Hybrid Lattice Boltzmann Scheme for Conductive-convective-radiative Heat Transfer

Document Type : Research Paper

Author
Alexander Nee
Research School of High-Energy Physics, National Research Tomsk Polytechnic University, Tomsk, Russia
10.22055/jacm.2025.47928.4848
Abstract
This paper presents the hybrid lattice Boltzmann model to study the interaction of conduction, natural convection and surface radiation. A square air-filled cavity with finite thickness walls is considered. The heat source is fixed at the top solid-fluid interface. The boundary conditions of the first, second, third and fourth kind are used to describe the problem under. The fluid flow and heat transfer under the Boussinesq approximation are analyzed by means of the lattice Boltzmann and energy equations discretized by the single relaxation time approximation and implicit finite difference schemes, respectively. Surface thermal radiation is computed in terms of the radiosity/irradiation model solved by the Gaussian elimination method. An in-house MATLAB code was carefully validated against three typical benchmark problems. For the first time, the full 2D conduction-convection-radiation coupling is numerically analyzed by the hybrid lattice Boltzmann (HLB) method. It is found that the HLB model reproduces the same conjugate heat transfer and fluid flow patterns as the vorticity-stream function (VS) formulation. For the first time, a comparative study of computational efficiency of the HLB and VS models is carried out. It is shown that the VS model outperforms the HLB scheme with a low grid resolution. However, the hybrid lattice Boltzmann model is faster than the vorticity-stream function formulation when using the mesh points more than 3612. With this regard, the HLB scheme is preferable to use in problems where the steep velocity or temperature gradients should be accurately resolved.
Keywords
Conjugate heat transfer
Surface radiation, Natural convection, Hybrid lattice Boltzmann method, Finite difference method
Subjects

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[1] Qi, C., Tang, J., Wang, G., Natural convection of composite nanofluids based on a two-phase lattice Boltzmann model, Journal of Thermal Analysis and Calorimetry, 141, 2020, 277–287.
[2] Wang, J., Wang, M., Li, Zh. A., lattice Boltzmann algorithm for fluid–solid conjugate heat transfer, International Journal of Thermal Sciences, 46, 2007, 228–234.
[3] Meng, F., Wang, M., Li, Zh., Lattice Boltzmann simulations of conjugate heat transfer in high-frequency oscillating flows, International Journal of Heat and Fluid Flow, 29, 2008, 1203–1210.
[4] Pirouz, M.M., Farhadi, M., Sedighi, K., Nemati, H., Fattahi, E., Lattice Boltzmann simulation of conjugate heat transfer in a rectangular channel with wall-mounted obstacles, Scientia Iranica, 18, 2011, 213–221.
[5] Seddiq, M., Maerefat, M., Mirzaei, M., Modeling of heat transfer at the fluid-solid interface by lattice Boltzmann method, International Journal of Thermal Sciences, 75, 2014, 28–35.
[6] Yue, L., Chai, Zh., Wang, L., Shi, B., A lattice Boltzmann model for the conjugate heat transfer, International Journal of Heat and Mass Transfer, 165, 2021, 120682.
[7] Hosseini, S.A., Darabiha, N., Thévenin, D., Lattice Boltzmann advection-diffusion model for conjugate heat transfer in heterogeneous media, International Journal of Heat and Mass Transfer, 132, 2019, 906–919.
[8] Lu, J.H., Lei, H.Y., Dai, C.S., A simple difference method for lattice Boltzmann algorithm to simulate conjugate heat transfer, International Journal of Heat and Mass Transfer, 114, 2017, 268–276.
[9] Lu, J.H., Lei, H.Y., Dai, C.S., A lattice Boltzmann algorithm for simulating conjugate heat transfer through virtual heat capacity correction, International Journal of Thermal Sciences, 116, 2017, 22–31.
[10] Lu, J.H., Lei, H.Y., Dai, C.S., A unified thermal lattice Boltzmann equation based on MRT model for conjugate heat transfer in anisotropic media, International Journal of Thermal Sciences, 130, 2018, 157–167.
