4] extended the theory of micropolar fluids to thermo-microfluids This theory takes into account thermal effects, that is, heat conduction, convection, and dissipation. These effects were not included in the classical field theories

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Conclusion