Hall Current and Joule Heating Effects on Flow of Couple Stress Fluid with Entropy Generation

A A Opanuga,S A Bishop,H I Okagbue,O O Agboola

doi:10.48084/etasr.1850

A A Opanuga, S A Bishop + Show 2 more

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https://doi.org/10.48084/etasr.1850

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Abstract

In this work, an analytical study of the effects of Hall current and Joule heating on the entropy generation rate of couple stress fluid is performed. It is assumed that the applied pressure gradient induces fluid motion. At constant velocity, hot fluid is injected at the lower wall and sucked off at the upper wall. The obtained equations governing the flow are transformed to dimensionless form and the resulting nonlinear coupled boundary value problems for velocity and temperature profiles are solved by Adomian decomposition method. Analytical expressions for fluid velocity and temperature are used to obtain the entropy generation and the irreversibility ratio. The effects of Hall current, Joule heating, suction/injection and magnetic field parameters are presented and discussed through graphs. It is found that Hall current enhances both primary and secondary velocities and entropy generation. It is also interesting that Joule heating raises fluid temperature and encourages entropy production. On the other hand Hartman number inhibited fluid motion while increase in suction/injection parameter resulted into a shift in flow symmetry.

Highlights

The study of hydromagnetic flow has been extensively investigated in the past years due to its applications in MHD generators, flow control, shock damping in car absorbers, nuclear reactors, plasma studies, purifications of metal from non-metal enclosures, geothermal energy extractions, polymer technology and metallurgy
To explain the effect of Hall current (m), Joule heating (J), suction/injection (s) and magnetic (M) parameters on velocity profile, the non-dimensional velocity u and w against y is presented in Figures 1 to 3
It is apparent from these figures that fluid motion is enhanced as hall current increases

Summary

INTRODUCTION

The study of hydromagnetic flow has been extensively investigated in the past years due to its applications in MHD generators, flow control, shock damping in car absorbers, nuclear reactors, plasma studies, purifications of metal from non-metal enclosures, geothermal energy extractions, polymer technology and metallurgy. Author in [3] considered the effect of a uniform magnetic field on the Eckman layer over an infinite horizontal plate at rest relative to an electrically conducting liquid rotating with uniform angular velocity about a vertical axis while authors in [4] analyzed the combined effect of free and forced convection on MHD flow in a rotating porous channel, authors in [5] investigated the radiation effect of magnetohydrodynamics flow of gas between concentric spheres. To the best of our knowledge similar study has not yet been reported in literature, various factors responsible for the entropy production have been studied, for instance in [17] authors considered effects of velocity slip and temperature jump on the entropy generation in MHD flow over a porous rotating disk. The method has been used to analyze various linear and nonlinear problems such as the fractional-order differential equations [32], the time dependent Edem–Fowler type equation [33], the Navier–Stokes equations [34], the evolution model [35], the Flierl–Petviashivili equation [36], the fourth-order wave equation [37], the peristaltic transport model [38], the Fokker–Planck equation [39] and the Bratu’s problem [40]

PROBLEM FORMULATION

Results Verification

RESULTS AND DISCUSSION

CONCLUSION