DOI: https://doi.org/10.14710/ijred.2022.45383

3D Numerical Investigation of Free Convection using Lattice Boltzmann and Finite Difference Methods

Laboratory of Mechanics & Energetics, Faculty of Sciences, Mohammed First University 60000 Oujda, Morocco

Received: 23 Mar 2022; Revised: 5 Jun 2022; Accepted: 16 Jun 2022; Available online: 27 Jun 2022; Published: 1 Nov 2022.
Editor(s): H. Hadiyanto
Open Access Copyright (c) 2022 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:
Abstract

Numerical study of various physical phenomena in three dimensions has become a necessity to better understand the physical process than in two dimensions. Thus, in this paper, the code is elaborated to be adapted to the simulation of heat transfer in three dimensions. The numerical simulations are performed using a hybrid method. This method is based on the lattice Boltzmann approach for the computation of velocities, and on the finite difference technique for the calculation of temperature. The used numerical code is validated by examining the free convection in a cubic enclosure filled with air. Then, the analysis of the heat exchange between two cold vertical walls and a heated block located at the center of a cubic cavity is considered.  The performed simulations showed that for a small value of the Rayleigh number (Ra=103 for example), the fluid exchanges its heat almost equally with all hot surfaces of the obstacle. However, for large values of Ra (Ra≥104), the numerical results found showed that the heat exchange rate is greater on the bottom face compared to the other faces of the obstacle.

Fulltext View|Download
Keywords: Lattice Boltzmann method; Finite difference method; Hybrid method; Free convection, Fluid flow, 3D simulation

Article Metrics:

