Lattice Boltzmann simulation of EGM and solid particle trajectory due to conjugate natural convection

Document Type: Original Research Paper


1 Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, I. R. Iran

2 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 91775-1111, I. R. Iran


The purpose of this paper is to investigate the EGM method and the behavior of a solid particle suspended in a twodimensional rectangular cavity due to conjugate natural convection. A thermal lattice Boltzmann BGK model is implemented to simulate the two dimensional natural convection and the particle phase was modeled using the Lagrangian–Lagrangian approach where the solid particles are treated as points moving in the computational domain as a result of the fluid motion. Entropy generation due to heat transfer irreversibility, isotherms, streamlines and Nusselt numbers were obtained and discussed. Total entropy generations in various cases are also reported and optimum case is presented based on minimum entropy generation.


[1]  J.W. Dally, P. Lall, J.C. Suhling: Mechanical Design of Electronic Systems. Knoxville, TN USA: College House Enterprises, LLS (2008). 

[2]  E. Samadiani, Y. Joshi, F. Mistree:The thermal desi-gn of a next generation data center: a conceptual exposition, J. Electron 130 (2008) 1104 −1112.

[3]  Y.K. Kim, K.H. Lee, H.R. Kim: Cold neutron source at KAERI, Korea, J. Nuclear Engng. and Design 238 (2008)1664−1669.

[4]  S. Karthikeyan, T. Sundararajan, U.S.P. Shet, P. Selvaraj: Effect of turbulent natural convection on sodium pool combustion in the steam generator building of a fast breeder reactor, J. Nuclear Engng. and Design 239(2009)2992−3002.

[5]  I. Rodriguez, J. Castro, C.D. Perez-Segarra, A. Oli va: L Unsteady numerical simulation of the cooling process of vertical storage tanks under laminar natural convection, Inter. J. Thermal Sci. 48(2009)708−721.

[6]  W. Lin, S.W. Armfield: Direct simulation of natural convection cooling in a vertical circular cylinder, Int. J. Heat Mass Transfer 42 (1999) 4117−4130.

[7]  V. Kurian, M.N. Varma, A. Kannan: Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio, Int. J. Heat Mass Transfer 52 (2009) 822−838.

[8]  G. V. Kuznetsov,  M. A. Sheremet: show all 2 hide:Two-dimensional problem of natural convection in a rectangular domain with local heating and heat-conducting boundaries of finite thickness, fluid dynamics 41(2006) 881-890.

[9]  S.G. Cherkasov: Natural convection and temperat -ure stratification in a cryogenic fuel tank in microgravity, Fluid Dynamics 29 (1994) 710−716.

[10] V.I. Polezhaev and S.G. Cherkasov, Unsteady thermal convection in a cylindrical vessel heated from the side, Fluid Dynamics 18 (1983) 620−629.

[11] S.G. Cherkasov: Natural convection in a vertical cylindrical vessel with heat supplied to its side and free surfaces, Fluid Dynamics 19 (1984) 902−906.

[12] L.A. Moiseeva, S.G. Cherkasov: Mathematical modeling of natural convection in a vertical cylindrical tank with alternating-sign heat flux distribution on the wall, Fluid Dynamics 31(1996)218−223.

[13] S.G. Martyushev, M.A. Sheremet: Mathematical Modeling of the Laminar Regime of Conjugate Convective Heat Transfer in an Enclosure with an Energy Source Under Surface-Radiation Conditions,” Journal of Engineering Physics and Thermophysics 86 (2013) 110–119.

[14] M.A. Sheremet: Unsteady conjugate thermo gravitational convection in a cylindrical region with local energy source, Thermophysics and Aeromechanics 18 (2011) 447-458.

[15] J. A. Esfahani, J. Alinejad: Entropy generation of conjugate natural convection in enclosures: the Lattice Boltzmann Method, Journal of Thermophysics and Heat Transfer  27 (2013) 498-505.

[16] A. C. Baytas: Entropy generation for natural con-vection in an inclined porous cavity, Int. J. Heat Mass Transfer 43 (2000) 2089–2099.

[17] G. Naterer: Transition criteria for entropy reduct - ion of convective heat transfer from micropatterned surfaces, J.  Thermophysics and Heat Transfer 22(2008)271-280.

[18] A. B. S. Alquaity, S. A. Al-Dini, B. S. Yilbas: Entropy generation in microchannel flow with presence of nanosized phase change particles, J. Thermophysics and Heat Transfer 26(2012)134-140.

[19] A. Vosoogh, A.R. Falahat: Effect of nanofluid on entropy generation and pumping power in coiled Tube, J. Thermophysics and Heat Transfer 26(2012)141-146.

[20] S. Chakraborty, D. Chatterjee: An enthalpy-based hybrid lattice-Boltzmann method for modelling solid-liquid phase transition in the presence of convective transport , J. Fluid Mechanics 592 (2007) 155-176.

[21] D. Chatterjee , S. Amiroudine : Lattice kinetic simulation of non isothermal magnet ohydrodynamics, Physical Review E 81(2010) 1-6.

[22] Z. Guo, T.S. Zhao: Lattice Boltzmann model for incompressible flows through porous media. Physical Review E 66 (2002) 304–312.

[23] A. D’Orazio,  M. Corcione,  G.P Celata: Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition. International Journal of Thermal Sciences 43 (2004) 575–586.

[24] C. Shu, Y. Peng, Y.T. Chew: Simulation of natural convection in a square cavity by Taylor series expansion and least squares-based lattice Boltzmann method. International Journal of Modern Physics 13 (2002) 1399–1414.

[25] B. Chopard, P. O. Luthi: Lattice Boltzmann computations and applications to physics. Theoret. Comput. Phys 217 (1999) 115–130.

[26] R. R. Nourgaliev, T. N. Dinh, T. G. Theofanous, D. Joseph: The lattice Boltzmann equation method: theoretical interpretation, numerics and implications. Int. J. Multiph. Flow 29 (2003) 117–169.

[27] D. Yu, R. Mei, L. S. Luo, W. Shyy: Viscous flow computations with the method of lattice Boltzmann equation. Progr. Aerospace. Sci  39 (2003) 329–367.

[28] A. A. Mohammad:  Applied Lattice Boltzmann Method for Transport Phenomena Momentum Heat Mass Transfer. University of Calgary Press, Calgary (2007).

[29] D. M. Aghajani, M. Farhadi, K. Sedighi: Effect of heater location on heat transfer and entropy generation in the cavity using the lattice Boltzmann method. Heat Transfer Research 40 (2009) 521–536.

[30] A. Mezrhab,  M. Jami, C. Abid, M. Bouzidi, P. Lallemand: Lattice Boltzmann modeling of natural convection in an inclined square enclosure with partitions attached to its cold wall. Int. J. Heat Fluid Flow 27 (2006) 456–465.

[31] X. He, L. S. Luo: Lattice Boltzmann model for the incompressible Navier–Stokes equations. J. Stat. Phys 88 (1997) 927–944.

[32] N. Thürey, U. Rüde: Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids. Comput. Vis. Sci12 (2009) 247–263.

[33] Y. Varol, H. F.Oztop, A. Koca: Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses, International Communications in Heat and Mass Transfer 35 (2008) 648–656.