Numerical modelling of double-diffusive natural convection within an arc shaped enclosure filled with a porous medium

Document Type : Full Length Research Article

Authors

1 Faculty of Mechanical Engineering, Semnan University, Semnan, Iran

2 Faculty of Chemical Engineering, Semnan University, Semnan, Iran

Abstract

Numerical study of double-diffusive natural convective heat transfer in a curved cavity filled
with a porous medium has been carried out in the current study. Polar system has been
selected as coordinate system. As a result, all equations have been discredited in r and θ
directions. Brinkmann extended Darcy model has been utilized to express fluid flow in
porous matrix in the enclosure. Smaller and larger curved walls are supposed to be hot and
cold sources, respectively. Other two walls are insulated. The numerical solution has been
obtained based on the finite volume methodology via staggered grid system, which will be
explained in detail in its respective section. Finally, at the result section the effects of all
pertinent parameters i.e. Grashof number, Lewis number, Darcy number, and Buoyancy ratio
on the fluid motion and medium thermal behavior have been illustratively discussed. Results
reveal that an increasing in Lewis number has a negative effect on heat transfer, while it has
a positive impact on mass transfer. It is also seen that the flow intensity is increased by
decreasing Lewis number. In addition, it is observed that for the aiding flow case, average
Nu and Sh numbers decrease with increasing buoyancy ratio, while for opposing flow cases
Nu and Sh augment with decreasing buoyancy ratio.

Keywords

References

[1].    C.Y. Hu, M.M. EL-Wakil, Simultaneous heat and mass transfer in a rectangular cavity, Proceeding of International Heat Transfer Conference 5 (1974) 24-28.
[2].    S. Ostrach, Natural convection with combined driving forces, Physico Chemical Hydrodynamics 1 (1980) 233-247.
[3].    S.Ostrach, Natural convection heat transfer in cavities and cells, 7th International Heat Transfer Conference 1 (1983) 365-379.
[4].    S. Ostrach, Fluid mechanics in crystal growth-the 1982 freeman scholar lecture, Journal of Fluid Engineering 105 (1983) 5-20.
[5].    T.S. Lee, P.G. Parikh, A. Acrivos, D. Bershader, Natural convection in a vertical channel with opposing buoyancy forces, International Journal of Heat and Mass Transfer 25 (1982) 499-511.
[6].    P. Nithiarasu, T. Sundararajan, K.N. Seetharamu, Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall, International Communications in Heat and Mass Transfer 24 (8) (1997) 1121–1130.
[7].    V.A.F. Costa,Double-diffusive natural convection in parallelogrammic enclosures filled with fluid saturated porous media, International Journal of Heat and Mass Transfer 47 (2004) 2699–2714
[8].    B.Goyeau, J.-P. Songbe and D. Gobin, Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-brinkman formulation, International Journal of Heat and Mass Transfer, 39 (7) (1996), 1363-1378.
[9].    A.J. Chamkha, A. Al-Mudhaf, Double-diffusive natural convection in inclined porous cavities with various aspect ratios and temperature-dependent heat source or sink, Heat and Mass Transfer/Waerme- und Stoffuebertragung 44 (6) (2008) 679–693.
[10]. J.T. Vander Der Eyden, TH. H. Van Der Meer, K. Hanjalic, E. Biezen, J. Bruining, Double-diffusive natural convection in trapezoidal enclosuresm International Journal of Heat and Mass transfer, 41 (13) (1998), 1885-1898.
[11]. M. Bourich, M. Hasnaoui, A. Amahmid, Double-diffusive natural convection in a porous enclosure partially heated from below and differentially salted, International Journal of Heat and Fluid Flow 25 (2004) 1034–1046.
[12]. M.A. Teamah, M.M.Khairat Dawood, M. El-Maghlany, Double-diffusive natural convection in a square cavity with segmental heat sources, European Journal of Scientific Research, 54 (2) (2011), 287-301.
[13]. R. El Ayachi, A. Raji, M. Hasnaoui, A. Abdelbaki, M. Naimi, Resonance of double-diffusive convection in a porous medium heated with a sinusoidal exciting temperature, Journal of Applied fluid Mechanics, 3 (2) (2010), 43-52.
[14]. M. Bourich, A. Amahmid, M. Hasnaoui, Double-diffusive convection in a porous enclosure submitted to cross gradients of temperature and concentration, Energy Conversion and Management, 45 (2004), 1655–1670.
[15]. M.A. Teamah, Double-diffusive laminar natural convection in a symmetrical trapezoidal enclosure, Alexandria Engineering Journal, 45 (3) (2006), 251-263.
[16]. A. Belazizia, S. Benissaad, S. Abboudi, Double-diffusion natural convection of binary fluid in a square enclosure with top Active vertical wall, Advances in Theoretical and Applied Mechanics, 5 (3) (2012), 119-131.
[17]. R. Nikbakhti, A. rahimi, Double-diffusive natural convection in a rectangular cavity with partially thermally active side walls, Journal of the Taiwan Institute of Chemical Engineers 43 (2012) 535–541.
[18]. M.S.Valipour, A.Z. Ghadi, Numerical investigation of fluid flow and heat transfer around a solid circular cylinder utilizing nanofluid, International communications in heat and mass transfer, 38 (2011), 1296-1304.
[19]. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing  Corporation, Washington, 1980.
[20]. H.K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics. The finite volume method, John Wiley & Sons Inc, New York, 1995. 
[21]. R. Iwatsu, J.M. Hyun, K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient, International Journal of Heat and Mass Transfer 36 (1993) 1601-1608.

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History

  • Receive Date: 14 December 2013
  • Revise Date: 16 February 2014
  • Accept Date: 16 February 2014

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