Numerical Simulation of Convection Heat Transfer in a Lid-Driven Cavity with an Open Side
In this manuscript, the LBM is applied for simulating of Mixed Convection in a Lid-Driven cavity with an open side. The cavity horizontal walls are insulated while the west Lid-driven wall is maintained at a uniform temperature higher than the ambient. Prandtl number (Pr) is fixed to 0.71 (air) while Reynolds number (Re) , Richardson number (Ri) and aspect ratio (A) of the cavity are changed in the range of 50-150 , of 0.1-10 and of 1-4 , respectively. The numerical code is validated for the standard square cavity, and then the results of an open ended cavity are presented. Result shows by increasing of aspect ratio, the average Nusselt number (Nu) on lid- driven wall decreases and with same Reynolds number (Re) by increasing of aspect ratio (A), Richardson number plays more important role in heat transfer rate.
[1] Y.H. Qian, D. d-Humieres, P. Lallemand, Lattice BGK models for
NaviereStokes equation, Europhys. Lett. 17 (6) (1992) 479-484.
[2] S. Chen, G.D. Doolen, Lattice Boltzmann method for fluid flows, Annu.
Rev. Fluid Mech. 30 (1998) 329-364.
[3] 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.
[4] S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and
Beyond, Clarendon Press, Oxford, London, 2001.
[5] E. Fattahi, M. Farhadi, K. Sedighi , Lattice Boltzmann simulation of
natural convection heat transfer in eccentric annulus, International
Journal of Thermal Sciences, 49 (2010) 2353-2362.
[6] M.A. Delavar, M. Farhadi, K. Sedighi, Numerical simulation of direct
methanol fuel cells using lattice Boltzmann method, international journal
of hydrogen energy, 35 (2010) 9306-9317.
[7] He X, Luo LS, A priori derivation of the lattice Boltzmann equation.
Phys Rev E, 55(1997),R6333.
[8] U. Ghia, K.N. Ghia, C.T. Shin, High-resolutions for incompressible
flow using Navier-Stokes equations and a multigrid method, Comput.
Phys, 48 (1982) 387-411.
[9] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi, A.A.R. Darzi, Lattice
Boltzmann simulation of nanofluid in lid-driven cavity, International
Communications in Heat and Mass Transfer, 37 (2010) 1528-1534.
[10] Y.L. Chan, C.L. Tien, Laminar natural convection in shallow open
cavities, J. Heat Transfer 108 (1986) 305-309.
[11] E. Bilgen, Passive solar massive wall systems with fins attached on the
heated wall and without glazing, J. Sol. Energ. Eng. 122 (2000) 30-34.
[12] S.S. Cha, K.J. Choi, An interferometric investigation of open cavity
natural convection heat transfer, Exp. Heat Transfer 2 (1989) 27-40.
[13] A. Javam, S.W. Armfield, Stability and transition of stratified natural
convection flow in open cavities, J. Fluid Mech. 44 (2001) 285-303.
[14] A.A. Mohamad, Natural convection in open cavities and slots,
International journal of Heat Transfer 27 (1995) 705-716.
[15] A.A. Mohamad, M. El-Ganaoui, R. Bennacer, Lattice Boltzmann
simulation of natural convection in an open ended cavity, International
Journal of Thermal Sciences 48 (2009) 1870-1875
[16] M.K. Moallemi, K.S. Jang, Prandtl number effects on laminar mixed
convection heat transfer in a lid-driven cavity, Int. J. Heat Mass Transfer
35 (1992) 1881-1892.
[1] Y.H. Qian, D. d-Humieres, P. Lallemand, Lattice BGK models for
NaviereStokes equation, Europhys. Lett. 17 (6) (1992) 479-484.
[2] S. Chen, G.D. Doolen, Lattice Boltzmann method for fluid flows, Annu.
Rev. Fluid Mech. 30 (1998) 329-364.
[3] 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.
[4] S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and
Beyond, Clarendon Press, Oxford, London, 2001.
[5] E. Fattahi, M. Farhadi, K. Sedighi , Lattice Boltzmann simulation of
natural convection heat transfer in eccentric annulus, International
Journal of Thermal Sciences, 49 (2010) 2353-2362.
[6] M.A. Delavar, M. Farhadi, K. Sedighi, Numerical simulation of direct
methanol fuel cells using lattice Boltzmann method, international journal
of hydrogen energy, 35 (2010) 9306-9317.
[7] He X, Luo LS, A priori derivation of the lattice Boltzmann equation.
Phys Rev E, 55(1997),R6333.
[8] U. Ghia, K.N. Ghia, C.T. Shin, High-resolutions for incompressible
flow using Navier-Stokes equations and a multigrid method, Comput.
Phys, 48 (1982) 387-411.
[9] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi, A.A.R. Darzi, Lattice
Boltzmann simulation of nanofluid in lid-driven cavity, International
Communications in Heat and Mass Transfer, 37 (2010) 1528-1534.
[10] Y.L. Chan, C.L. Tien, Laminar natural convection in shallow open
cavities, J. Heat Transfer 108 (1986) 305-309.
[11] E. Bilgen, Passive solar massive wall systems with fins attached on the
heated wall and without glazing, J. Sol. Energ. Eng. 122 (2000) 30-34.
[12] S.S. Cha, K.J. Choi, An interferometric investigation of open cavity
natural convection heat transfer, Exp. Heat Transfer 2 (1989) 27-40.
[13] A. Javam, S.W. Armfield, Stability and transition of stratified natural
convection flow in open cavities, J. Fluid Mech. 44 (2001) 285-303.
[14] A.A. Mohamad, Natural convection in open cavities and slots,
International journal of Heat Transfer 27 (1995) 705-716.
[15] A.A. Mohamad, M. El-Ganaoui, R. Bennacer, Lattice Boltzmann
simulation of natural convection in an open ended cavity, International
Journal of Thermal Sciences 48 (2009) 1870-1875
[16] M.K. Moallemi, K.S. Jang, Prandtl number effects on laminar mixed
convection heat transfer in a lid-driven cavity, Int. J. Heat Mass Transfer
35 (1992) 1881-1892.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60928", author = "M.Jafari and M.Farhadi and K.sedighi and E.Fattahi", title = "Numerical Simulation of Convection Heat Transfer in a Lid-Driven Cavity with an Open Side", abstract = "In this manuscript, the LBM is applied for simulating of Mixed Convection in a Lid-Driven cavity with an open side. The cavity horizontal walls are insulated while the west Lid-driven wall is maintained at a uniform temperature higher than the ambient. Prandtl number (Pr) is fixed to 0.71 (air) while Reynolds number (Re) , Richardson number (Ri) and aspect ratio (A) of the cavity are changed in the range of 50-150 , of 0.1-10 and of 1-4 , respectively. The numerical code is validated for the standard square cavity, and then the results of an open ended cavity are presented. Result shows by increasing of aspect ratio, the average Nusselt number (Nu) on lid- driven wall decreases and with same Reynolds number (Re) by increasing of aspect ratio (A), Richardson number plays more important role in heat transfer rate.
", keywords = "Lattice Boltzmann Method, Open ended cavity, Mixed convection, Lid-driven cavity.", volume = "5", number = "11", pages = "2436-5", }
