Mixed convection Darcy flow in a vertical porous annulus around a straight electric cable is investigated. It is assumed that the flow is fully developed and parallel. Moreover, the Boussinesq approximation is used. The magnetic field with a steady electric current in the cable is radially varying according to the Biot–Savart law. Two flow regimes are investigated. The first is mixed convection with negligible effects of internal heat generation due to Joule heating and viscous dissipation. The second is forced convection with important effects of heat generation. In these two special cases, closed form expressions of the velocity profile and of the temperature profile, as well as of the flow rate and the Nusselt number, are obtained. The main features of these solutions are discussed.

1.
Nield
,
D. A.
, 1999, “
Modeling the Effects of a Magnetic Field or Rotation on Flow in a Porous Medium: Momentum Equation and Anisotropic Permeability Analogy
,”
Int. J. Heat Mass Transfer
,
42
, pp.
3715
3718
. 0017-9310
2.
Al–Nimr
,
M. A.
, and
Hader
,
M. A.
, 1999, “
MHD Free Convection Flow in Open–Ended Vertical Porous Channels
,”
Chem. Eng. Sci.
,
54
, pp.
1883
1889
. 0009-2509
3.
Chamkha
,
A. J.
, 2001, “
Unsteady Laminar Hydromagnetic Flow and Heat Transfer In Porous Channels With Temperature–Dependent Properties
,”
Int. J. Numer. Methods Heat Fluid Flow
,
11
, pp.
430
448
. 0961-5539
4.
Geindreau
,
C.
, and
Auriault
,
J. -L.
, 2002, “
Magnetohydrodynamic Flows in Porous Media
,”
J. Fluid Mech.
,
466
, pp.
343
363
. 0022-1120
5.
Mahmud
,
S.
, and
Fraser
,
R. A.
, 2004, “
Magnetohydrodynamic Free Convection and Entropy Generation in a Square Porous Cavity
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
3245
3256
.
6.
Postelnicu
,
A.
, 2004, “
Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection From Vertical Surfaces in Porous Media Considering Soret and Dufour Effects
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
1467
1472
.
7.
Partha
,
M. K.
,
Murthy
,
P. V. S. N.
, and
Raja Sekhar
,
G. P.
, 2006, “
Soret and Dufour Effects in a Non-Darcy Porous Medium
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
605
610
.
8.
Rakoto Ramambason
,
D. S.
, and
Vasseur
,
P.
, 2007, “
Influence of a Magnetic Field On Natural Convection in a Shallow Porous Enclosure Saturated With A Binary Fluid
,”
Acta Mech.
,
191
, pp.
21
35
. 0001-5970
9.
Bhadauria
,
B. S.
, 2007, “
Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries
,”
ASME J. Heat Transfer
0022-1481,
129
, pp.
835
843
.
10.
Bhadauria
,
B. S.
, 2008, “
Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
052601
.
11.
Makinde
,
O. D.
, and
Sibanda
,
P.
, 2008, “
Magnetohydrodynamic Mixed-Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
112602
.
12.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006,
Convection in Porous Media
,
3rd ed.
,
Springer
,
New York
.
13.
Morton
,
B. R.
, 1960, “
Laminar Convection in Uniformly Heated Vertical Pipes
,”
J. Fluid Mech.
0022-1120,
8
, pp.
227
240
.
14.
Erdélyi
,
A.
,
Magnus
,
W.
,
Oberhettinger
,
F.
, and
Tricomi
,
F. G.
, 1953,
Higher Transcendental Functions
, Vol.
1
,
McGraw-Hill
,
New York
, p.
31
.
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