[11] Hua, Ya., Li, D., Shu, Sh., Niu, X., Simulation of steady fluid–solid conjugate heat transfer problems via immersed boundary-lattice Boltzmann method, Computers and Mathematics with Applications, 70, 2015, 2227–2237.
[12] Yang, L.M., Shu, C., Yang, W.M., Wu, J., Simulation of conjugate heat transfer problems by lattice Boltzmann flux solver, International Journal of Heat and Mass Transfer, 137, 2019, 895–907.
[13] Imani, G., Lattice Boltzmann method for conjugate natural convection with heat generation on non-uniform meshes. Computers and Mathematics with Applications, 79, 2020, 1188–1207.
[14] Mohebbi, R., lakzayi, H., Rasam, H., Numerical simulation of conjugate heat transfer in a square cavity consisting the conducting partitions by utilizing lattice Boltzmann method, Physica, A, 546, 2020, 123050.
[15] Chen, S., Yan, Y.Y., Gong, W., A simple lattice Boltzmann model for conjugate heat transfer research, International Journal of Heat and Mass Transfer, 107, 2017, 862–870.
[16] Wang, L., Zhao, Yo., Yang, X., Shi, B., Chai, Zh., A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder, Applied Mathematical Modelling, 71, 2019, 31–44.
[17] Gao, X.-L., Wu, J., Luo, K., Yi, H.-L., Tan, H.-P., Lattice Boltzmann analysis of conjugate heat transfer in the presence of electrohydrodynamic flow, International Communications in Heat and Mass Transfer, 132, 2022, 105878.
[18] Liu, X., Tong, Z.-X., He, Y.-L., Du, S., Li, M.-J., Enthalpy-based cascaded lattice Boltzmann method for conjugate heat transfer, International Communications in Heat and Mass Transfer, 159, 2024, 107956.
[19] Zhang, S.-T., Hu, Y., He, Q., Li, Q.-P., A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface, Computers and Mathematics with Applications, 151, 2023, 134–152.
[20] Ferhi, M., Djebali, R., Appraising conjugate heat transfer, heatlines visualization and entropy generation of Ag-MgO/H2O hybrid nanofluid in a partitioned medium, International Journal of Numerical Methods for Heat and Fluid Flow, 30, 2020, 4529–4562.
[21] Guo, K., Li, L., Xiao, G., AuYeung, N., Mei, R., Lattice Boltzmann method for conjugate heat and mass transfer with interfacial jump conditions, International Journal of Heat and Mass Transfer, 88, 2015, 306–322.
[22] Lu, J.H., Lei, H.Y., Dai, C.S., Analysis of Henry’s law and a unified lattice Boltzmann equation for conjugate mass transfer problem, Chemical Engineering Science, 199, 2019, 319–331.
[23] Korba, D., Wang, X., Li, L., Accuracy of interface schemes for conjugate heat and mass transfer in the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 156, 2020, 119694.
[24] Gao, D., Chen, Zh., Chen, L., Zhang, D., A modified lattice Boltzmann model for conjugate heat transfer in porous media. International Journal of Heat and Mass Transfer, 105, 2017, 673–683.
[25] Wang, Ch.-Sh., Shen, P.-Y., Liou, T.-M., A consistent thermal lattice Boltzmann method for heat transfer in arbitrary combinations of solid, fluid, and porous media, Computer Methods in Applied Mechanics and Engineering, 368, 2020, 113200.
[26] Ross-Jones, J., Gaedtke, M., Sonnick, S., Rädle, M., Nirschl, H., Krause, M. J., Conjugate heat transfer through nano scale porous media to optimize vacuum insulation panels with lattice Boltzmann methods, Computers and Mathematics with Applications, 77, 2019, 209–221.
[27] Lallemand, P., Lou, L.-S., Hybrid finite-difference thermal lattice Boltzmann equation, International Journal of Modern Physics B, 17, 2003, 41–47.
