Lattice Boltzmann Simulation of Heat Transfer in a Square Cavity Coupled with Copper–Graphene Nanocomposite Wall

Authors

  • Delara Daneshvar Department of Mechanical Engineering, Ayandegan University, Tonekabon, Iran.

https://doi.org/10.48313/mtei.v2i4.62

Abstract

A numerical investigation is performed to study conjugate natural convection heat transfer in a square cavity coupled with a copper–graphene nanocomposite solid wall. The cavity is filled with a Newtonian fluid and subjected to a constant heat flux applied over a finite portion of the bottom wall, while the vertical sidewalls are maintained at a constant cold temperature, and the remaining boundaries are adiabatic. Heat conduction in the solid wall and convection in the fluid domain are simultaneously considered. The Lattice Boltzmann Method (LBM) with the Bhatnagar–Gross–Krook (BGK) collision model is employed to solve the governing equations. The effective thermal conductivity of the copper–graphene nanocomposite is evaluated using a micromechanical model accounting for graphene nanoplatelet waviness, alignment, and Interfacial Thermal Resistance (ITR). The numerical model is validated against well-established experimental correlations for natural convection, showing excellent agreement.Parametric analyses are conducted to examine the effects of Rayleigh number, constant heat flux length, and solid wall thickness on flow structure and heat transfer characteristics. The results indicate that the copper–graphene nanocomposite significantly enhances heat transfer compared to pure copper by reducing surface temperature and increasing local and average Nusselt numbers. Increasing Rayleigh number intensifies buoyancy-driven convection, while larger heat flux lengths reduce heat transfer efficiency. Thicker nanocomposite walls improve conductive heat spreading and overall thermal performance.        

Keywords:

Conjugate heat transfer, Natural convection, Copper–graphene nanocomposite, Lattice Boltzmann method, Constant heat flux