Article Info
Section: Original Research Article
Language : EN
Recent articles
Enhancing Hydrogen Generation using CdS-modified TiO2 Nanotube Arrays in 2,4,6-Trichlorophenol as a Hole Scavenger Comparative Study on Oven and Solar Drying of Agricultural Residues and Food Crops 3D Numerical Investigation of Free Convection using Lattice Boltzmann and Finite Difference Methods Prospects and Challenges of Malaysia's Distributed Energy Resources in Business Models Towards Zero – Carbon Emission and Energy Security Green Port Strategies in Developed Coastal Countries as Useful Lessons for the Path of Sustainable Development: A case study in Vietnam A Review on the Recent Breakthrough Methods and Influential Parameters in the Biodiesel Synthesis and Purification More recent articles
Most cited articles
Experimental and Numerical Investigation of Nanofluid Usage in a Plate Heat Exchanger for Performance Improvement Variations of wave energy power in shoaling zone of Benin coastal zone Performance Evaluation of PV Panel Under Dusty Condition Passive Design of Buildings for Extreme Weather Environment Financial Measures for Electric Vehicles:Supporting the Integration of Renewable Energy in the Mobility Sector in Germany More cited articles
  1. Admi, Y., Moussaoui, M. A., & Mezrhab, A. (2022). Numerical Investigation of Convective Heat Transfer and Fluid Flow Past a Three-Square Cylinders Controlled by a Partition in Channel. International Journal of Renewable Energy Development, 11(3), 766-781. doi: 10.14710/ijred.2022.43790
  2. Baïri, A., Zarco-Pernia, E., & De María, J. M. G. (2014). A review on natural convection in enclosures for engineering applications. The particular case of the parallelogrammic diode cavity. Applied Thermal Engineering, 63(1), 304-322. doi: 10.1016/j.applthermaleng.2013.10.065
  3. Bejan, A., & Kraus, A. D. (2003). Heat transfer handbook (Vol. 1). John Wiley & Sons
  4. Benhamou, J., Jami, M., Mezrhab, A., Botton, V., & Henry, D. (2020). Numerical study of natural convection and acoustic waves using the lattice Boltzmann method. Heat Transfer, 49(6), 3779-3796. doi: 10.1002/htj.21800
  5. Benhamou, J., Jami, M., Mezrhab, A., Henry, D., & Botton, V. (2022). Numerical simulation study of acoustic waves propagation and streaming using MRT-lattice Boltzmann method. International Journal for Computational Methods in Engineering Science and Mechanics, 1-14. doi: 10.1080/15502287.2022.2050844
  6. Benhamou, J., & Jami, M. (2022). Three-dimensional numerical study of heat transfer enhancement by sound waves using mesoscopic and macroscopic approaches. Heat Transfer. doi: 10.1002/htj.22482
  7. Benhamou, J., Channouf, S., Jami, M., Mezrhab, A., Henry, D., & Botton, V. (2021). Three-Dimensional Lattice Boltzmann Model for Acoustic Waves Emitted by a Source. International Journal of Computational Fluid Dynamics, 35(10), 850-871. doi: 10.1080/10618562.2021.2019226
  8. Bettaibi, S., Kuznik, F., & Sediki, E. (2014). Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity. Physics Letters A, 378(32-33), 2429-2435.. doi: 10.1016/j.physleta.2014.06.032
  9. Chorin, P., Moreau, F., & Saury, D. (2020). Heat transfer modification of a natural convection flow in a differentially heated cavity by means of a localized obstacle. International Journal of Thermal Sciences, 151, 106279. doi: 10.1016/j.ijthermalsci.2020.106279
  10. D’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., & Luo, L. S. (2002). Multiple–relaxation–time lattice Boltzmann models in three dimensions. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 360(1792), 437-451. doi: 10.1098/rsta.2001.0955
  11. Fusegi, T., Hyun, J. M., Kuwahara, K., & Farouk, B. (1991). A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure. International Journal of Heat and Mass Transfer, 34(6), 1543-1557. doi: 10.1016/0017-9310(91)90295-P
  12. Ghachem, K., Hassen, W., Maatki, C., Kolsi, L., Al-Rashed, A. A., & Naceur, M. (2018). Numerical simulation of 3D natural convection and entropy generation in a cubic cavity equipped with an adiabatic baffle. International Journal of Heat and Technology, 36(3), 1047-1054. doi: 10.18280/ijht.360335
  13. Hasnaoui, S., Amahmid, A., Beji, H., Raji, A., Hasnaoui, M., El Mansouri, A., & Alouah, M. (2018). Hybrid lattice Boltzmann finite difference simulation of Soret convection flows in a square cavity with internal heat generation. Numerical Heat Transfer, Part A: Applications, 74(1), 948-973. doi: 10.1080/10407782.2018.1487690
