Swirling flow of couple stress fluid due to a rotating disk

Najeeb Alam Khan,Nadeem Alam Khan,Farah Naz,Saif Ullah

doi:10.1515/nleng-2017-0062

Najeeb Alam Khan, Nadeem Alam Khan + Show 2 more

Open Access

https://doi.org/10.1515/nleng-2017-0062

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Abstract

AbstractThe main objective of the present investigation is to examine the couple stress fluid flow occurring as a result of rotation of a disk. On implementing a suitable transformation, the governing system of partial differential equations (PDEs) is converted into nonlinear differential equations of a single independent variable. These equations are solved analytically by virtue of the Homotopy Analysis Method (HAM) which gives solutions in the form of a series. The solution of most of the governing problems is determined in terms of the absolute exponential and decaying functions by means of this powerful technique. To support analytic results, some graphs are plotted for determining the convergence of the solution. Also the graphical interpretation of velocity profiles corresponding to the effects of pertinent parameters are shown and discussed in detail. The numerical results are calculated for evaluation of the influence of fluid parameter. It can also be anticipated that the radial and axial velocity components show decreasing behavior due to rise in the values of couple stress parameter which conflict the behavior of the tangential component of velocity.

Highlights

The ow which appears due to a rotating disk has gained a signi cant amount of attention in many mathematical models and has become an intriguing topic in recent in-The pioneering work related to the Newtonian uid ow as a result of an in nite rotating disk was examined by Karman [1] in latent ambient
A comprehensive study related to the time-dependent boundary layer ow of a magnetic nano uid over a rotating disk with the combined e ects of thermal radiation and variable viscosity has been encountered by Joshi et al [4]
This ow has been discussed in the presence of a porous medium and inspected the e ects of geothermal viscosity with viscous dissipation.Further, for inspecting the in uence of porosity of the medium, the viscous incompressible uid ow in the presence of temperature-dependent viscosity has been presented by Attia [6]

Summary

Introduction

The pioneering work related to the Newtonian uid ow as a result of an in nite rotating disk was examined by Karman [1] in latent ambient. An inclusive e ort to examine the solution of the problem governing the time dependent boundary layer ow of magnetic nano uids due to rotation of stretchable plate has been conferred by Ram et al [5]. This ow has been discussed in the presence of a porous medium and inspected the e ects of geothermal viscosity with viscous dissipation.Further, for inspecting the in uence of porosity of the medium, the viscous incompressible uid ow in the presence of temperature-dependent viscosity has been presented by Attia [6]. The solution of the steady laminar ow of an incompressible viscous electrically conducting uid on account of the ro-

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Mathematical formulation of the problem

The convergence of the aforementioned series given in

Graphical and numerical results and discussion

Findings

The thickness δ for couple