Numerical Study of Mixed Convection Flows around Large-Scale Heat Sinks: Application to Data Center Cooling

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In this work, we present a numerical study of mixed convection flows around large-scale heat sinks. It is based on the Cascade Lattice Boltzmann Method (LBM) for values of the Rayleigh number, in transitional regime, in the range 5×107≤Ra≤5×108 and for a Reynolds value fixed at Re=1000. The study is carried out in a rectangular cavity of dimension H subjected to periodic thermal and dynamic boundary conditions on its vertical walls. Two heat sources of (L', l', H/2) with a hot temperature Th, are placed on the bottom wall of the cavity to simulate heat sinks. Fresh air (for cooling these heat sinks) is injected at a temperature Tc< Th from the bottom of the cavity through two openings of length L''. The hot air is extracted through an opening (2L'' long) managed on the upper horizontal wall. The preliminary results, presented in this paper, are in the form of streamlines, isotherms and thermal profiles in the range of the Rayleigh number considered. Heat transfer is studied in terms of the average Nusselt number calculated over the entire surface of the two heat sources.

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37-46

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March 2026

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© 2026 Trans Tech Publications Ltd. All Rights Reserved

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[1] M. Sahini, E. Kumar, T. Gao, C. Ingalz, A. Heydari, S. Xiaogang; Study of airflowenergy within data center room and sizing of hot aisle containment foran active vs passive cooling design.2016 15th IEEE Intersociety Conferenceon Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Applied Energy, ICAE2016, 8-11 October 2016, Beijing, China.

DOI: 10.1109/itherm.2016.7517719

Google Scholar

[2] K. Nemati, H.A. Alissa, B.T. Murray, B. Sammakia; Steady-state and transient comparison of cold and hot aisle containment and chimney. 2016 15thIEEE Intersociety Conference on Thermal and Thermomechanical Phenomena In Electronic Systems (ITherm), 2016, p.1435–1443, http://dx.doi.org/10.1109/ ITHERM.2016. 7517717.

DOI: 10.1109/itherm.2016.7517717

Google Scholar

[3] Y.U. Makwana, A.R. Calder, S.K. Shrivastava; Benefits of properly sealing a cold aisle containment system. Fourteenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2014, p.793–797.

DOI: 10.1109/itherm.2014.6892362

Google Scholar

[4] R. Grantham, K. Lemke; Method and apparatus for installation and removal of overhead cooling equipment. 2013, United States Patent 8, 405, 982.

Google Scholar

[5] K. Dunlap, N. Rasmussen; Choosing between room, row, and rack-based cooling for data centers. 2012, URL https://download.schneiderelectric.com/filep_DocRef=SPD_VAVR-6J5VYJ_EN.

Google Scholar

[6] Y. Qian, D. d'Humières, P. Lallemand, Lattice bgk models for Navier-Stokes equation, EPL (Europhys. Lett.) 17 (6) (1992) 479.

DOI: 10.1209/0295-5075/17/6/001

Google Scholar

[7] M. Geier, A. Greiner, J.G. Korvink, Cascaded digital lattice Boltzmann automata for high Reynolds number flow, Phys. Rev. E 73 (6) (2006) 066705.

DOI: 10.1103/physreve.73.066705

Google Scholar

[8] I. Ginzburg, D. d'Humières, Multireflection boundary conditions for lattice Boltzmann models, Phys. Rev. E 68 (6) (2003) 066614.

DOI: 10.1103/physreve.68.066614

Google Scholar

[9] A. De Rosis, Alternative formulation to incorporate forcing terms in a lattice Boltzmann scheme with central moments, Phys. Rev. E 95 (2) (2017) 023311.

DOI: 10.1103/physreve.95.023311

Google Scholar

[10] D. Lycett-Brown, K.H. Luo, Multiphase cascaded lattice Boltzmann method, Comput. Math. Appl. 67 (2) (2014) 350–362.

DOI: 10.1016/j.camwa.2013.08.033

Google Scholar

[11] D. Lycett-Brown, K.H. Luo, R. Liu, P. Lv, Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method, Phys. Fluids 26 (2) (2014) 023303.

DOI: 10.1063/1.4866146

Google Scholar

[12] A. De Rosis, A central moments-based lattice Boltzmann scheme for shallow water equations, Comput. Methods Appl. Mech. Eng. 319 (2017) 379–392.

DOI: 10.1016/j.cma.2017.03.001

Google Scholar

[13] F. Hajabdollahi, K.N. Premnath, Improving the low Mach number steady state convergence of the cascaded lattice Boltzmann method by preconditioning, Comput. Math. Appl. (2017).

DOI: 10.1016/j.camwa.2016.12.034

Google Scholar

[14] D. Lycett-Brown, K.H. Luo, Cascaded lattice Boltzmann method with improved forcing scheme for large-density-ratio multiphase flow at high Reynolds and Weber numbers, Phys. Rev. E 94 (5) (2016) 053313.

DOI: 10.1103/physreve.94.053313

Google Scholar

[15] K.N. Premnath, S. Banerjee, Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments, Phys. Rev. E 80 (3) (2009) 036702.

DOI: 10.1103/physreve.80.036702

Google Scholar

[16] L. Fei, K.H. Luo, Consistent forcing scheme in the cascaded lattice Boltzmann method, Phys. Rev. E 96 (2017) 053307.

DOI: 10.1103/physreve.96.053307

Google Scholar

[17] L. Fei, K.H. Luo, Thermal cascaded lattice Boltzmann method. Available from: arXiv preprint <1610.07114>.

Google Scholar

[18] N. Shah, P. Dhar, S.K. Chinige, M. Geier, A. Pattamatta, Cascaded collision lattice Boltzmann model (clbm) for simulating fluid and heat transport in porous media, Numer. Heat Transfer, Part B: Fundam. 72 (3) (2017) 211–232.

DOI: 10.1080/10407790.2017.1377530

Google Scholar

[19] K.V. Sharma, R. Straka, F.W. Tavares, New cascaded thermal lattice Boltzmann method for simulations of advection-diffusion and convective heat transfer, Int. J. Therm. Sci. 118 (2017) 259–277.

DOI: 10.1016/j.ijthermalsci.2017.04.020

Google Scholar

[20] P. Asinari, Generalized local equilibrium in the cascaded lattice Boltzmann method, Phys. Rev. E 78 (2) (2008) 016701.

DOI: 10.1103/physreve.78.016701

Google Scholar

[21] X. He, X. Shan, G.D. Doolen, Discrete Boltzmann equation model for nonideal gases, Phys. Rev. E 57 (1) (1998) R13–R16.

DOI: 10.1103/physreve.57.r13

Google Scholar

[22] X. He, L.-S. Luo, Lattice Boltzmann model for the incompressible Navier–Stokes equation, J. Stat. Phys. 88 (3) (1997) 927–944.

DOI: 10.1023/b:joss.0000015179.12689.e4

Google Scholar

[23] G. De Vahl Davis, Natural convection of air in a square cavity: a benchmark numerical solution. Int. J. Numer. Meth. Fluids 3, 249 (1983).

DOI: 10.1002/fld.1650030305

Google Scholar