  14. Ibrahim, M., Saeed, T., Algehyne, E. A., Alsulami, H., & Chu, Y. M. (2021). Optimization and effect of wall conduction on natural convection in a cavity with constant temperature heat source: Using lattice Boltzmann method and neural network algorithm. Journal of Thermal Analysis and Calorimetry, 144(6), 2449-2463. doi: 10.1007/s10973-021-10654-0
  15. Karki, P., Yadav, A. K., & Arumuga Perumal, D. (2019). Study of adiabatic obstacles on natural convection in a square cavity using lattice Boltzmann method. Journal of Thermal Science and Engineering Applications, 11(3). doi: 10.1115/1.4041875
  16. Khan, Z. H., Hamid, M., Khan, W. A., Sun, L., & Liu, H. (2021). Thermal non-equilibrium natural convection in a trapezoidal porous cavity with heated cylindrical obstacles. International Communications in Heat and Mass Transfer, 126, 105460. doi: 10.1016/j.icheatmasstransfer.2021.105460
  17. Krivovichev, G. V. (2019). Stability analysis of body force action models used in the single-relaxation-time single-phase lattice Boltzmann method. Applied Mathematics and Computation, 348, 25-41. doi: 10.1016/j.amc.2018.11.056
  18. Lahmer, E. B., Benhamou, J., Admi, Y., Moussaoui, M. A., Jami, M., Mezrhab, A., & Phanden, R. K. (2022). Assessment of Conjugate and Convective Heat Transfer Performance over a Partitioned Channel within Backward-Facing Step using the Lattice Boltzmann Method. Journal of Enhanced Heat Transfer, 29(3), 51-77. doi: 10.1615/JEnhHeatTransf.2022040357
  19. Lallemand, P., & Luo, L. S. (2003). Hybrid finite-difference thermal lattice Boltzmann equation. International Journal of Modern Physics B, 17(01n02), 41-47.. doi: 10.1142/s0217979203017060
  20. Lee, J. R. (2018). On the three-dimensional effect for natural convection in horizontal enclosure with an adiabatic body: Review from the 2D results and visualization of 3D flow structure. International Communications in Heat and Mass Transfer, 92, 31-38. doi: 10.1016/j.icheatmasstransfer.2018.02.010
  21. Li, Z., Yang, M., & Zhang, Y. (2016). Lattice Boltzmann method simulation of 3-D natural convection with double MRT model. International Journal of Heat and Mass Transfer, 94, 222-238. doi: 10.1016/j.ijheatmasstransfer.2015.11.042
  22. Liu, H., Ba, Y., Wu, L., Li, Z., Xi, G., & Zhang, Y. (2018). A hybrid lattice Boltzmann and finite difference method for droplet dynamics with insoluble surfactants. Journal of Fluid Mechanics, 837, 381-412. doi: 10.1017/jfm.2017.859
  23. Luo, L. S. (1998). Unified theory of lattice Boltzmann models for nonideal gases. Physical review letters, 81(8), 1618. doi: 10.1103/PhysRevLett.81.1618
  24. Mezrhab, A., Moussaoui, M. A., Jami, M., Naji, H., & Bouzidi, M. H. (2010). Double MRT thermal lattice Boltzmann method for simulating convective flows. Physics Letters A, 374(34), 3499-3507. doi: 10.1016/j.physleta.2010.06.059
  25. Minkowycz, W. J., Sparrow, E. M., & Murthy, J. Y. (2000). Handbook of Numerical Heat Transfer, Second Edition. In John Wiley & Sons. doi: 10.1002/9780470172599
  26. Mohamad, A. A. (2019). Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes: Second Edition. Springer London. doi: 10.1007/978-1-4471-7423-3
  27. Mohamad, A. A., & Kuzmin, A. (2010). A critical evaluation of force term in lattice Boltzmann method, natural convection problem. International Journal of Heat and Mass Transfer, 53(5–6), 990–996. doi: 10.1016/j.ijheatmasstransfer.2009.11.014
  28. Nee, A. (2020a). Hybrid lattice Boltzmann––Finite difference formulation for combined heat transfer problems by 3D natural convection and surface thermal radiation. International Journal of Mechanical Sciences, 173, 105447. doi: 10.1016/j.ijmecsci.2020.105447
  29. Nee, A. (2020b). Hybrid meso-macroscopic simulation of three-dimensional natural convection combined with conjugate heat transfer. Thermal Science and Engineering Progress, 19, 100584.. doi: 10.1016/j.tsep.2020.100584
  30. Nee, A. (2021). Hybrid Lattice Boltzmann Simulation of Three-Dimensional Natural Convection. Journal of Computational and Theoretical Transport, 50(4), 280-296. doi: 10.1080/23324309.2021.1942061
  31. Nouni, M., Bendaraa, A., Ouhroum, M., Charafi, M. M., & Hasnaoui, A. (2021). Numerical study of obstacles effect on natural convection inside square cavity: Lattice Boltzmann method. AIP Conference Proceedings, 2345(1), 020010. doi: 10.1063/5.0050208
  32. Özişik, M. N., Orlande, H. R., Colaco, M. J., & Cotta, R. M. (2017). Finite difference methods in heat transfer: Second Edition. CRC press. doi: 10.1201/9781315121475
