The unsteady Couette flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the magnetic field and the uniform suction and injection on both the velocity and temperature distributions is examined.

1.
Hartmann, J. and Lazarus, F., 1937, “Kgl. Danske Videnskab,” Selskab, Mat.-Fys. Medd. 15 (6, 7).
2.
Tao
I. N.
,
1960
, “
Magnetohydrodynamic effects on the formation of Couette flow
,”
J. of Aerospace Sci.
27
, pp.
334
342
.
3.
Alpher
R. A.
,
1961
, “
Heat transfer in magnetohydrodynamic flow between parallel plates
,”
Int. J. Heat and Mass Transfer
3
, pp.
108
108
.
4.
Sutton, G.W. and Sherman, A., 1965, Engineering Magnetohydrodynamics, McGraw-Hill Book Co.
5.
Cramer, K. and Pai, S.-I., 1973, Magnetofluid dynamics for engineers and applied physicists, McGraw-Hill Book Co. 1973.
6.
Nigam
S. D.
and
Singh
S. N.
,
1960
, “
Heat transfer by laminar flow between parallel plates under the action of transverse magnetic field
,”
Quart. J. Mech. Appl. Math.
13
, pp.
85
85
.
7.
Tani
I.
,
1962
, “
Steady motion of conducting fluids in channels under transverse magnetic fields with consideration of Hall effect
,”
J. of Aerospace Sci.
29
, pp.
287
296
.
8.
Soundalgekar
V. M.
,
Vighnesam
N. V.
and
Takhar
H. S.
,
1979
, “
Hall and ion-slip effects in MHD Couette flow with heat transfer
,”
IEEE Trans. Plasma Sci.
PS-7
(
3
), pp.
178
182
.
9.
Soundalgekar
V. M.
and
Uplekar
A. G.
,
1968
, “
Hall effects in MHD Couette flow with heat transfer
,”
IEEE Trans. Plasma Sci.
PS-14
(
5
), pp.
579
583
.
10.
Attia
H. A.
,
1999
, “
Transient MHD flow and heat transfer between two parallel plates with temperature dependent viscosity
,”
Mech. Res. Comm.
26
(
1
), pp.
115
121
.
11.
Schlichting, H., 1968, Boundary layer theory, McGraw-Hill Book Co. 1968.
12.
Spiegel, M.R., 1986, Theory and problems of Laplace transform, McGraw-Hill Book Co. 1986.
13.
Ames, W.F., 1977, Numerical solutions of partial differential equations, 2nd ed., Academic Press, New York.
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