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.

Issue Section:
Technical Briefs
Keywords:
porous media, mixed convection, viscous dissipation, magnetohydrodynamics, analytical solution, cables (electric), convection, flow through porous media, magnetohydrodynamics
Topics:
Annulus, Cables, Energy dissipation, Flow (Dynamics), Heat, Heating, Magnetic fields, Magnetohydrodynamics, Mixed convection, Porous materials, Joules, Fluids, Forced convection, Temperature, Electric current
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Copyright © 2009
 by American Society of Mechanical Engineers
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