Numerical Study of Buoyancy Natural Convection in An Open Cavity
Abstract - 80


Natural convection
lattice boltzmann method
open room

How to Cite

M. Almas. (2015). Numerical Study of Buoyancy Natural Convection in An Open Cavity. Journal of Advances in Applied & Computational Mathematics, 2(2), 38–46.


Numerical study of buoyancy natural convection in open building rooms has been performed using Lattice Boltzmann Method (LBM). The right wall of the room is open, bottom is hot and the other walls are adiabatic. Numerical results are presented in terms of isotherms, streamlines and average Nusselt number to investigate the effects of various Rayleigh numbers and aspect ratios on heat transfer and fluid flow. It is concluded that as the aspect ratio decreases maximum rate of heat transfer happens when Rayleigh number increases.


Randriazanamparany MA, Skouta A and Daguenet M. Numerical study of the transition toward chaos of twodimensional natural convection within a square cavity. Numeric Heat Transfer Part A: Appl 2005; 48(2): 127-147.

Dalal A, and Das MK. Natural convection in a rectangular cavity heated from below and uniformly cooled from the top and both sides. Numeric. Heat Transfer Part A: Appl 2006; 49 (3): 301-322.

Saeid NH and Yaacob Y. Natural convection in a square cavity with spatial side-wall temperature variation. Numeric Heat Transfer Part A: Appl 2006; 49(7): 683-697.

Penot F. Numerical calculation of two-dimensional natural convection in isothermal open cavities. Numeric Heat Transfer Part A: Appl 1982; 5(4): 421-437.

Chan Y and Tien C. A numerical study of two-dimensional natural convection in square open cavities. Numeric Heat Trans 1985; 8(1): 65-80.

Mohamad A. Natural convection in open cavities and slots. Numeric Heat Transfer Part A: Appl 1995; 27(6): 705-716.

Quere PL, Humphrey JA and Sherman FS. Numerical calculation of thermally driven two-dimensional unsteady laminar flow in cavities of rectangular cross section. Numeric Heat Trans 1981; 4(3): 249-283.

Chan Y and Tien C. Laminar natural convection in shallow open cavities. J Heat Trans 1986; 108(2): 305-309.

Cha S and Choi K. An Interferometric Investigation of Open- Cavity Natural-Convection Heat Transfer. Int J Experiment Heat Trans 1989; 2(1): 27-40.

Hess C and Henze R. Experimental investigation of natural convection losses from open cavities. J heat trans 1984; 106(2): 333-338.

Shao J, Liu J, Zhao J, Zhang W, Sun D and Fu Z. A novel method for full-scale measurement of the external convective heat transfer coefficient for building horizontal roof. Energy Build 2009; 41(8): 840-847.

Clear R, Gartland L and Winkelmann F. An empirical correlation for the outside convective air-film coefficient for horizontal roofs. Energy Build 2003; 35(8): 797-811.

Biwole P, Woloszyn M and Pompeo C. Heat transfers in a double-skin roof ventilated by natural convection in summer time. Energy Build 2008; 40(8): 1487-1497.

Higishima A and Tanimoto J. Field measurements for estimating the convective heat transfer coefficient at building surface. Energy Build 2003; 38: 873-881.

Varol Y, Oztop HF and Varol A. Effects of thin fin on natural convection in porous triangular enclosures. Int J therm Scienc 2007; 46(10): 1033-1045.

Mohamad A. Applied lattice Boltzmann method for transport phenomena, momentum. Heat and Mass Transfer Sure Print Calgary 2007.

Succi S. The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford university press 2001.

Mohamad A, El-Ganaoui M and Bennacer R. Lattice Boltzmann simulation of natural convection in an open ended cavity. Int J Therm Scienc 2009; 48(10): 1870-1875.

Qian Y, Ren D, Lai S and Chen S. Analytical approximations to nonlinear vibration of an electrostatically actuated microbeam. Commun Nonlin Sci Numer Simul 2012; 17(4): 1947-1955.

Ren ZF and Gui WK. He’s frequency formulation for nonlinear oscillators using a golden mean location. Compu Math Appl 2001; 61(8): 1987-1990.

Shou DH. The homotopy perturbation method for nonlinear oscillators. Compu Math Appl 2009; 58(11-12): 2456-2459.

Zeng DQ. Nonlinear oscillator with discontinuity by the max– min approach. Chaos Solitons Fractals 2009; 42(5): 2885- 2889.

He JH. Hamiltonian approach to nonlinear oscillators Phys Lett A 2010; 374(23): 2312-2314.

Xu L. Application of Hamiltonian approach to an oscillation of a mass attached to a stretched elastic wire. Math Comput Appl 2010; 15(5): 901-906.