[28] Obrecht, C., Kuznik, F., Tourancheau, B., Roux, J.-J., Multi-GPU implementation of a hybrid thermal lattice Boltzmann solver using the TheLMA framework, Computers and Fluids, 80, 2013, 269–275.
[29] Bettaibi, S., Kuznik, F., Sediki, E., Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity, Physics Letters A, 378, 2014, 2429–2435.
[30] Guo, S., Feng, Y., Feng, Y., Sagaut, P., On the use of conservative formulation of energy equation in hybrid compressible lattice Boltzmann method, Computers and Fluids, 219, 2021, 104866.
[31] Benhamou, J., Lahmer, E.B., Jami, M., Three-dimensional simulation of conjugate heat transfer using the hybrid lattice Boltzmann-finite difference method, International Communications in Heat and Mass Transfer, 139, 2022, 106486.
[32] Mezrhab, A., Bouzidi, M., Lallemand, P., Hybrid lattice-Boltzmann finite-difference simulation of convective flows, Computers and Fluids, 33, 2004, 623–641.
[33] Benhamou, J., Channouf, S., Lahmer, E.B., Jami, Mezrhab, A., Hybrid-lattice Boltzmann Method for the Simulation of Magnetohydrodynamic Conjugate Heat Transfer and Entropy Generation in Three Dimensions, Arabian Journal for Science and Engineering, 49, 2024, 1181–1206.
[34] Nee, A., Chamkha, A.J., Hybrid Simulation of Turbulent Natural Convection in an Enclosure with Thermally-Conductive Walls, International Journal of Applied Mechanics, 13, 2021, 2150059.
[35] Sathiyamoorthi, A., Anbalagan, S., Öztop, H.F., Abu-Hamdeh, N.H., MHD Double-Diffusive Natural Convection in a Closed Space Filled with Liquid Metal: Mesoscopic Analysis, Journal of Applied and Computational Mechanics, 7, 2021, 1448-1465.
[36] Mohammadifar, H., Sajjadi H., Rahnama, M., Jafari, S., Wang, Y., Investigation of Nanofluid Natural Convection Heat Transfer in Open Ended L-shaped Cavities utilizing LBM, Journal of Applied and Computational Mechanics, 7, 2021, 2064–2083.
[37] Djebali, R., Jaouabi, A., Naffouti, T., Abboudi, S., Accurate LBM appraising of pin-fins heat dissipation performance and entropy generation in enclosures as application to power electronic cooling, International Journal of Numerical Methods for Heat & Fluid Flow, 30, 2020, 742–768.
[38] Samarskii, A.A., The Theory of Difference Schemes, Nauka Press, Moscow, 1977, (in Russian).
[39] Kuznetsov, G.V., Kurilenko, N.I., Nee, A.E., Mathematical modelling of conjugate heat transfer and fluid flow inside a domain with a radiant heating system, International Journal of Thermal Sciences, 131, 2018, 27–39.
[40] Davis, G.D., Natural convection of air in a square cavity: a bench mark numerical solution, International Journal for Numerical Methods in Fluids, 3, 1983, 249–264.
[41] Barakos, G., Mitsoulis, E., Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions, International Journal for Numerical Methods in Fluids, 18, 1994, 695–719.
[42] Dixit, H.N., Babu, V., Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 49, 2006, 727–739.
[43] Ben Yedder, R., Bilgen, E., Laminar natural convection in inclined enclosures bounded by a solid wall, Heat and Mass Transfer, 32, 2018, 455–462.
[44] Wang, H., Xin, S., Le Quere, P., Etude numerique du couplage de la convection naturelle avec le rayonnement de surfaces en cavite carree remplie d'air, Comptes Rendus Mécanique, 334, 2006, 48–57.
[45] Martyushev, S.G., Sheremet, M.A., Conjugate natural convection combined with surface thermal radiation in an air filled cavity with internal heat source, International Journal of Thermal Sciences, 76, 2014, 51–67.
Journal of Applied and Computational Mechanics
Volume 11, Issue 4
Autumn 2025
Pages 1149-1161