Heat and Mass Transfer in an Inclined Bi-L-Shaped Layered Porous Media: Effect of Buoyancy Ration

Abstract:

The effect of buoyancy ratio on the two dimensional natural convection heat and mass transfer generated in an inclined square bi-L-shaped layered porous cavity filled with Newtonian fluid has been investigated numerically. Each porous layer is considered isotropic, homogeneous and saturated with the same fluid. The cavity is heated and salted from below where as the vertical walls are assumed to be adiabatic and impermeable. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman-Forcheimer model, and the set of coupled equations is solved using a finite volume approach. The power-law scheme is used to evaluate the flow, heat and mass fluxes across each of the control volume boundaries. Tri diagonal matrix algorithm with under-relaxation is used in conjunction with iterations to solve the nonlinear discretized equations. An in-house code developed for this study is validated using previous studies. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers.

• Periodical: Defect and Diffusion Forum (Volume 406)
• Pages: 87-97
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.406.87
• Online since: January 2021
• Authors: Latreche Abdelkrim*, Djezzar Mahfoud
• Keywords: Buoyancy Ratio, Darcy-Brinkman-Forcheimer Model, Heat and Mass Transfer, Natural Convection, Porous Media

References

[1] Islama, M. Sharif, E. Carlsona. Numerical investigation of double diffusive natural convection of CO2 in a brine saturated geothermal reservoir. Geothermics. 48(2013) 101-111.

DOI: 10.1016/j.geothermics.2013.07.001

[2] T. Nagel, H. Shao, A. Singh, N. Watanabe, C. Roßkopf, M. Linder. Non equilibrium thermo-chemical heat storage in porous media: part 1-conceptual model. Energy 60 (2013) 254-270.

DOI: 10.1016/j.energy.2013.06.025

[3] H. Shao, T. Nagel, C. Roßkopf, M. Linder, A. W€orner, O. Kolditz. Non-equilibrium thermo-chemical heat storage in porous media: part 2-A 1D computational model for a calcium hydroxide reaction system. Energy 60 (2013)271-282.

DOI: 10.1016/j.energy.2013.07.063

[4] Y. Liu, H. Wang, Z. Shen, Y. Song. Estimation of CO2 storage capacity in porous media by using X-ray micro-CT. Energy Procedia 37(2013) 5201-5208.

DOI: 10.1016/j.egypro.2013.06.436

[5] A.Nouri-Borujerdi, SI. Tabatabai. Porous media approach in thermo-hydraulic analysis of high temperature reactors in pressurized/depressurized cool down: an improvement. ProgNucl Energy 80(2015) 119-127.

DOI: 10.1016/j.pnucene.2014.11.017

[6] C.Beghein, F. Haghighat, F. Allard, Numerical study of double-diffusive natural convection in a square cavity, Int J Heat Mass Transf. 35(1992) 833-846.

DOI: 10.1016/0017-9310(92)90251-m

[7] R.W. Schmitt, Double diffusion in oceanography, Fluid Mech. 26(1994) 255–285.

[8] J.S. Turner, Double diffusive phenomena, Fluid Mech. 6 (1974) 37–56.

[9] S. Ostrach, Natural convection with combined driving forces, Physicochem. Hydrodyn. 1(1980) 233–247.

[10] Nield, and A. Bejan, Convection in Porous Media, 3rd ed. Spinger, New York Inc,(2006).

[11] B. Ingham, and I. pop, Transport phenomena in porous media, 3rd ed. Elsevier, Oxford, (2005).

[12] P. Vadász, emerging topics in heat and mass transfer in porous media. Spinger, New York Inc. (2008).

[13] R. Viskanta, T.L. Bergman, F.P. Incropera, Double diffusive natural convection, in: S. Kakac,W. Aung, R. Viskanta (Eds.), Natural Convection: Fundamentals and Applications, Hemisphere, Washington, DC, (1985).

[14] H. Fernando, Buoyancy transfer across a diffusive interface, J. Fluid Mech. 209(1989) l–34.

DOI: 10.1017/s0022112089003010

[15] T. Makayssi, M. Lamsaadi, M. Naimi, M. Hasnaoui, A. Raji, A. Bahlaoui, Natural double-diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and filled with non-Newtonian power-law fluids: the cooperating case, Energy Convers. Manage. 49 (2008) 2016–(2025).

DOI: 10.1016/j.enconman.2008.02.008

[16] M.A. Teamah, Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field and heat source, Int. J. Therm. Sci. 47 (2008) 237–248.

DOI: 10.1016/j.ijthermalsci.2007.02.003

[17] H.S. Harzallah, A. Jbara, K. Slimi, Double-diffusive natural convection in anisotropic porous medium bounded by finite thickness walls: validity of local thermal equilibrium assumption, Transp. Porous Med. 103 (2014) 207–231.

