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Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

Published online by Cambridge University Press:  21 July 2015

Ashok Kumar ,
Pravez Alam  and
Prachi Fartyal
Ashok Kumar*
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
Pravez Alam
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
Prachi Fartyal
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
*
*Corresponding author. Email: [email protected] (A. Kumar)
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Abstract

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number (Da), heat source intensity i.e., thermal Rayleigh number (Ra), permeability ratio (K*), orientation angle (ϕ). The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, Nub, side Nus) and mass transfer (bottom, Shb, side, Shs) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of K*, the heat and mass transfer rates are negligible for 10−7 ≤ Da ≤ 10−5, Ra = 2 × 105 and ϕ = 45°. However a significant impact appears on Nusselt and Sherwood numbers when Da lies between 10−5 to 10−4. The maximum bottom heat and mass transfer rates (Nub, Sub) is attained at ϕ = 45°, when K* =0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number (Ra) for all the values of K*. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.

Keywords

65M1078A48Spectral element methodanisotropic porous mediumnon-Darcy Brinkmann modelnon-uniform heating
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 5 , October 2015 , pp. 644 - 662
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Schmidt, R. W., Double diffusion in oceanography, Ann. Rev. Fluid Mech., 26 (1994), pp. 255–285.Google Scholar
[2]Nield, D. A. and Bejan, A., Convection in Porous Media, Springer, New York, 2006.Google Scholar
[3]Kamotani, Y., Wang, W., Ostrach, S. and Jiang, H. D., Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients, Int. J. Heat Mass Transf., 28 (1985), pp. 165–173.Google Scholar
[4]Lee, J., Hyun, M. T. and Kim, K. W., Natural convection in confined fluids with combined horizontal temperature and concentration gradients, Int. J. Heat. Mass Transf., 31 (1969), pp. 1969–1973.CrossRefGoogle Scholar
[5]Beghein, C., Haghighat, F. and Allarad, F., Numerical study of double diffusive natural convection in square cavity, Int. J. Heat. Mass Transf., 35 (1992), pp. 833–845.CrossRefGoogle Scholar
[6]Bennacer, R. and Gobin, D., Cooperating thermosolutal convection in enclosures-I, scale analysis and mass transfer, Int. J. Heat. Mass Transf., 39 (1996), pp. 2671–2681.Google Scholar
[7]Bennacer, R. and Gobin, D., Cooperating thermosolutal convection in enclosures-II, heat transfer and flow structure, Int. J. Heat. Mass Transf., 39 (1996), pp. 2683–2697.Google Scholar
[8]Ghorayeb, K. and Mojtabi, A., Double diffusive convection in vertical rectangular cavity, Phys. Fluid, 9 (1997), pp. 2339–2348.Google Scholar
[9]Sezai, A. and Mohamad, A. A., Double diffusive convection in a cubic enclosure with opposing temperature and concentration gradients, Phys. Fluid, 12 (2000), pp. 2210–2223.Google Scholar
[10]Trevisan, O. V. and Bejan, A., Mass and heat transfer by natural convection in a vertical slot filled with porous medium, Int. J. Heat. Mass Transf., 29 (1986), pp. 403–415.Google Scholar
[11]Mehta, K. N. and Nandkishor, K., Natural convection with combine heat and mass transfer buoyancy effects in non homogeneous porous medium, Int. J. Heat. Mass Transf., 30 (1987), pp. 2651–2656.Google Scholar
[12]Mamou, M., Vasseur, P. and Bilgen, E., Multiple solutions for double diffusive convection in vertical porous enclosure, Int. J. Heat. Mass Transf., 38 (1995), pp. 1787–1798.CrossRefGoogle Scholar
[13]Mamou, M., Vasseur, P. and Bilgen, E., Analytical and numerical study of double diffusive convection in vertical enclosure, Int. J. Heat. Mass Transf., 32 (1996), pp. 115–125.Google Scholar
[14]Trevisan, O. V. and Bejan, A., Natural convection with combine heat and mass transfer buoyancy effects in porous medium, Int. J. Heat. Mass Transf., 28 (1985), pp. 1997–1611.Google Scholar
[15]Goyeau, B., Songbe, J. P. and Gobin, D., Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation, Int. J. Heat. Mass Transf., 39 (1996), pp. 1363–1378.Google Scholar
[16]Kramer, J., Jecl, R. and Skerget, L., Boundary domain integral method for the study of double-diffusive natural convection in a porous media, Eng. Ana. Bou. Element, 31 (2007), pp. 897–905.CrossRefGoogle Scholar
[17]Alavyoon, F., On natural convection in vertical porous enclosures due to prescribed fluxes of heat and mass at the vertical boundaries, Int. J. Heat. Mass Transf., 36 (1993), pp. 2479–2498.Google Scholar
[18]Alavyoon, F., Masuda, Y. and Kimura, S., On natural convection in vertical porous enclosure due to opposing fluxes of heat and mass prescribed at the vertical walls, Int. J. Heat. Mass Transf., 37 (1994), pp. 195–206.Google Scholar
[19]Nithiarasu, P., Seetharamu, K. N. and Sundararajan, T., Double-diffusive natural convection in an enclosure filled with fluid saturated porous medium: A generalized non-Darcy approach, Numer. Heat Transf. Part A, 30 (1996), pp. 413–426.CrossRefGoogle Scholar
[20]Bera, P., Eswaran, V. and Singh, P., Numerical study of heat and mass transfer in an anisotropic porous enclosure due to constant heating and cooling, Numer. Heat Transf. Part A, 34 (1998), pp. 887–905.Google Scholar
[21]Bera, P., Eswaran, V. and Singh, P., Double-diffusive convection in slender anisotropic porous enclosure, J. Porous Media, 3 (2000), pp. 11–29.Google Scholar
[22]Bera, P. and Khalili, A., Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: Multi-solutions and oscillations, Int. J. Heat. Mass Transf., 45 (2002), pp. 3205–3222.Google Scholar
[23]Bennacer, R., Tobbal, A., Beji, H. and Vasseur, P., Double diffusive convection in a vertical enclosure filled with anisotropic porous media, Int. J. Thermal. Sci., 40 (2001), pp. 30–41.Google Scholar
[24]Kumar, A. and Bera, P., Natural convection in an anisotropic porous enclosure due to non-uniform heating from the bottom wall, ASME J. Heat. Transf., 131 (2009), 07260-1-13.Google Scholar
[25]Mojtaba, M. S. and Reza, S. M., Invistigation of natural convection in a vertical cavity filled with a anisotropic porous media, Iran J. Chemistry. Chem. Eng., 27 (2008), pp. 39–45.Google Scholar
[26]Safi, S. and Benissaad, S., Heat and mass transfer in anisotropic porous media, Adv. Theoretical Appl. Mech., 5 (2012), pp. 11–22.Google Scholar
[27]Patera, A. T., A Spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys., 54 (1984), pp. 468–488.Google Scholar
[28]Canuto, C., Hussaine, M. Y., Quarteroni, A. and Zang, T. A., Spectral Method in Fluid Dynamics, Springer, New York, Berlin Heidelberg, 1986.Google Scholar
[29]Neale, G., Degrees of anisotropy for fluid flow and diffusion (Electrical Conduction) through anisotropic porous media, AIChE. J., 23 (1977), pp. 56–62.Google Scholar
[30]Tyvand, P. A., Thermohaline instability in anisotropic porous media, Water Res. Resources, 16 (1980), pp. 325–330.Google Scholar