Research Papers: Natural and Mixed Convection

Influence of Gravitational Modulation on Natural Convection in a Horizontal Porous Annulus

[+] Author and Article Information
Jabrane Belabid

Mohammadia School of Engineers,
Mohammed V University in Rabat,
Agdal Rabat, Morocco
e-mail: belabide@gmail.com

Karam Allali

Laboratory of Mathematics and Applications,
Faculty of Sciences and Technologies,
University Hassan II of Casablanca,
Mohammedia, Morocco
e-mail: allali@hotmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 22, 2016; final manuscript received August 29, 2016; published online October 18, 2016. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 139(2), 022502 (Oct 18, 2016) (6 pages) Paper No: HT-16-1411; doi: 10.1115/1.4034795 History: Received June 22, 2016; Revised August 29, 2016

The influence of gravitational modulation on natural convection in a horizontal porous annulus is investigated in this paper. The mathematical model describing the phenomenon consists of the heat equation coupled by the hydrodynamics equations under the Boussinesq approximation. The derived system of equations with the stream function–temperature formulation is obtained and solved numerically using the alternating direction implicit method. It is shown that the convective stability of the fluid can be gained for small amplitudes of the vibration, while it will be lost for large ones. It was also observed that increasing the frequency has a destabilizing effect.

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Fig. 1

Sketch of the problem under consideration

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Fig. 2

Mesh effect on Nu¯ for λ=0 and Ra=100

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Fig. 3

Isotherms (left) and streamlines (right) for λ=0 and for different values of Rayleigh number: (a) Ra=62 and (b) Ra=63

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Fig. 4

Nusselt number versus Rayleigh number for λ=0

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Fig. 5

Nusselt number versus time for Ra=50

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Fig. 6

ψmax  versus time for Ra=50

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Fig. 7

Nu¯ versus time for λ=0.1

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Fig. 8

Critical Rayleigh number as function of the amplitude

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Fig. 9

Critical Rayleigh number as function of σ




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