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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Charrier-Mojtabi, M. C. , 1997, “ Numerical Simulation of Two- and Three-Dimensional Free Convection Flows in a Horizontal Porous Annulus Using a Pressure and Temperature Formulation,” Int. J. Heat Mass Transfer, 40(7), pp. 1521–1533.
Khanafer, K. , Al-Amiri, A. , and Pop, I. , 2008, “ Numerical Analysis of Natural Convection Heat Transfer in a Horizontal Annulus Partially Filled With a Fluid-Saturated Porous Substrate,” Int. J. Heat Mass Transfer, 51(7), pp. 1613–1627.
Chandran, R. B. , Bader, R. , and Lipiński, W. , 2015, “ Transient Heat and Mass Transfer Analysis in a Porous Ceria Structure of a Novel Solar Redox Reactor,” Int. J. Therm. Sci., 92, pp. 138–149.
Dawood, H. K. , Mohammed, H. A. , Sidik, N. A. C. , Munisamy, K. M. , and Wahid, M. A. , 2015, “ Forced, Natural and Mixed-convection Heat Transfer and Fluid Flow in Annulus: A Review,” Int. Commun. Heat Mass Transfer, 62, pp. 45–57.
Caltagirone, J. P. , 1976, “ Thermoconvective Instabilities in a Porous Medium Bounded by Two Concentric Horizontal Cylinders,” J. Fluid Mech., 76(2), pp. 337–362.
Rao, Y. F. , Fukuda, K. , and Hasegawa, S. , 1987, “ Steady and Transient Analysis of Natural Convection in a Horizontal Porous Annulus With the Galerkin Method,” ASME J. Heat Transfer, 109(4), pp. 919–927.
Himasekhar, K. , and Bau, H. H. , 1988, “ Two-Dimensional Bifurcation Phenomena in Thermal Convection in Horizontal, Concentric Annuli Containing Saturated Porous Media,” J. Fluid Mech., 187, pp. 267–300.
Charrier-Mojtabi, M. C. , Mojtabi, A. , Azaiez, A. , and Labrosse, G. , 1991, “ Numerical and Experimental Study of Multicellular Free Convection Flows in an Annular Porous Layer,” Int. J. Heat Mass Transfer, 34(12), pp. 3061–3074.
Alfahaid, A. F. , Sakr, R. Y. , and Ahmed, M. I. , 2005, “ Natural Convection Heat Transfer in Concentric Horizontal Annuli Containing Saturated Porous Media,” IIUM Eng. J., 6(1), pp. 41–54.
Leong, J. C. , and Lai, F. C. , 2006, “ Natural Convection in a Concentric Annulus With a Porous Sleeve,” Int. J. Heat Mass Transfer, 49(17), pp. 3016–3027.
Braga, E. J. , and de Lemos, M. J. S. , 2006, “ Simulation of Turbulent Natural Convection in a Porous Cylindrical Annulus Using a Macroscopic Two-equation Model,” Int. J. Heat Mass Transfer, 49(23), pp. 4340–4351.
Alloui, Z. , and Vasseur, P. , 2011, “ Natural Convection in a Horizontal Annular Porous Cavity Saturated by a Binary Mixture,” Comput. Therm. Sci., 3(5), pp. 407–417.
Belabid, J. , and Cheddadi, A. , 2013, “ Multicellular Flows Induced by Natural Convection in a Porous Horizontal Cylindrical Annulus,” Phys. Chem. News, 70, pp. 67–71.
Benjamin, T. B. , and Ursell, F. , 1954, “ The Stability of the Plane Free Surface of a Liquid in Vertical Periodic Motion,” Proc. R. Soc. London A, 225(1163), pp. 505–515.
Gresho, P. M. , and Sani, R. L. , 1970, “ The Effects of Gravity Modulation on the Stability of a Heated Fluid Layer,” J. Fluid Mech., 40(4), pp. 783–806.
Pelce, P. , and Rochwerger, D. , 1992, “ Parametric Control of Microstructures in Directional Solidification,” Phys. Rev. A, 46(8), pp. 5042–5053. [PubMed]
Campbell, J. , 1981, “ Effects of Vibration During Solidification,” Int. Met. Rev., 26(1), pp. 71–108.
Allali, K. , Volpert, V. , and Pojman, J. A. , 2001, “ Influence of Vibrations on Convective Instability of Polymerization Fronts,” J. Eng. Math., 41(1), pp. 13–31.
Alexander, J. I. D. , Ouazzani, J. , and Rosenberger, F. , 1989, “ Analysis of the Low Gravity Tolerance of Bridgman-Stockbarger Crystal Growth—I: Steady and Impulse Accelerations,” J. Cryst. Growth, 97(2), pp. 285–302.
Biringen, S. , and Peltier, L. J. , 1990, “ Numerical Simulation of 3-D Bénard Convection With Gravitational Modulation,” Phys. Fluids A: Fluid Dyn., 2(5), pp. 754–764.
Ostrach, S. , 1982, “ Low-Gravity Fluid Flows,” Ann. Rev. Fluid Mech., 14(1), pp. 313–345.
Peaceman, D. W. , and Rachford, J. H. H. , 1955, “ The Numerical Solution of Parabolic and Elliptic Differential Equations,” J. Soc. Ind. Appl. Math., 3(1), pp. 28–41.
Facas, G. N. , 1995, “ Natural Convection From a Buried Pipe With External Baffles,” Numer. Heat Transfer, Part A, 27(5), pp. 595–609.
Mota, J. P. B. , Esteves, I. A. A. C. , Portugal, C. A. M. , Esperança, J. M. S. S. , and Saatdjian, E. , 2000, “ Natural Convection Heat Transfer in Horizontal Eccentric Elliptic Annuli Containing Saturated Porous Media,” Int. J. Heat Mass Transfer, 43(24), pp. 4367–4379.
Mota, J. P. B. , and Saatdjian, E. , 1994, “ Natural Convection in a Porous Horizontal Cylindrical Annulus,” ASME J. Heat Transfer, 116(3), pp. 621–626.


Grahic Jump Location
Fig. 1

Sketch of the problem under consideration

Grahic Jump Location
Fig. 2

Mesh effect on Nu¯ for λ=0 and Ra=100

Grahic Jump Location
Fig. 5

Nusselt number versus time for Ra=50

Grahic Jump Location
Fig. 6

ψmax  versus time for Ra=50

Grahic Jump Location
Fig. 7

Nu¯ versus time for λ=0.1

Grahic Jump Location
Fig. 8

Critical Rayleigh number as function of the amplitude

Grahic Jump Location
Fig. 9

Critical Rayleigh number as function of σ

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

Nusselt number versus Rayleigh number for λ=0



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In