Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice Boltzmann Method

Document Type : Original Research Paper

Authors

Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran

Abstract

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr = 0.71) and Rayleigh numbers ranging from 103 to 106 at the macroscopic scale (Kn = 10-4). In every case, an appropriate value of the characteristic velocity is chosen using a simple model based on the kinetic theory.  By considering the obtained dimensionless velocity and temperature values, the distributions of entropy generation due to heat transfer and fluid friction are determined. It is found that for an enclosure with high value of Rayleigh number (i.e., Ra=105), the total entropy generation due to fluid friction and total Nu number increases with decreasing the aspect ratio.

Keywords

References

[1]  Y.H Qian., D. d’Humieres, P. Lallemand, LatticeBGK models for Navier–Stokes equation, Europhys.Lett. 17 (6) (1992) 479–484.
[2]  S. Chen, G.D. Doolen, Lattice Boltzmann methodfor fluid flows, Annu. Rev. Fluid Mech. 30 (1998)329–364.
[3]  D. Yu, R. Mei, L.S. Luo, W. Shyy, Viscous flowcomputations with the method of lattice Boltzmannequation, Progr. Aerospace Sci. 39 (2003) 329–367.
[4]  S. Succi, The Lattice Boltzmann Equation for FluidDynamics and Beyond, Clarendon Press, Oxford,2001.
[5]  X. Shan, Simulation of Rayleigh–Benard convectionusing a lattice Boltzmann method, Phys. Rev. E 55(1997) 2780–2788.
[6]  X. He, S. Chen, G.D. Doolen, A novel thermalmodel for the lattice Boltzmann method inincompressible limit, J. Comput. Phys. 146 (1998)282–300.
[7]  Y. Zhou, R. Zhang, I. Staroselsky, H. Chen,Numerical simulation of laminar and turbulentbuoyancy-driven flows using a lattice Boltzmannbased algorithm, Int. J. Heat Mass Transfer 47(2004) 4869–4879.
[8]  H.N. Dixit, V. Babu, Simulations of high Rayleighnumber natural convection in a square cavity usingthe lattice Boltzmann method, Int. J. Heat MassTransfer 49 (2006) 727–739.
[9]  P.H. Kao, R.-J. Yang, Simulating oscillatory flowsin Rayleigh– Benard convection using the latticeBoltzmann method, Int. J. Heat Mass Transfer 50(2007) 3315–3328.
[10] Y. Peng, C. Shu, Y.T.Chew, Simplified thermallattice Boltzmann model for incompressible thermalflows, Phys. Rev. E 68 (2003) 026701.
[11] G. Barrios, R. Rechtman, J. Rojas, Tovar R., Thelattice Boltzmann equation for natural convection ina two-dimensional cavity with a partially heatedwall, J. Fluid Mech. 522 (2005) 91–100.
[12] A. Bejan, Heat Transfer, Wiley, New York, 1993.
[13] I. Catton, Natural Convection in Enclosures, Proc.the 6th Int. Heat Transfer Conference, 6 (1978) 13-31.
[14] S. Ostrach, Natural Convection in Enclosures, J.Heat Transfer 110 (1988) 1175-1190.
[15] S. Kakaç, Y. Yener, Convective Heat Transfer, CRCPress, 2nd ed. (1995) 340-350.
[16] D. Poilikakos, Natural convection in a confined fluid- filled space driven by a single vertical wall withwarm and cold regions. J. Heat Transfer 107 (1985)867-876.
[17] D. Angirasa, M. J. B. M. Pourquié, F. T. M.Nieuwstadt, Numerical study of transient and steadylaminar buoyancy - driven flows and heat transfer ina square open cavity. Numerical Heat Transfer PartA 22 (1992) 223-239.
[18] O. Ayhan, A. Ünal, T. Ayhan, Numerical solutionsfor buoyancy - driven flow in a 2-D square enclosureheated from one side and cooled from above,Advanced in Computational Heat Transfer, TR,(1997) 337–394.
