MHD Double-Diffusive Natural Convection in a Closed Space ‎Filled with Liquid Metal: Mesoscopic Analysis

Document Type : Research Paper

Authors

1 School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamilnadu, 632014, India‎

2 Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig/Turkey

3 Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21511, Saudi Arabia‎

Abstract

< p>In this paper, the lattice Boltzmann approach is carried out to study the double-diffusive natural convection in a space encapsulating liquid metal is presented. The Uniform magnetic field is applied horizontally at the square domain and an insulated rectangular block is kept stationary at the center of the cavity. The linear increment of temperature and concentration is used at the left wall and cold temperature is applied at the right wall. Horizontal walls are adiabatic conditions. Horizontal walls are adiabatic conditions. The numerical analysis is performed at the range of Rayleigh number (103 ≤ Ra ≤ 105), Lewis number (2 ≤ Le ≤ 10), buoyancy ratio (-2 ≤ N ≤ 2), Hartmann number (0 ≤ Ha ≤ 50) with Prandtl number (Pr) = 0.054. Results show that the increase in Ra tends to maximize heat and mass transfer rate while increasing Ha, decreases the same. The rise in Le diminishes heat transfer marginally but increasing the mass transfer significantly. The effect of N differs with different operating conditions, in general, the rate of heat and mass transfer is found to decrease with a decrease of N value.

