International Journal of Physics
ISSN (Print): 2333-4568 ISSN (Online): 2333-4576 Website: http://www.sciepub.com/journal/ijp Editor-in-chief: B.D. Indu
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International Journal of Physics. 2017, 5(5), 162-170
DOI: 10.12691/ijp-5-5-4
Open AccessArticle

Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall

Alhadj Hisseine Issaka Ali1, 2, , Cheikh Mbow1, Samba Dia1, Mahamoud Youssouf Khayal3 and A.C. Beye1

1Department of Physics, Cheikh Anta Diop University of Dakar, Dakar, Senegal

2Department of Hydrocarbons Exploitation, Higher National Petroleum Institute of Mao, Mao, Chad

3Department of Technical Sciences, University of N’Djamena, N’Djamena, Chad

Pub. Date: October 23, 2017

Cite this paper:
Alhadj Hisseine Issaka Ali, Cheikh Mbow, Samba Dia, Mahamoud Youssouf Khayal and A.C. Beye. Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall. International Journal of Physics. 2017; 5(5):162-170. doi: 10.12691/ijp-5-5-4

Abstract

This current study focuses on the simulation of free convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a localized temperature varying sinusoidally with the space while the upper horizontal wall and rest of the bottom walls are insulated. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in FORTRAN 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number, amplitude and length of source heating on the dynamic and thermal fields are investigated. On the other hand, the effects of the amplitude on the horizontal velocity distribution and the mean horizontal temperature distribution(y=0.5) were presented and discussed. It emerges from this study that the increasing of the amplitude and Rayleigh-Darcy number intensify the flow and the global heat transfer in our physical domain.

Keywords:
free convection porous media finite difference method sinusoidal temperature localized heating

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References:

[1]  Saied, N.H., 2005. Natural convection in a square porous cavity with an oscillating wall temperature. Arabian J.Sci.Eng. 31: 35-46.
 
[2]  Nield, DA and A.Bejan, 2006. Convection in porous Media, 3rd Edn. Springer Science and Business Media, New York, pp. 640.
 
[3]  M. Kaviany (1995). "Principles of Heat Transfer in porous Media" Second.
 
[4]  Vafai, K. 2005. Handbook of porous Media, 2nd Edition, CRC Press, New York, 784.
 
[5]  Ingham, D.B and Pop., I. (2005). Transport Phenomena in Porous Media III. Elsevier, Oxford, 450.
 
[6]  Schaladaw, S., Patterson, J.C and Street, R.L, (1989). Transient Flow in a side-Heated Cavity at high Rayleigh number: a numerical study. Journal of Fluid Mechanics, 200, 121-148.
 
[7]  H.F. Oztop, M Oztop and Y. varol, Numerical simulation of magneto-hydrodynamic Buoyancy-Induced Flow in a non-isothermally Heated Square Enclosure, Com Nonlinear Sci. Numer., simul., vol.14, pp. 770-778, 2009.
 
[8]  E.V. Kalabin, M.V. Kanashina, and P.T. Zubkov, Natural-convective Heat Transfer in a square cavity with Time-Varying side-wall Temperature, Numer. Heat Transfer A, Vol. 47, pp. 621-631, 2005.
 
[9]  Kazmierczak and Chinoda, Z., (1992). Buoyancy-Driven Flow in an enclosure with time periodic Boundary Conditions. International Journal of Heat and Mass Transfer, 35, 1507-1518.
 
[10]  Varol, Y., Oztop, H.F., and Pop, I., Numerical Analysis of Natural convection for Porous Rectangular Enclosure with sinusoidal Varying Temperature Profile on the Bottom wall, International Communication in Heat and mass Transfer,Vol.35, 2008, pp. 56,64.
 
[11]  Q.H Deng and J.J Chang, Natural Convection in a rectangular Enclosure with sinusoidal Temperature Distribution on Both Side walls, Numer.Heat Transfer A, vol.54. pp. 507-524, 2008.
 
[12]  Baytas, A.C and I. Pop, (2002). Free convection in a square porous cavity using a thermal no equilibrium model. Int. J. Thermal Sci., 41, 861-870.
 
[13]  Kimura, S.K, Vynnycky.M and Alavyoon Unicellular natural circulation in a shallow horizontal porous layer heated from below by a constant flux, Fluid Mech. 294, 231-257.
 
[14]  Darcy, H.P.C. Les fontaines publiques de la ville de Dijon (Victor, Dalmont, paris 1856).
 
[15]  Moya, S.L and Ramos, 1987.Numerical study of a natural convection in tilted rectangular porous material.Int.J hem Mass T, 30: 741-756.
 
[16]  Sheremet, M.A. and I. Pop and Ramos, 2014. Natural convection in square porous cavity with sinusoidal temperature distributions in both side walls filled with a Nanofluid: Buongiorno’s mathematical mdel. Transp. Porous Med., 105: 411-429.
 
[17]  Bejan, A., (1979). On the boundary layer regime in a vertical enclosure filled with a porous medium. Lett. Heat Mass Transfer, 6, 93-102.
 
[18]  Ali, A.H.I., Dia, S., Khayal, M.Y., Mbow, C. And Beye, A.C. (2017). Natural Study of Natural Convection in a Porous Square Enclosure with sinusoidally varying Temperature Profile on the Bottom wall. Open Journal of Fluid Dynamics, 7, 263-275.
 
[19]  Saha, Suvash, Molla, Md. Mamum &. Khan, M. A.I (2012). Natural convection flow in a porous enclosure with localized heating from below. JP Journal of Heat and Mass Transfer, 6(1), pp.1-16.