Ghasemi E, Soleimani S and Bayat M. Control Volume Based Finite Element Method Study of Nano-fluid Natural Convection Heat Transfer in an Enclosure Between a Circular and a Sinusoidal Cylinder 2013; 1-12.

Ghasemi E, Soleimani S and Bararnia H. Natural convection between a circular enclosure and an elliptic cylinder using Control Volume based Finite Element Method. Int Communicat Heat Mass Trans 2012; 39: 1035-1044.

Bararnia H, Ghasemi E, Soleimani S, Baraei A and Ganji DD. HPM-Padé method on natural convection of Darcian fluid about a vertical full cone embedded in porous media. J Porous Media 2011; 14: 545-553.

Soleimani KS, Ghasemi E and Bayat M. Mesh-free modeling of two-dimensional heat conduction between eccentric circular cylinders Thermal Physics; Int J Physic Scienc 2011; 6(16): 4044-4052.

Soleimani S, Ganji DD, Gorji M, Bararnia H and Ghasemi E. Optimal location of a pair heat source-sink in an enclosed square cavity with natural convection through PSO algorithm. Int Communicat Heat Mass Trans 2011; 38: 652-658.

Ghasemi E, Soleimani S, Bararnia H and Domairry G. Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media. J Engineer Mech ASCE 2012; 138(1): 82-88.

Ghasemi E, Bayat M and Bayat M. Visco-Elastic MHD flow of Walters liquid b fluid and heat transfer over a non-isothermal stretching sheet. Int J Phys Scienc 2011; 6(21): 5022-5039.

Moghimi SM, Domairry G, Bararni H, Soleimani S and Ghasemi E. Numerical Study of Natural Convection in an Inclined L-shaped Porous Enclosure. Adv Theor Appl Mech 2012; 5: 237-245.

Alinia M, Gorji M, Ganji DD, Soleimani S and Ghasemi E. Two-phase natural convection of SiO2-water Nano fluid in an inclined square enclosure. Transac B: Mech Engin 2014; 21(5): 1643-1654.

Seyyedi SM, Soleimani S, Ghasemi E, Ganji DD, gorji M and Bararnia H. Numerical Investigation of Laminar Mixed Convection in a Cubic Cavity by MRT-LBM: Effects of the Sliding Direction. Numeric Heat Trans A 2013; 63: 285-304.

Ghasemi E, McEligot DM, Nolan K, Crepeau J, Siahpush A, Budwig RS and Tukohiro A. Effects of adverse and favorable pressure gradients on entropy generation in a transitional boundary layer region under the influence of freestream turbulence. Int J Heat Mass Transfer 2014; 77: 475-488.

Soleimani S, Ghasemi E and Almas MA. Effects of Pressure Gradients on Energy Dissipation Coefficient. J Advanc Therm Sci Res 2014; 1: 71-77.

Ghasemi E, Soleimani S and Almas MA. Finite Element Simulation of Jet Combustor Using Local Extinction Approach within Eddy Dissipation Concep. J Advanc Therm Sci Res 2014; 1: 57-65.

Bararnia H, Jalaal M, Ghasemi E, Soleimani S, Ganji DD, Mohammadi F. Numerical simulation of joule heating phenomenon using meshless RBF-DQ method. Int J Therm Sci 2010; 49: 2117-2127.

Soleimani S, Jalaal M, Bararnia H, Ghasemi E, Ganji DD, Mohammadi F. Local RBF-DQ method for two-dimensional transient heat conduction problems. Int Communicat Heat Mass Trans 2010; 37: 411-1418.

Jalaal M, Soleimani S, Domairry G, Ghasemi E, Bararnia H, Mohammadi F and Barari A. Numerical simulation of voltage electric field in complex geometries for different electrode arrangements using meshless local MQ-DQ method. J Electrostatics 2011; 69: 168-175.

Taeibi RM, Ramezanizadeh M, Ganji DD, Darvan A, Ghasemi E, Soleimani S and Bararni H. Comparative study of large eddy simulation of film cooling using a dynamic global-coefficient subgrid scale eddy-viscosity model with RANS and Smagorinsky Modeling. Int Communicat Heat Mass Trans 2011; 38: 659-667.

Ghasemi E, McEligot DM, Nolan K, Crepeau J, Tukohiro A, Budwig RS. Entropy generation in transitional boundary layer region under the influence of free stream turbulence using transitional RANS models and DNS. Int Comm Heat Mass Trans 2013; 41: 10-16.

Ghasemi E, Soleimani S and Lin CX. Secondary reactions of turbulent reacting flows over a film-cooled surface. Int Communicate Heat Mass Trans 2014; 55: 93-101.

Ghasemi E, Soleimani S and Lin CX. RANS simulation of methane-air burner using local extinction approach within eddy dissipation concept by Open FOAM. Int Communicate Heat Mass Trans 2014; 54: 96-102.

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