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Magnetohydrodynamic (MHD) flow of a second grade fluid in a channel with porous wall

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Abstract

An analysis has been carried out to study the effect of magnetic field on an electrically conducting fluid of second grade in a parallel channel. The coolant fluid is injected into the porous channel through one side of the channel wall into the other heated impermeable wall. The combined effect of inertia, viscous, viscoelastic and magnetic forces are studied. The basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations by using appropriate transformations for velocity and temperature. Numerical solutions of these equations are obtained with the help of Runge-Kutta fourth order method in association with quasi-linear shooting technique. Numerical results for velocity field, temperature field, skin friction and Nusselt number are presented in terms of elastic parameter, Hartmann number, Prandtl number and Reynolds number. Special case of our results is in good agreement with earlier published work.

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Abbreviations

v :

Dimensional velocity vector

T :

Dimensional temperature

p :

Pressure

c :

Specific heat of the fluid at constant pressure

x,y :

Dimensional space variables

k :

Thermal conductivity

h :

Heat transfer coefficient

M:

Hartmann number

Pr :

Prandtl number

F :

Lorentz force

B :

Magnetic field

E :

Electric field

J :

Current density

I :

Identity tensor

A 1,A 2 :

First two Rivlin Erickson tensors

t :

Dimensional time variable

K :

Non-dimensional viscoelastic parameter

Nu :

Nusselt number

Re :

Reynolds number

ρ :

Density

σ 0 :

Electric conductivity

η :

Non-dimensional space variable

σ :

Stress tensor

μ :

Dynamic viscosity

ν:

Kinematic viscosity

θ :

Non-dimensional temperature

α i (i=1,2):

Material constants

∇:

Nabla operator

∇2 :

Laplacian operator

d/dt :

Material time derivative

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Authors and Affiliations

  1. Dept. of Maths, NM Institute of Engineering and Technology, Bhubaneswar, 751019, India

    S. K. Parida

  2. Department of Mathematics, NIT Calicut, Calicut, 673601, India

    S. Panda

  3. Dept. of Physics, College of Basic Sc. and Humanities, OUAT, Bhubaneswar, 751003, India

    M. Acharya

Authors
  1. S. K. Parida
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  2. S. Panda
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  3. M. Acharya
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Correspondence to S. Panda.

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Parida, S.K., Panda, S. & Acharya, M. Magnetohydrodynamic (MHD) flow of a second grade fluid in a channel with porous wall. Meccanica 46, 1093–1102 (2011). https://doi.org/10.1007/s11012-010-9368-y

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