[19] K. Küblbeck, G. P. Merker, J. Straub, Advancenumerical computation of two – dimensional time -dependent free convection in cavities. Int. J. HeatMass Transfer 23 (1980) 203-217.
[20] N. C. Markatos, K. A. Pericleous, Laminer andturbulent natural convection in an enclosed cavity,Int. J. Heat Mass Transfer 27 (1984) 755-772.
[21] L. Lage, A. Bejan, The Ra-Pr domain of laminarnatural convection in an enclosure heated from theside. Numerical Heat Transfer Part A 19 (1991) 21-41.
[22] A. Bejan, Entropy generation through heat and fluidflow. New York: Wiley; 1982.
[23] A. Bejan, Entropy generation minimization. NewYork: CRC Press; 1996
[24] A. Bejan, Advanced engineering thermodynamics,2nd ed. New York: Wiley
[25] G. de Vahl Davis, Natural convection of air in asquare cavity: a bench mark numerical solution, Int.J. Numer. Methods Fluids. 3 (1983) 249–264.
[26] D. Rejane, C. Oliveski, H. Mario Macagnan, B.Jacqueline Copetti, Entropy generation and naturalconvection in rectangular cavities, J. AppliedThermal Engineering
[27] M.Y. Ha, M.J. Jung, A numerical study on threedimensionalconjugate heat transfer of naturalconvection and conduction in a differentially heatedcubic enclosure with a heat-generating cubicconducting body, Int. J. Heat and Mass Tran. 43(2000) 4229–4248.
[28] A. Mezrhab, H. Bouali, C. Abid, Modelling ofcombined radiative and convective heat transfer inan enclosure with a heat-generating conductingbody, International Journal of ComputationalMethods 2 (3) (2005) 431–450.
[29] I. Dagtekin, H.F. Oztop, A. Bahloul., Entropygeneration for natural convection in _-shapedenclosures, Int. Commun. Heat Mass Transf. 34(2007) 502–510.
[30] P.H. Kao, Y.H. Chen, R.J. Yang, Simulations of themacroscopic and mesoscopic natural convectionflows within rectangular cavities, J. Heat Mass Tran.51 (2008) 3776–3793.
[31] Z. Guo, B. Shi, C. Zheng, A coupled lattice BGKmodel for the Boussinesq equations, Int. J. ofNumerical Methods in Fluids, 39(4) (2002) 325-342.
[32] Z.L. Guo, Ch. Zheng, B.C. Shi, An extrapolationmethod for boundary conditions in lattice Boltzmannmethod, Phys. Fluids, 14 (6) (2002) 2007-2010.
[33] R. Mei, D. Yu, W. Shyy, L. Sh. Luo, Forceevaluation in the lattice Boltzmann methodinvolving curved geometry, Phys. Rev. E,.65 (2002)1-14.
[34] Z.L. Guo, B.C. Shi, Ch. Zheng, A coupled latticeBGK model for the Boussinesq equations, Int. J.Numer. Methods Fluids, 39 (4) (2002), 325-342.
[35] E. K. Glapke, C.B. Watkins, J. N. Cannon, Constantheat flux solutions for natural convection betweenconcentric and eccentric horizontal cylinders,Numer. Heat Transfer, 10 (1986), 279-295.
[36] X. He, Q. Zou, L.S. Luo, M. Dembo, Analyticsolutions of simple flows and analysis of nonslipboundary condition for the lattice Boltzmann BGKmodel, J. Stat. Phys. 87 (1997), pp. 115–136.
[37] H.N. Dixit, Simulation of flow and temperaturefields in enclosures using the lattice Boltzmannmethod. MS Thesis, 2005, Indian Institute ofTechnology Madras, India.
[38] Z.L. Guo, Ch. Zheng, B.C. Shi, An extrapolationmethod for boundary conditions in lattice Boltzmannmethod, Phys. Fluids, 14 (6) (2002), 2007-2010.
[39] C. Cercignani, Mathematical Methods in KineticTheory, Plenum, New York, 1969.
[40] G. Wannier, Statistical Physics, Diver, New York,1966.
[41] C. Shu, X.D. Niu, Y.T. Chew, A lattice Boltzmannkinetic model for microflow and heat transfer, J.Stat. Phys. 121 (1–2) (2005) 239–255

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