  33. Purusothaman, A., Murugesan, K., & Chamkha, A. J. (2019). 3D modeling of natural convective heat transfer from a varying rectangular heat generating source. Journal of Thermal Analysis and Calorimetry, 138(1), 597-608. doi: 10.1007/s10973-019-08259-9
  34. Purusothaman, A., Baïri, A., & Nithyadevi, N. (2016). 3D natural convection on a horizontal and vertical thermally active plate in a closed cubical cavity. International Journal of Numerical Methods for Heat & Fluid Flow, 26(8), 2528-2542. doi: 10.1108/HFF-08-2015-0341
  35. Rahimi, A., Dehghan Saee, A., Kasaeipoor, A., & Hasani Malekshah, E. (2019). A comprehensive review on natural convection flow and heat transfer: The most practical geometries for engineering applications. In International Journal of Numerical Methods for Heat and Fluid Flow. doi: 10.1108/HFF-06-2018-0272
  36. Shan, X., & Chen, H. (1993). Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47(3), 1815. doi: 10.1103/PhysRevE.47.1815
  37. Shan, X., & Chen, H. (1994). Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Physical Review E, 49(4), 2941. doi: 10.1103/PhysRevE.49.2941
  38. Shi, Y., Zhao, T. S., & Guo, Z. L. (2006). Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus. Computers and Fluids, 35(1), 1-15. doi: 10.1016/j.compfluid.2004.11.003
  39. Subhani, S., & Kumar, R. S. (2021). Natural Convection Heat Transfer Enhancement of Circular Obstacle within Square Enclosure. Journal of Thermal Analysis and Calorimetry, 1-19. doi: 10.1007/s10973-021-10829-9
  40. Theodore, L. (2011). Heat Transfer Applications for the Practicing Engineer. John Wiley & Sons. doi: 10.1002/9780470937228
  41. Ugurlubilek, N., Sert, Z., Selimefendigil, F., & Öztop, H. F. (2022). 3D laminar natural convection in a cubical enclosure with gradually changing partitions. International Communications in Heat and Mass Transfer, 133, 105932. doi: 10.1016/j.icheatmasstransfer.2022.105932
  42. Vesper, J. E., Tietjen, S. C., Chakkingal, M., & Kenjereš, S. (2022). Numerical analysis of effects of fins and conductive walls on heat transfer in side heated cavities — Onset of three-dimensional phenomena in natural convection. International Journal of Heat and Mass Transfer, 183, 122033. doi: 10.1016/j.ijheatmasstransfer.2021.122033
  43. Wang, P., Zhang, Y., & Guo, Z. (2017). Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers. International Journal of Heat and Mass Transfer, 113, 217-228. doi: 10.1016/j.ijheatmasstransfer.2017.05.057
  44. Xiong, P. Y., Hamid, A., Iqbal, K., Irfan, M., & Khan, M. (2021). Numerical simulation of mixed convection flow and heat transfer in the lid-driven triangular cavity with different obstacle configurations. International Communications in Heat and Mass Transfer, 123, 105202. doi: 10.1016/j.icheatmasstransfer.2021.105202
  45. Xu, A., Gonnella, G., & Lamura, A. (2006). Simulations of complex fluids by mixed lattice Boltzmann - Finite difference methods. Physica A: Statistical Mechanics and Its Applications, 362(1), 42-47. doi: 10.1016/j.physa.2005.09.015
  46. Yousif, A. A., Alomar, O. R., & Hussein, A. T. (2022). Impact of using triple adiabatic obstacles on natural convection inside porous cavity under non-darcy flow and local thermal non-equilibrium model. International Communications in Heat and Mass Transfer, 130, 105760. doi: 10.1016/j.icheatmasstransfer.2021.105760

Last update:

  1. New higher-order accurate super-compact scheme for three-dimensional natural convection and entropy generation

    Ashwani Punia, Rajendra K. Ray. Physics of Fluids, 36 (3), 2024. doi: 10.1063/5.0196736

  2. Lattice Boltzmann simulation of natural convection heat transfer phenomenon for thermal management of multiple electronic components

    Hamza Faraji, Mohamed Teggar, Adeel Arshad, Müslüm Arıcı, El Mehdi Berra, Khadija Choukairy. Thermal Science and Engineering Progress, 45 , 2023. doi: 10.1016/j.tsep.2023.102126

  3. Three-dimensional simulation of conjugate heat transfer using the hybrid lattice Boltzmann-finite difference method

    Jaouad Benhamou, El Bachir Lahmer, Mohammed Jami. International Communications in Heat and Mass Transfer, 139 , 2022. doi: 10.1016/j.icheatmasstransfer.2022.106486

  4. A new higher-order super compact finite difference scheme to study three-dimensional non-Newtonian flows

    Ashwani Punia, Rajendra K. Ray. Physics of Fluids, 36 (10), 2024. doi: 10.1063/5.0231951

Last update: 2024-12-26 09:06:23

No citation recorded.