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Research Papers: Porous Media

Magnetohydrodynamics Flow and Heat Transfer Around a Solid Cylinder Wrapped With a Porous Ring

[+] Author and Article Information
Mohammad Sadegh Valipour

School of Mechanical Engineering,
Semnan University,
P.O. Box 35131-19111,
Semnan, Iran
e-mail: msvalipour@semnan.ac.ir

Saman Rashidi

School of Mechanical Engineering,
Semnan University,
P.O. Box 35131-19111,
Semnan, Iran

Reza Masoodi

School of Design and Engineering,
Philadelphia University,
4201 Henry Avenue,
Philadelphia, PA 19144

Salty water was considered as a conductor of electricity.

A resistive type force which experienced by a fluid carrying a current density J in a magnetic field B.

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 5, 2013; final manuscript received December 24, 2013; published online March 10, 2014. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 136(6), 062601 (Mar 10, 2014) (9 pages) Paper No: HT-13-1002; doi: 10.1115/1.4026371 History: Received January 05, 2013; Revised December 24, 2013

The problem of the effect of an external magnetic field on fluid flow and heat transfer characteristics is relevant to several physical phenomena. In this paper, flow and heat transfer of an electrically-conductive fluid around a cylinder, wrapped with a porous ring and under the influence of a magnetic field, is studied numerically. The ranges of the Stuart (N), Reynolds (Re), and Darcy (Da) numbers are 0–7, 1–40, and 10−8–10−1, respectively. The Darcy–Brinkman–Forchheimer model was used for simulating flow in the porous layer. The governing equations provide a coupling between flow and magnetic fields. The governing equations, together with the relevant boundary conditions, are solved numerically using the finite-volume method (FVM). The effect of the Stuart, Reynolds, and Darcy numbers on the flow patterns and heat transfer rate are explored. Finally, two empirical equations for the average Nusselt number were suggested, in which the effect of a magnetic field and the Darcy numbers are taken into account. It was found that in the presence of a magnetic field, the drag coefficient and the critical radius of the insulation increases, while the wake length and Nusselt number decrease.

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Figures

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Fig. 1

(a) Coordinate system, computational domain, and geometry of cylinder

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Fig. 2

(a) Schematic of the recirculation zone for cylinder and (b) structured grid near the wall

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Fig. 3

(a) A comparison of numerical Nusselt number with experimental results for a horizontal cylinder embedded in a porous medium (absence of magnetic field) and (b) a comparison of numerical wake length with other numerical results for a cylinder with streamwise magnetic field intensity

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Fig. 4

Configuration of streamlines at different Stuart numbers and Re = 40 for (a) a cylinder without porous layer and (b) a cylinder with porous layer, δ=0.25 and Da=1 × 10−3

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Fig. 5

The wake length versus Stuart numbers for different Darcy numbers and δ=0.25

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Fig. 6

The critical Stuart numbers for disappearing re-circulating wake versus Darcy numbers for Re=20, 40 and δ=0.25

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Fig. 7

The drag coefficient on porous cylinder versus Darcy numbers for different Stuart numbers, Re = 20 and δ=10

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Fig. 8

The average Nusselt number versus Stuart numbers for a cylinder without porous layer and Re = 40

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Fig. 9

The average Nusselt number versus Darcy numbers for different Stuart numbers at Re = 40 (porous ring is composed of insulation material (ks < kf))

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Fig. 10

The critical radius of insulation versus Darcy numbers for different porous layer thickness at Re = 40 (symbols refer to without exerting magnetic field and lines refer to with exerting magnetic field)

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Fig. 11

The average Nusselt number versus Darcy numbers for different Stuart numbers at Re = 40 (porous ring is composed of conductive material (ks > kf))

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Fig. 12

Comparison between numerical and proposed equations for the average Nusselt number

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