DOI: 10.1007/s11242-014-0298-3

[18] Z. Alloui, P. Vasseur, Convection of a binary fluid in a shallow porous cavity heated and salted from the sides, Computers & Fluids 81 (2013) 85–94.

DOI: 10.1016/j.compfluid.2013.04.011

[19] R. Nikbakhti, J. Khodakhah, Numerical investigation of double diffusive buoyancy forces induced natural convection in a cavity partially heated and cooled from sidewalls, Engineering Science and Technology, an International Journal(2015).

DOI: 10.1016/j.jestch.2015.08.003

[20] M.A. Teamah, M.M. Khairat Dawood, W.M. El-Maghlany, Double diffusive natural convection in a square cavity with segmental heat sources, Eur. J. Sci. Res. 54 (2) (2011) 287–301.

[21] K. Al-Farhany, A. Turan, Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous, International Communications in Heat and Mass Transfer 39 (2012) 174–181.

DOI: 10.1016/j.icheatmasstransfer.2011.11.014

[22] V.J. Bansod, R.K. Jadhav, An integral treatment for combined heat and mass transfer by natural convection along a horizontal surface in a porous medium, International Journal of Heat and Mass Transfer 52 (2009) 2802–2806.

DOI: 10.1016/j.ijheatmasstransfer.2008.12.015

[23] Zhao, D. Liu, G. Tang, Natural convection in an enclosure with localized heating and salting from below, International Journal of Heat and Mass Transfer 51 (2008) 2889–2904.

DOI: 10.1016/j.ijheatmasstransfer.2007.09.032

[24] A.Latreche, M. Djezzar, Convective heat and solute transfer in Newtonian fluid saturated inclined porous cavity, International Journal of Physical Research 2(2) (2014) 78-84.

DOI: 10.14419/ijpr.v2i2.3372

[25] A.Mohamad, R. Bennacer, Natural convection in a confined saturated porous medium with horizontal temperature and vertical solutal gradients, Int. J. Therm. Sci.40 (2001) 82–93.

DOI: 10.1016/s1290-0729(00)01182-0

[26] 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.

DOI: 10.1016/j.enconman.2003.10.003

[27] S. Roy, T. Basak, Finite element analysis of natural convection flows in a square cavity with non-uniformly heated wall(s), Int. J. Eng. Sci. 43 (2005) 668–680.

DOI: 10.1016/j.ijengsci.2005.01.002

[28] N.Hadidi, Y. Ould-Amer, R. Bennacer, Bi-layered and inclined porous collector: optimum heat and mass transfer. Energy 51 (2013) 422-430.

DOI: 10.1016/j.energy.2013.01.012

[29] N.Hadidi, R. Bennacer, Y. Ould-Amer, Two-dimensional thermosolutal natural convective heat and mass transfer in a bi-layered and inclined porous enclosure. Energy 93 (2015) 2582-2592.

DOI: 10.1016/j.energy.2015.10.121

[30] AC. Baytas , AF. Baytas, DB. Ingham, I. Pop. Double diffusive natural convection in an enclosure filled with a step type porous layer: non-darcy flow. Int J Therm Sci. 48 (2009) 665-673.

DOI: 10.1016/j.ijthermalsci.2008.06.001

[31] R. Bennacer, H. Beji, A.A. Mohamad, Double diffusive convection in a vertical enclosure insertedwith two saturated porous layers confining a fluid layer, International Journal of Thermal Sciences 42 (2003) 141–151.

DOI: 10.1016/s1290-0729(02)00014-5

[32] S. Patankar, Numerical Heat Transfer and Fluid flow, Hemisphere, New York, (1980).

[33] S.L. Moya, E. Ramos,M. Sen, Numerical study of natural convection in a tilted rectangular porousmaterial.International Journal of Heat andMass Transfer 30 (4) (1987) 741-756.

DOI: 10.1016/0017-9310(87)90204-3

[34] J.P. Caltagirone, S. Bories, Solutions and stability criteria of natural convective flow in an inclined porous layer.Journal of Fluid Mechanics 155 (1985) 267-287.

DOI: 10.1017/s002211208500180x

[35] A. Latreche, M. Djezzar, Numerical study of natural convective heat and mass transfer in an inclined porous media, Engineering, Technology & Applied Science Research 8(4) (2018) 3223-3227.

DOI: 10.48084/etasr.2179

[36] S. Safi,   S. Benissaad, Double-diffusive convection in an anisotropic porous layer using the Darcy–Brinkman–Forchheimer formulation, Archives of Mechanics, 70(1) (2018) 89-102.

[37] N. Hadidi, R. Bennacer, Heat and mass transfer by natural convection in a bi-layered cubic enclosure with opposing temperature and concentration gradients, International Journal of Thermal Sciences, 132 (2018) 534-551.

DOI: 10.1016/j.ijthermalsci.2018.06.013