Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

doi:10.1007/s10483-018-2353-6

Abstract

Abstract:

The lattice Boltzmann method (LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90°. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.

Key words: impact force, elastic wave, Galerkin principle, natural convection, porous, lattice Boltzmann method (LBM), cavity

2010 MSC Number:

76D17
80A20

K. JAVAHERDEH, A. NAJJARNEZAMI. Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1187-1200.

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References

[1] DAVIS, D. V. Natural convection of air in a square cavity:a benchmark numerical solution. International Journal of Numerical Methods in Fluids, 3, 249-264(1983)
[2] OSTRACH, S. Natural convection in enclosures. Journal of Heat Transfer, 110, 1175-1190(1988)
[3] CHENG, P. Heat transfer in geothermal systems. Advances in Heat Transfer, 14, 1-105(1979)
[4] NIELD, D. A. and BEJAN, A. Convection in Porous Media, Springer, New York (2006)
[5] AL-NIMR, M. A. and HADER, M. A. MHD free convection flow in open-ended vertical porous channels. Chemical Engineering Science, 54, 1883-1889(1999)
[6] NIELD, D. A. Impracticality of MHD convection in a porous medium. Transport in Porous Media, 73, 379-380(2008)
[7] GHASEMI, B., AMINOSSADATI, S. M., and RAISI, A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure. International Journal of Thermal Sciences, 50, 1748-1756(2011)
[8] RAHMAN, M. M., HAKAN, F., ÖZTOP, H. Ã., AHSAN, A., KALAM, M. A., and BILLAH, M. M. MHD mixed convection in a channel with a triangular cavity. Numerical Heat Transfer, Part A, 61, 268-282(2012)
[9] KEFAYATI, G. R. Simulation of magnetic field effect on non-Newtonian blood flow between two-square concentric duct annuli using FDLBM. Journal of the Taiwan Institute of Chemical Engineers, 45, 1184-1196(2014)
[10] KEFAYATI, G. R. Mesoscopic simulation of double-diffusive mixed convection of pseudoplastic fluids in an enclosure with sinusoidal boundary conditions. Computers and Fluids, 97, 94-109(2014)
[11] ATA, A., SERVATI, V., JAVAHERDEH, K., and ASHORYNEJAD, H. R. Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using lattice Boltzmann method. Advanced Powder Technology, 25, 666-675(2014)
[12] KEFAYATI, G. R. Mesoscopic simuation of magnetic field effect on natural convection of powerlaw fluids in a partially heated cavity. Chemical Engineering Research and Design, 94, 337-354(2015)
[13] RAHMATI, A. R. and NAJJARNEZAMI, A. A double multi-relaxation-time lattice Boltzmann method for simulation of magnetohydrodynamics natural convection of nanofluid in a square cavity. Journal of Applied Fluid Mechanics, 9, 1201-1214(2016)
[14] AHMED, S. E. and MAHDY, A. Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media. Applied Mathematics and Mechanics (English Edition), 37(4), 471-484(2016) https://doi.org/10.1007/s10483-016-2044-9
[15] CHATTERJEE, D. and GUPTA, S. K. Magnetohydrodynamic natural convection in a square enclosure with four circular cylinders positioned at different rectangular locations. Heat Transfer Engineering, 38, 1449-1465(2017)
[16] PANGRLE, B. J., WALSH, E. G., MOORE, S. C., and DIBIASIO'O, D. Magnetic resonance imaging of laminar flow in porous tube and shell systems. Chemical Engineering Science, 47, 517-526(1992)
[17] SATHIYAMOORTHY, M., BASAK, T., POP, I., and ROY, S. Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side walls. International Journal of Heat and Mass Transfer, 50, 1892-1901(2007)
[18] SHEIKHZADEH, G. and NAZARI, S. Numerical study of natural convection in a square cavity filled with a porous medium saturated with nanofluid. Transport Phenomena in Nano and Micro Scales, 1, 138-146(2013)