References

  1. [1] Ostrach, S. (1988). Natural convection in enclosures. Journal of heat transfer, 110(4b), 1175–1190. http://dx.doi.org/10.1115/1.3250619
  2. [2] Calcagni, B., Marsili, F., & Paroncini, M. (2005). Natural convective heat transfer in square enclosures heated from below. Applied thermal engineering, 25(16), 2522–2531. https://doi.org/10.1016/j.applthermaleng.2004.11.032
  3. [3] Abu-Nada, E. (2010). Natural convection heat transfer simulation using energy conservative dissipative particle dynamics. Physical review e—statistical, nonlinear, and soft matter physics, 81(5), 56704. https://doi.org/10.1103/PhysRevE.81.056704
  4. [4] Choi, S. U. (1995). Enhancing thermal conductivity of fluids with nanoparticles. ASME international mechanical engineering congress and exposition (pp. 99-105). American Society of Mechanical Engineers. https://doi.org/10.1115/IMECE1995-0926
  5. [5] Kim, J., Kang, Y. T., & Choi, C. K. (2004). Analysis of convective instability and heat transfer characteristics of nanofluids. Physics of fluids, 16(7), 2395-2401. https://doi.org/10.1063/1.1739247
  6. [6] Wen, D., & Ding, Y. (2005). Formulation of nanofluids for natural convective heat transfer applications. International journal of heat and fluid flow, 26(6), 855–864. https://doi.org/10.1016/j.ijheatfluidflow.2005.10.005
  7. [7] Khanafer, K., Vafai, K., & Lightstone, M. (2003). Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer, 46(19), 3639–3653. https://doi.org/10.1016/S0017-9310(03)00156-X
  8. [8] Aminossadati, S. M., & Ghasemi, B. (2009). Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. European journal of mechanics-b/fluids, 28(5), 630–640. https://doi.org/10.1016/j.euromechflu.2009.05.006
  9. [9] Ho, C. J., Chen, M. W., & Li, Z. W. (2008). Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity. International journal of heat and mass transfer, 51(17–18), 4506–4516. https://doi.org/10.1016/j.ijheatmasstransfer.2007.12.019
  10. [10] Abu-Nada, E. (2009). Effects of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection. International journal of heat and fluid flow, 30(4), 679–690. https://doi.org/10.1016/j.ijheatfluidflow.2009.02.003
  11. [11] Abu-Nada, E., & Chamkha, A. J. (2010). Effect of nanofluid variable properties on natural convection in enclosures. International journal of thermal sciences, 49(3), 479–491. https://doi.org/10.1016/j.ijthermalsci.2009.09.002
  12. [12] Kharati, M., & Jelodari, I. (2014). Numerical study of effective techniques to increase mixed convection heat transfer rate within the enclosure subjected to magnetic field. Modares mechanical engineering, 14(3), 69-77 (In Persian). https://mme.modares.ac.ir/article_7935.html?lang=en
  13. [13] Barrios, G., Rechtman, R., Rojas, J., & Tovar, R. (2005). The lattice Boltzmann equation for natural convection in a two-dimensional cavity with a partially heated wall. Journal of fluid mechanics, 522, 91–100. https://doi.org/10.1017/S0022112004001983
  14. [14] Fattahi, E., Farhadi, M., & Sedighi, K. (2010). Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus. International journal of thermal sciences, 49(12), 2353–2362. https://doi.org/10.1016/j.ijthermalsci.2010.07.014
  15. [15] Gao, D., & Chen, Z. (2011). Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media. International journal of thermal sciences, 50(4), 493–501. https://doi.org/10.1016/j.ijthermalsci.2010.11.010
  16. [16] Mohammadipoor, O. R., Niazmand, H., & Mirbozorgi, S. A. (2013). A new curved boundary treatment for the lattice Boltzmann method. Modares mechanical engineering, 13(8), 28-41 (In Persian). https://mme.modares.ac.ir/article_7804.html?lang=en
  17. [17] Nazari, M. (2014). Natural convection in semi-ellipse cavities with variable aspect ratios using lattice Boltzmann method. Modares mechanical engineering, 13(10), 1–13 (In Persian). https://mme.modares.ac.ir/article_8055_en.html
  18. [18] Ghasemi, B., Aminossadati, S. M., & Raisi, A. (2011). Magnetic field effect on natural convection in a nanofluid-filled square enclosure. International journal of thermal sciences, 50(9), 1748–1756. https://doi.org/10.1016/j.ijthermalsci.2011.04.010
  19. [19] Nouri, R., Gorji-Bandpy, M., & Domiri Ganji, D. (2014). Numerical investigation of magnetic field effect on forced convection heat transfer of nanofluid in a sinusoidal channel. Modares mechanical engineering, 13(14), 43-55 (In Persian). https://mme.modares.ac.ir/article_7840.html?lang=en
  20. [20] Nazari, M., Kayhani, M. H., & Shokri, H. (2013). LBM for modeling cavities with curved and moving boundaries. Modares mechanical engineering, 13(5), 117-129 (In Persian). https://mme.modares.ac.ir/article_1616_en.html
