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Flow and heat transfer for a power-law electrically conducting fluid flowing between parallel plates under transverse magnetic field with viscous dissipation

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Abstract

The flow and heat transfer problem with viscous dissipation for electrically conducting non-Newtonian fluids with power-law model in the thermal entrance region of two parallel plates with magnetic field under constant heat flux and constant wall temperature conditions has been studied. The governing equations have been solved numerically using quasilinearization technique and implicit finite-difference scheme. It has been found that the effect of viscous dissipation on heat transfer is quite significant for heating and cooling conditions at the wall.

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Abbreviations

a:

half of the distance between the plates

bx :

induced magnetic field

bx :

dimensionless induced magnetic field

B0 :

applied magnetic field

Br:

Brinkman number

Cv :

specific heat at constant volume

Ey :

electric field alongy-direction

h:

enthalpy

Hm:

Hartmann number defined by equation (3b)

y:

current iny-direction

Jy :

dimensionless current iny-direction

K:

dimensionless parameter defined by equation (3a)

k1 :

thermal conductivity

n:

index of the power-law model

Nu:

Nusselt number defined by equation (15)

px :

pressure gradient along axial direction given by (3c)

Px :

dimensionless pressure gradient in axial direction defined by equation (3b)

qw :

wall heat flux

Re:

Reynold’s number defined by equation (3b)

Rm:

magnetic Reynold’s number

T:

temperature

Tb :

bulk temperature

u:

axial velocity

ū:

average axial velocity defined by equation (3a)

U:

dimensionless axial velocity

Ū:

dimensionless axial velocity defined by equation (11)

z:

vertical distance

Z:

dimensionless vertical distance

θ:

dimensionless temperature

θb :

dimensionless bulk temperature

μ:

viscosity

μ1 :

magnetic permeability

ξ:

dimensionless axial distance

ρ:

density

σ:

electrical conductivity

τ:

shear stress.

′:

prime denotes differentiation with respect toZ.

c:

critical value

o:

inlet condition

w:

wall condition

References

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Author notes

  1. K. M. Sundaram

    Present address: Laboratorium Voor Petrochemische Technick, Krijgalaan 271, 9000, Ghent, Belgium

Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Science, 560012, Bangalore

    K. M. Sundaram & G. Nath

  2. Department of Chemical Engineering, Indian Institute of Science, 560012, Bangalore

    K. M. Sundaram

Authors
  1. K. M. Sundaram
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  2. G. Nath
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Sundaram, K.M., Nath, G. Flow and heat transfer for a power-law electrically conducting fluid flowing between parallel plates under transverse magnetic field with viscous dissipation. Proc. Indian Acad. Sci. 83, 188–201 (1976). https://doi.org/10.1007/BF03051339

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  • DOI: https://doi.org/10.1007/BF03051339

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