[19] FRISCH, U., HASSLACHER, B., and POMEAU, Y. Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters, 56, 1505-1508(1986)
[20] SUCCI, S., FOTI, E., and HIGUERA, F. Three-dimensional flows in complex geometries with the lattice Boltzmann method. Europhysics Letters, 10, 433-438(1989)
[21] HE, Y. L., WANG, Y., and LI, Q. Lattice Boltzmann Method:Theory and Applications, Science Press, Beijing (2009)
[22] GONG, S. and CHENG, P. Lattice Boltzmann simulation of periodic bubble nucleation, growth and departure from a heated surface in pool boiling. International Journal of Heat and Mass Transfer, 64, 122-132(2013)
[23] NAZARI, M., SHOKRI, H., and MOHAMMAD, A. A. Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall. Applied Mathematics and Mechanics (English Edition), 36(4), 523-540(2015) https://doi.org/10.1007/s10483-015-1928-9
[24] XU, A., SHI, L., and ZHAO, T. S. Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management. International Journal of Heat and Mass Transfer, 109, 577-588(2017)
[25] TANG, G. H., TAO, W. Q., and HE, Y. L. Gas slippage effect on microscale porous flow using the lattice Boltzmann method. Physical Review E, 72, 056301(2005)
[26] KANG, Q. J., LICHTNER, P. C., and ZHANG, D. X. An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale. Water Resources Research, 43, 2578-2584(2007)
[27] KANG, Q., ZHANG, D., and CHEN, S. Unified lattice Boltzmann method for flow in multiscale porous media. Physical Review E, 66, 056307(2002)
[28] GUO, Z. and ZHAO, T. S. Lattice Boltzmann model for incompressible flows through porous media. Physical Review E, 66, 036304(2002)
[29] GUO, Z. and ZHAO, T. S. A lattice Boltzmann model for convection heat transfer in porous media. Numerical Heat Transfer B, 47, 157-177(2005)
[30] DARDIS, O. and MCCLOSKEY, J. Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media. Physical Review E, 57, 4834-4837(1998)
[31] XU, A., SHYY, W., and ZHAO, T. Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries. Acta Mechanica Sinica, 33, 555-574(2017)
[32] SETA, T., TAKEGOSHI, E., and OKUI, K. Lattice Boltzmann simulation of natural convection in porous media. Mathematics and Computer in Simulation, 72, 195-200(2006)
[33] MEHRIZI, A., SEDIGHI, K., and HASSANZADE, H. Lattice Boltzmann simulation of force convection in vented cavity filled by porous medium with obstruction. World Applied Science Journal, 16, 31-36(2012)
[34] ASHORYNEJAD, H. A., FARHADI, M., SEDIGHI, K., and HASANPOUR, A. Free convection in a MHD porous cavity with using lattice Boltzmann method. World Academy of Science, Engineering and Technology, 73, 735(2011)
[35] LIU, Q. and HE, Y. L. Lattice Boltzmann simulations of convection heat transfer in porous media. Physica A:Statistical Mechanics and Its Applications, 465, 742-753(2017)
[36] CRAMER, K. R. and PAI, S. I. Magnatofluid Dynamics for Engineers and Physicists, McGrawHill, New York (1973)
[37] IRWAN, M. and AZWADI, C. Simplified mesoscale lattice Boltzmann numerical model for predication of natural convection in a square enclosure filled with homogeneous porous media.Wseas Transactions on Fluid Mechanics, 5, 186-195(2010)
[38] KEFAYATI, G. R. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution. Powder Technology, 243, 171-183(2013)
[39] SIVARAJ, C. and SHEREMET, M. A. MHD natural convection in an inclined square porous cavity with a heat conducting solid block. Journal of Magnetism and Magnetic Materials, 426, 351-360(2017)
[40] MOHAMAD, A. Lattice Boltzmann Method, Springer, New York (2011)
[41] MEJRI, I., MAHMOUDI, A., ABBASSI, M. A., and OMRI, A. MHD natural convection in a nanofluid-filled rnclosure with non-uniform heating on both side walls. Fluid Dynamics and Materials Processing, 10, 83-114(2014)