Keywords

Main Subjects

[1] Moufekkir, F., Moussaoui, M.A., Mezrhab, A., Lemonnier, D., Naji, H., MRT-lattice Boltzmann computations of natural convection and volumetric radiation in a tilted square enclosure, International Journal of Thermal Science, 54, 2012, 125–141.
[2] Peng, Y., Shu, C., Chew, Y., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Physical Review E, 2003, 68, 026701.
[3] Mussa, M.A., Abdullah, S., Nor Azwadi, C.S, Muhamad, N., Simulation of natural convection heat transfer in an enclosure by the lattice-Boltzmann method, Computers and Fluids, 44, 2011, 162–168.
[4] Xuan, Y., Zhao, K., Li, Q., Transient modeling of CPL based on mesoscaled analysis by lattice Boltzmann method, Frontiers in Heat Pipes, 2010, 1, 013003.
[5] Arun, S., Satheesh, A., Analysis of flow behaviour in a two sided lid driven cavity using lattice Boltzmann technique, Alexandria Engineering Journal, 54(4), 2015, 795-806.
[6] Wolff, F., Beckermann, C., Viskanta, R., Natural convection of liquid metals in vertical cavities, Experimental Thermal and Fluid Science, 1(1), 1988, 83–91.
[7] Viskanta, R., Kim, D.M., Gau, C., Three-dimensional natural convection heat transfer of a liquid metal in a cavity, International Journal of Heat and Mass Transfer, 29(3), 1986, 475–485.
[8] Rady, M.A., Mohanty, A.K., Natural convection during melting and solidification of pure metals in a cavity, Numerical Heat Transfer, Part A: Applications, 29(1), 1996, 49–63.
[9] Chen, H., Chen, Y., Hsieh, H-T., Zhang, J., A lattice Boltzmann modeling of corrosion behavior and oxygen transport in the natural convection lead-alloy flow, Nuclear Engineering and Design, 237(18), 2007, 1987–1998.
[10] Saravanan, S., Kandaswamy, P., Buoyancy convection in low Prandtl number liquids with large temperature variation, Meccanica, 37, 2002, 599–608.
[11] Ozoe, H., Maruo, E., Magnetic and gravitational natural convection of melted silicon-two dimensional numerical computations for the rate of heat transfer: Heat Transfer, Combustion, Power, Thermophysical Properties, JSME International Journal, 30, 1987, 774–784.
[12] Ozoe, H., Okada, K., The effect of the direction of the external magnetic field on the three-dimensional natural convection in a cubical enclosure, International Journal of Heat and Mass Transfer, 32(10), 1989, 1939–1954.
[13] Sathiyamoorthy, M., Chamkha, A., Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s), International Journal of Thermal Science, 49(10), 2010, 1856–1865.
[14] Yu, P.X., Qiu, J.X., Qin, Q., Tian, Z.F., Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field, International Journal of Heat and Mass Transfer, 67, 2013, 1131–1144.
[15] Yu, P.X., Xiao, Z., Wu, S., Tian, Z.F., Cheng, X., High accuracy numerical investigation of double-diffusive convection in a rectangular cavity under a uniform horizontal magnetic field and heat source, International Journal of Heat and Mass Transfer, 110, 2017, 613–628.
[16] Hussain, S.H., Analysis of heatlines and entropy generation during double-diffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure, Engineering Science and Technology, an International Journal, 19(1), 2016, 926–945.
[17] Roslan, R., Saleh, H., Hashim, I., Bataineh, A.S., Natural convection in an enclosure containing a sinusoidally heated cylindrical source, International Journal of Heat and Mass Transfer, 70, 2014, 119–127.
[18] Kalidasan, K., Velkennedy, R., Rajesh Kanna, P., Natural convection heat transfer enhancement using nanofluid and time-variant temperature on the square enclosure with diagonally constructed twin adiabatic blocks, Applied Thermal Engineering, 92, 2016, 219–235.
[19] Bhave, P., Narasimhan, A., Rees, D.A.S., Natural convection heat transfer enhancement using adiabatic block: Optimal block size and Prandtl number effect, International Journal of Heat Mass Transfer, 49(21-22), 2006, 3807–3818.
[20] Nazari, M., Louhghalam, L., Kayhani, M.H., Lattice Boltzmann simulation of double diffusive natural convection in a square cavity with a hot square obstacle, Chinese Journal of Chemical Engineering, 23(1), 2015, 22–30.
[21] Zhang, T., Che, D., Double MRT thermal lattice Boltzmann simulation for MHD natural convection of nanofluids in an inclined cavity with four square heat sources, International Journal of Heat and Mass Transfer, 94, 2016, 87–100.
[22] Maatki, C., Ghachem, K., Kolsi, L., Hussein, A.K., Borjini, M.N., Ben Aissia, H., Inclination effects of magnetic field direction in 3D double-diffusive natural convection, Applied Mathematics and Computation, 273, 2016, 178–189.
[23] Kefayati, G.H.R., Tang, H., Double-diffusive laminar natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder (Part II: Entropy generation), International Journal of Heat and Mass Transfer, 120, 2018, 683–713.
[24] Muthtamilselvan, M., Periyadurai, K., Doh, D.H., Impact of nonuniform heated plate on double-diffusive natural convection of micropolar fluid in a square cavity with Soret and Dufour effects, Advanced Powder Technology, 29(1), 2018, 66–77.
[25] Mahapatra, T.R., Pal, D., Mondal, S., Effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity, International Journal of Heat and Mass Transfer, 57(2), 2013, 771–785.
[26] Mondal, S., Sibanda, P., Unsteady double diffusive convection in an inclined rectangular lid-driven enclosure with different magnetic field angles and non-uniform boundary conditions, International Journal of Heat and Mass Transfer, 90, 2015, 900–910.
[27] Kumar, V., Murthy, S.V.S.S.N.V.G.K., Kumar, B.V.R., Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects – A numerical study, International Journal of Heat and Mass Transfer, 117, 2018, 1041–1062.
[28] Hussain, S., Oztop, H.F., Jamal, M., Hamdeh, N.A., Double diffusive nanofluid flow in a duct with cavity heated flow below, International Journal of Mechanical Sciences, 131-132, 2017, 535–545.
[29] Sheikholeslami, M., Oztop, H.F., MHD free convection of nanofluid in a cavity with sinusoidal walls by using CVFEM, Chinese Journal of Physics, 55(6), 2017, 2291–2304.
[30] Mehryan, S.A.M., Izadi, M., Chamkha, A.J., Sheremet, M.A., Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field, Journal of Molecular Liquids, 263, 2018, 510525.
[31] Purushothaman, P., Satheesh, A., Natural convection heat transfer and fluid flow analysis in a 2D square enclosure with sinusoidal wave and different convection mechanism, International Journal of Numerical Methods for Heat and Fluid Flow, 28(9), 2018, 2158-2188.
[32] Teamah, M.A., Shehata, A.I., Magnetohydrodynamic double diffusive natural convection in trapezoidal cavities, Alexandria Engineering Journal, 55, 2016, 1037-1046.
[33] Ghalambaz, M., Chamkha, A.J., Wen, D., Natural convective flow and heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) in a cavity, International Journal of Heat and Mass Transfer, 138, 2019, 738-749.
[34] Ghalambaz, M., Mehryan, S.A.M., Zahmatkesh, I., Chamkha, A., Free convection heat transfer analysis of a suspension of nano–encapsulated phase change materials (NEPCMs) in an inclined porous cavity, International Journal of Thermal Sciences, 157, 2020, 106503.
[35] Hajjar, A., Mehryan, S.A.M., Ghalambaz, M., Time periodic natural convection heat transfer in a nano-encapsulated phase-change suspension, International Journal of Mechanical Sciences, 166, 2020, 105243.
[36] Selimefendigil, F., Oztop, H.Z., Mixed convection and entropy generation of nanofluid flow in a vented cavity under the influence of inclined magnetic field, Microsystem Technologies, 25, 2019, 4427–4438.
[37] Ratnadeep, N., Murugesan, K., Optimization of double diffusive mixed convection in a BFS channel flled with Alumina nanoparticle using Taguchi method and utility concept, Scientific Reports, 9, 2019, 19536, 1-19.
[38] Yasmin, A., Ali, K., Ashraf, M., Study of Heat and Mass Transfer in MHD Flow of Micropolar Fluid over a Curved Stretching Sheet, Scientific Reports, 10, 2020, 4581, 1-11.
[39] Bhatnagar, P.L., Gross, E.P., Krook, M., A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Physical Review Journals Archive, 94, 1954, 511–525.
[40] Mohammed, A.A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer, 2012.
[41] Mohamad, A.A., Kuzmin, A., A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International Journal of Heat and Mass Transfer, 53, 2010, 990–996.
[42] Kefayati, G.R., Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution, Powder Technology, 243, 2013, 171–183.
[43] Arun, S., Satheesh, A., Mesoscopic analysis of MHD double diffusive natural convection and entropy generation in an enclosure filled with liquid metals, Journal of the Taiwan Institute of Chemical Engineers, 95, 2019, 155-173.