[1]. Y. L. Chan, C. L. Tien, A numerical study of two-dimensional natural convection in square open cavities, Int. J. Heat Mass Transfer, vol. 28, No.3, pp. 65–80, 1985.
[2]. E. Bilgen, A. Muftuoglu, Natural convection in an open square cavity with slots, Int. Communications. Heat and Mass Transfer, vol. 35, pp. 896–900, 2008.
[3]. T. Inamuro, M. Yoshino, F. Ogino, A non-slip boundary condition for lattice Boltzmann simulations, Phisics of Fliuds, vol. 7, pp. 2928–2930, 1995.
[4]. R. S. Maier, R. S. Bernard, D. W. Grunau, Boundary conditions for the lattice Boltzmann method, Phys. Fluids, vol. 8, pp. 1788–1801, 1996.
[5]. Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, vol. 9, pp. 1591–1598, 1997.
[6]. C. Chang, C. H. Liu, C. A. Lin, Boundary conditions for lattice Boltzmann simulations with complex geometry flows, Computers & Mathematics with Applications, vol. 58, Issue 5, pp. 940–949, 2009.
[7]. I. Ginzburg, Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations, Advances in Water Resources, vol. 28, pp. 1196–1216, 2005.
[8]. V. Sofonea, R. F. Sekerka, Boundary conditions for the upwind finite difference Lattice
Boltzmann model: Evidence of slip velocity in micro-channel flow, J. Computational Physics, vol. 207, pp. 639–659, 2005.
[9]. P. A. Skordos, Initial and boundary conditions for the lattice Boltzmann method, Phys, Rev. E, vol. 48, pp. 4823–4842, 1993.
[10]. 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, Int. J. Thermal Sci, vol. 43, pp. 575–586, 2004.
[11]. M. A. Gallivan, D. R. Noble, J. G. Georgiadis, R. O. Buckius, An evaluation of bounce-back boundary condition for lattice Boltzmann simulations, International journal for numerical methods in fluids, vol.25, pp. 249–263, 1997.
[12]. Z-L. Guo, C-G. Zheng, B-C. Shi , Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chinese Phys. vol.4, No.11, pp. 366–374, 2002.
[13]. D. P. Zeigler, Boundary condition for lattice Boltzmann simulations, Journal of statistical physics, vol.71, Nos.5/6, pp. 1171–1177, 1993.
[14]. D. R. Noble, S. Chen, J. G. Georgiadis, R. O. Buckius, A consistent hydrodynamics boundary condition for the lattice Boltzmann method, Phys. Fluids, vol. 7, No. 1, pp. 203–209, 1995.
[15]. S. Chen, D. Martnez, R. Mei, On boundary conditions in lattice Boltzmann methods, Phys. Fluids, vol. 8, No. 1, pp. 2527–2536, 1996.
[16]. G. H. Tang, W. Q. Tao, Y. L. He, Thermal boundary condition for the thermal lattice Boltzmann equation, Physical Review, E, Vol. 72, pp. 016703.1–016703.6, 2005.
[171]. H. Huang, T. S. Lee, C. Shu, Thermal curved boundary treatment for the thermal lattice Boltzmann equation, International Journal of Modern Physics C, vol. 17, No.5, pp. 631–643, 2006.
[18]. L. Zheng, Z. L. Guo, B. C. Shi, Discrete effects on thermal boundary conditions for the thermal lattice Boltzmann method in simulating micro scale gas flows, Europhysics Letters, vol. 82 ,No. 4, pp. 44002, 2008.
[19]. M. Corcione, Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above, International. J. Thermal Sci, vol. 42, No. 2, pp. 199–208, 2003.
[201]. A. D’Orazio, S. Succi, Boundary conditions for thermal lattice Boltzmann simulations, Lecture Notes Comput. Sci, vol. 2657, pp. 977–986, 2003.
[21]. A. D'Orazio, S. Succi, Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions, Future Generation Computer Systems, vol. 20, pp. 935–944, 2004.
[22]. L. S. Kuo, P. H. Chen, Numerical implementation of thermal boundary conditions in the lattice Boltzmann method, Int. J. Heat and Mass Transfer, vol. 52, pp. 529–532, 2009.
[23]. A. A. Mohamad, R. Bennacer, M. El-Ganaoui, Lattice Boltzmann simulation of natural convection in an open ended cavity, Int. J. Thermal Sci, vol.48, pp. 1870–1875, 2009.
[24]. H. N. Dixit, V. Babu, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat and Mass Transfer, vol. 49, pp. 727–739, 2006.
[25]. A. A. Mohamad, R. Bennacer, M. El-Ganaoui, Double dispersion, natural convection in an open end cavity simulation via Lattice Boltzmann Method. Int. J. Thermal Sci, vol. 49, pp. 1944–1953, 2010.
[26]. M. C. Sukop, D. T. Thorne.Jr, Lattice Boltzmann Modeling, Springer-Verlag, Berlin, 2006.
[27]. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon Press, Oxford, London, 2001.
[28]. J. Wang, M. Wang, Z. Li, A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer, Int. J. Thermal Sciences, vol. 46, pp. 228–234, 2007.
[29]. A. A. Mohamad, A. Kuzmin, A critical evaluation of force term in lattice Boltzmann method, natural convection problem. Int. J. Heat and Mass Transfer, vol. 53, pp. 990–996, 2010.
[30]. A. A. Mohamad, Natural convection in open cavities and slots, Numer. Heat Transfer, vol. 27, pp. 705–716, 1995.
[31]. J. F. Hinojosa, R. E. Cabanillas, G. Alvarez, C. E. Estrada, Nusslet number for the natural convection and surface thermal radiation in a square tilted open cavity, Int. Comm. Heat Mass Transfer, vol. 32, pp. 1184–1192, 2005.