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MHD Flow and Heat Transfer Over a Slender Elastic Permeable Sheet in a Rotating Fluid with Hall Current

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Abstract

Magnetohydrodynamic flow and heat transfer over a stretching sheet with a variable thickness in a rotating fluid with Hall current is investigated. Both analytical and numerical methods are employed to solve the governing coupled nonlinear differential equations. The analytical solutions are obtained through the optimal homotopy analysis method where the numerical solutions are computed by a second-order finite difference scheme. The solutions for the non-dimensional velocity and temperature fields are obtained and presented graphically for various physical parameters. The accuracy of the analytical solution is verified by plotting the residual errors and by comparing solutions with available results in the literature for some special cases. The Hall current gives rise to a cross flow. The rotating fluid frame and the wall transpiration (suction/injection) can have strong effects on the shear stress and the Nusselt number.

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Abbreviations

\(B_0 \) :

Uniform magnetic field

\(C_p \) :

Specific heat at constant pressure

\(C_{f_x } ,C_{f_z } \) :

Skin friction coefficient in the x- and z-directions

e :

Electric charge

f, h :

Dimensionless velocities or real functions

J :

Current density vector

K :

Thermal conductivity

\(K_\infty \) :

Thermal conductivity of the fluid far away from the sheet

l :

Characteristic length

m :

Hall effect parameter

Mn :

Magnetic parameter

n :

Velocity power index parameter

\(n_{e}\) :

Electron number density

\(Nu_x \) :

Nusselt number

\(\Pr \) :

Prandtl number

\(p_{e}\) :

Electronic pressure

\(\hbox {Re}_\mathrm{x}\) :

Local Reynolds number

r :

Wall temperature parameter

\(\Delta T\) :

Sheet temperature

T :

Temperature

\(T_w \) :

Temperature of the plate

\(T_\infty \) :

Ambient temperature or temperature away from the wall

u, v, w :

Velocity components in the x-, y- and z-directions

\(U_w ( x )\) :

Stretching velocity

\(U_0 \) :

Reference velocity

V :

Velocity vector

x, y, z :

Cartesian coordinates

\(\eta ,\xi \) :

Similarity variables

\(\alpha \) :

Wall thickness parameter

\(\Omega \) :

Angular velocity

\(\beta \) :

Fluid rotation parameter \(\beta =4\Omega /\left[ {\left( {n+1} \right) \rho U_0 } \right] \)

\(\theta \) :

Dimensionless temperature \(\theta =\left( {T-T_\infty } \right) /\left( {T_w -T_\infty } \right) \)

\(\nu \) :

Kinematic viscosity away from the sheet

\(\rho \) :

Constant fluid density

\(\sigma \) :

Electric conductivity

\(\mu \) :

Dynamic viscosity

\(\psi \) :

Stream function

\(\phi \) :

Kummers’ function

\(\infty \) :

Condition at infinity

w :

Condition at the wall

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Acknowledgements

This paper was finalized when K.V.P. was visiting the University of Hong Kong in May 2016. Financial support by the Research Grants Council of the Hong Kong Special Administrative Region, China, through General Research Fund Project No. 17206615 is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816, USA

    K. Vajravelu

  2. Department of Mathematics, VSK University, Vinayaka Nagar, Bellary, Karnataka, 583 105, India

    K. V. Prasad & Hanumesh Vaidya

  3. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    Chiu-On Ng

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Correspondence to Chiu-On Ng.

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Vajravelu, K., Prasad, K.V., Ng, CO. et al. MHD Flow and Heat Transfer Over a Slender Elastic Permeable Sheet in a Rotating Fluid with Hall Current. Int. J. Appl. Comput. Math 3, 3175–3200 (2017). https://doi.org/10.1007/s40819-016-0291-3

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  • DOI: https://doi.org/10.1007/s40819-016-0291-3

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