MAC simulation of thermosolutal natural convection in a porous enclosure with opposing temperature and concentration gradients

B Md Hidayathulla Khan; V Ramachandra Prasad; R Bhuvana Vijaya

doi:https://doi.org/10.14445/22315373/IJMTT-V49P546

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 49 | Number 5 | Year 2017 | Article Id. IJMTT-V49P546 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P546

MAC simulation of thermosolutal natural convection in a porous enclosure with opposing temperature and concentration gradients

B Md Hidayathulla Khan, V Ramachandra Prasad, R Bhuvana Vijaya

Citation :

B Md Hidayathulla Khan, V Ramachandra Prasad, R Bhuvana Vijaya, "MAC simulation of thermosolutal natural convection in a porous enclosure with opposing temperature and concentration gradients," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 5, pp. 291-297, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P546

Abstract

A numerical study is conducted on thermosolutal natural convective flow inside a porous mixture of a rectangular enclosure with aspect ratio four. The flow enhancement is observed due to rising of Rayleigh number and Darcy number with buoyancy parameter. The transport equations for continuity, momentum, energy and species transfer are solved numerically with Marker and Cell (MAC) method. Two dimensional computational visualization results illustrating the influence of fluid parameters such as Darcy number, Rayleigh number and buoyancy ratio on contour maps of the Streamlines, Isotherms, and Iso-concentrations as well as the mid-section of velocity of the cavity are reported and discussed. The local Nusselt number and Sherwood numbers are increasing along the vertical walls for increasing Darcy number.

Keywords

Porous medium, Isothermal walls, Double Diffusive Natural Convection, Aspect ratio, Rectangular Enclosure, MAC method.

References

[1] (Gebhart, B. et al., Buoyancy-induced Flows and Transport, Hemisphere, Washington, USA (1988).
[2] S. Ostrach, Natural Convection in Enclosures, Advances in Heat Transfer, 8, 161-227 (1972).
[3] Li-Zhi Zhang, Coupled heat and mass transfer in an application scale cross-flow hollow fibre membrane module for air humidification, International Journal of Heat and Mass Transfer, 55 (2012), 5861-5869.
[4] Mohamed A.Teamah, Medhat M.Sorour, Wael M. El- Maghlany, Amr Afifi, Numerical simulation of double diffusive laminar mixed convection in shallow inclined cavities with moving lid, Alexandria Engineering Journal, 52 (2013), 227-239.
[5] A.K.Naik, S.Bhattacharyya, Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients, Theoretical and Computational Fluid Dynamics, 26 (2012), 565-581.
[6] K.T.Chen, C.C.Tsai, W.J.Luo, C.N.Chen, Multiplicity of steady solutions in a two-sided lid-driven cavity with different aspect ratios, Theoretical and Computational Fluid Dynamics, 27 (2013), 767-776.
[7] S.H. Xin, P.L. Quere, L.S. Tuckerman, Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients, Phys. Fluids 10 (1998), 850- 855.
[8] A. Cibik, S. Kaya, Finite element analysis of a projectionbased stabilization method for the Darcy-Brinkman equations in double-diffusive convection, Appl. Numer. Math. 64 (2013), 35-49.
[9] J. Serrano-Arellano, M. Gijon-Rivera, J.M. Riesco-Avila, F. Elizalde-Blancas, Numerical study of the double diffusive convection phenomena in a closed cavity with internal CO2 point sources, International Journal of Heat and Mass Transfer 71 (2014), 664-674.
[10] K. Roy, P.V.S.N. Murthy, Soret effect on the double diffusive convection instability due to viscous dissipation in a horizontal porous channel, International Journal of Heat and Mass Transfer, 91 (2015), 700-710.
[11] S. Bettaibi, F. Kuznik, E. Sediki, Hybrid LBM-MRT model coupled with finite difference method for double-diffusive mixed convection in rectangular enclosure with insulated moving lid, Physica A 444 (2016) 311-326.
[12] Q.L. Ren, C.L. Chan, Numerical study of double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on GPU, International Journal of Heat and Mass Transfer, 93 (2016), 538-553.
[13] A.M. Al-Amiri, K.M. Khanafar and I. Pop, Numerical simulation of a combined thermal mass transport in a square lid-driven cavity, International Journal of Thermal Science, 46 (2007), 662-671.
[14] Bhargava, R., S. Sharma, P. Bhargava, O. Anwar Bég and A. Kadir, Finite element simulation of nonlinear convective heat and mass transfer in a micropolar fluidfilled enclosure with Rayleigh number effects, Int. J. Applied Computational Mathematics, 3, 1347–1379 (2017).
[15] Beg O. Anwar, N. Ali, A. Zaman, Eemaan T. A. Bég and Ayesha Sohail, Computational modelling of heat transfer in annular porous medium solar energy absorber with a P1- radiative differential approximation, J. Taiwan Inst. Chemical Eng. 66, 258-268 (2016).
[16] Ali Mchirgui, Nejib Hidouri, Mourad Magheribi, Ammar Ben Brahim, Second law analysis in double diffusive convection through an inclined porous cavity, Computers and Fluids, 96 (2014), 105-115.
[17] A.J. Chamkha, A.N. Hameed, Double-diffusive convection in an inclined porous enclosure with opposing temperature and concentration gradients, International Journal of Thermal Science, 40 (2001), 227-244.
[18] K. Al-Farhany, A. Turan, Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous medium, International Communications in Heat and Mass Transfer, 39 (2012), 174-181.
[19] Sofen K. Jena, Swarup K. Mahapatra, Amitava Sarkar, Double diffusive buoyancy opposed natural convection in a porous cavity having partially active vertical walls, International Journal of Heat and Mass Transfer, 62 (2013), 805-817.
[20] H.T. Xu, T.T. Wang, Z.G. Qu, J.Chen, B.B. Li, Lattice Boltzmann Simulation of the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium, International Communications in Heat and Mass Transfer, 81 (2017), 104-115.
[21] Tanmay Basak, S. Roy, Sandeep Kumar Singh, I. Pop, Analysis of mixed convection in a lid-driven porous square cavity with linearly heated side wall(s), International Journal of Heat and Mass Transfer, 53 (2010) 1819–1840
[22] Brown DL, Cortez R, Minion ML, Accurate projection methods for the incompressible Navier–Stokes equations. J. Comp. Phys 168 (2011) 464–499.
[23] V. Ambethkar, Mohit Kumar Srivastava, Numerical study of an unsteady 2-d incompressible viscous flow with heat transfer at moderate Reynolds number with slip boundary conditions, International Journal of Applied Mathematics, 25 (2012) 883-908.
[24] Francis H. Harlow, J. Eddie Welch, Numerical calculation of time dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8 (1965), 2182-2189.
[25] Barrett R et al. (1994) Templates for the solution of linear systems: building blocks for iterative methods. SIAM Press, Philadelphia, USA.
[26] Tapas Ray Mahapatra, Dulal Pal, Sabyasachi Mondal, Effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity, International Journal of Heat and Mass Transfer 57 (2013) 771–785.
[27] Zhao, F-Y. et al., Free heat and mass transfer in a porous enclosure with side vents, Drying Technology, 29, 91-104 (2010).