Pulsating flow of an incompressible micropolar fluid between permeable beds

Punnamchandar Bitla,Telikicherla Kandala Venkatacharyulu Iyengar

doi:10.15388/na.18.4.13969

Punnamchandar Bitla, Telikicherla Kandala Venkatacharyulu Iyengar

Open Access

https://doi.org/10.15388/na.18.4.13969

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Abstract

The paper deals with the pulsating flow of an incompressible micropolar fluid through a channel bounded by permeable beds. The fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by micropolar fluid flow equations and that in the permeable regions by Darcy law. The Beavers–Joseph (BJ) slip boundary conditions are used at the interfaces of the permeable beds. The governing equations are solved analytically and the expressions for velocity, microrotation, mass flux and shear stress are obtained. The effects of diverse parameters on the velocity and microrotation are studied numerically and the results are presented through graphs.

Highlights

Pulsating flow is a special kind of unsteady flow in which a periodic variation in flow velocity is superimposed on steady velocity
As Pj increases, the shear stress at the lower permeable bed (LPB) is decreasing while it is increasing at the upper permeable bed (UPB)
0.621639 0.156648 In Table 5, we notice that for ωt = 0 and π/4, as the coupling parameter m is increasing, the shear stress is increasing at the LPB while it is decreasing at the UPB

Summary

Introduction

Pulsating flow is a special kind of unsteady flow in which a periodic variation in flow velocity is superimposed on steady velocity. In the case of flow past porous medium, Beavers and Joseph [10] have shown that the usual no-slip condition at the porous boundaries is no longer valid and they have postulated the existance of a slip at the interface of a permeable boundary resulting in the condition called BJ slip condition According to this condition, the Poiseuille velocity in the channel and the Darcy’s velocity in the porous wall can be coupled through the following equation: du α dy. To the extent the present authors have surveyed the pulsatile flow of an incompressible micropolar fluid between two permeable beds has not been studied so far. In this paper we have chosen to study the flow of an incompressible micropolar fluid between permeable beds, because of its importance in many industrial problems and its www.mii.lt/NA. The effects of the pertinent parameters on the velocity and microrotation are studied numerically and the results are presented through graphs

Mathematical formulation

Non-dimensionalization of the flow quantities

Steady flow solution

Results and discussion

Conclusions