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Technical Briefs

Closed Form Solutions For Mixed Convection With Magnetohydrodynamic Effect in a Vertical Porous Annulus Surrounding an Electric Cable

[+] Author and Article Information
A. Barletta

Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Via dei Colli 16, I-40136 Bologna, Italyantonio.barletta@mail.ing.unibo.it

E. Magyari1

Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Via dei Colli 16, I-40136 Bologna, Italymagyari@bluewin.ch

S. Lazzari

Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Via dei Colli 16, I-40136 Bologna, Italystefano.lazzari@mail.ing.unibo.it

I. Pop

Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romaniapop.ioan@yahoo.co.uk

1

On leave from Institute of Building Technology, ETH–Zürich, Switzerland.

J. Heat Transfer 131(6), 064504 (Apr 10, 2009) (4 pages) doi:10.1115/1.3085874 History: Received February 27, 2008; Revised December 03, 2008; Published April 10, 2009

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.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Special case Br→0: plots of um versus M, for γ=3 and increasing values of Ξ

Grahic Jump Location
Figure 3

Special case Ξ→0: plots of t(r) for γ=3, ϕ=0.5, and M=2

Grahic Jump Location
Figure 1

Drawing of the system

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