  21. [21] Sheikholeslami, M., Gorji-Bandpy, M., & Ganji, D. D. (2014). Investigation of nanofluid flow and heat transfer in presence of magnetic field using KKL model. Arabian journal for science and engineering, 39(6), 5007–5016. https://doi.org/10.1007/s13369-014-1060-4
  22. [22] House, J. M., Beckermann, C., & Smith, T. F. (1990). Effect of a centered conducting body on natural convection heat transfer in an enclosure. Numerical heat transfer, 18(2), 213–225. https://doi.org/10.1080/10407789008944791
  23. [23] Cheikh, N. B., Beya, B. B., & Lili, T. (2007). Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below. International communications in heat and mass transfer, 34(3), 369-379. https://doi.org/10.1016/j.icheatmasstransfer.2006.11.001
  24. [24] Wejrzanowski, T., Grybczuk, M., Chmielewski, M., Pietrzak, K., Kurzydlowski, K. J., & Strojny-Nedza, A. (2016). Thermal conductivity of metal-graphene composites. Materials & design, 99, 163–173. https://doi.org/10.1016/j.matdes.2016.03.069
  25. [25] Sathiyamoorthy, M., & J. Chamkha, A. (2014). Analysis of natural convection in a square cavity with a thin partition for linearly heated side walls. International journal of numerical methods for heat & fluid flow, 24(5), 1057-1072. https://doi.org/10.1108/HFF-02-2012-0050
  26. [26] Shi, X., & Khodadadi, J. M. (2003). Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall. Journal of heat transfer, 125(4), 624–634. https://doi.org/10.1115/1.1571847
  27. [27] Elatar, A., Teamah, M. A., & Hassab, M. A. (2016). Numerical study of laminar natural convection inside square enclosure with single horizontal fin. International journal of thermal sciences, 99, 41–51. https://doi.org/10.1016/j.ijthermalsci.2015.08.003
  28. [28] Shi, X., & Khodadadi, J. M. (2004). Fluid flow and heat transfer in a lid-driven cavity due to an oscillating thin fin: Transient behavior. Journal of heat transfer, 126(6), 924–930. https://doi.org/10.1115/1.1833362
  29. [29] Jamesahar, E., Ghalambaz, M., & Chamkha, A. J. (2016). Fluid-solid interaction in natural convection heat transfer in a square cavity with a perfectly thermal-conductive flexible diagonal partition. International journal of heat and mass transfer, 100, 303–319. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.046
  30. [30] Ghalambaz, M., Jamesahar, E., Ismael, M. A., & Chamkha, A. J. (2017). Fluid-structure interaction study of natural convection heat transfer over a flexible oscillating fin in a square cavity. International journal of thermal sciences, 111, 256–273. https://doi.org/10.1016/j.ijthermalsci.2016.09.001
  31. [31] Cai, Z., Wang, R., Zhang, C., Peng, C., & Wang, L. (2015). Microstructure and properties of Al/Sip composites for thermal management applications. Journal of materials science: Materials in electronics, 26(6), 4234-4240. https://doi.org/10.1007/s10854-015-2973-8
  32. [32] Jhong, Y. S., Tseng, H. T., & Lin, S. J. (2019). Diamond/Ag-Ti composites with high thermal conductivity and excellent thermal cycling performance fabricated by pressureless sintering. Journal of alloys and compounds, 801, 589-595. https://doi.org/10.1016/j.jallcom.2019.06.167
  33. [33] Qureshi, Z. A., Ali, H. M., & Khushnood, S. (2018). Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: A review. International journal of heat and mass transfer, 127, 838-856. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.049
  34. [34] Kim, H. S., Jang, J., Yu, J., & Kim, S. Y. (2015). Thermal conductivity of polymer composites based on the length of multi-walled carbon nanotubes. Composites part b: Engineering, 79, 505–512. https://doi.org/10.1016/j.compositesb.2015.05.012
  35. [35] Yu, J., Lacy Jr, T. E., Toghiani, H., & Pittman Jr, C. U. (2013). Micromechanically-based effective thermal conductivity estimates for polymer nanocomposites. Composites part b: Engineering, 53, 267–273. https://doi.org/10.1016/j.compositesb.2013.04.055
  36. [36] Chen, J., & Han, J. (2019). A combination of graphene and graphene nanoplatelets: An effective way to improve thermal conductivity for polymers. Results in physics, 15, 102803. https://doi.org/10.1016/j.rinp.2019.102803
  37. [37] Fang, H., Bai, S. L., & Wong, C. P. (2018). Microstructure engineering of graphene towards highly thermal conductive composites. Composites part a: Applied science and manufacturing, 112, 216–238. https://doi.org/10.1016/j.compositesa.2018.06.010
  38. [38] Hopkins, P. E., Baraket, M., Barnat, E. V., Beechem, T. E., Kearney, S. P., Duda, J. C., ... ., & Walton, S. G. (2012). Manipulating thermal conductance at metal–graphene contacts via chemical functionalization. Nano letters, 12(2), 590-595. https://doi.org/10.1021/nl203060j
  39. [39] Chu, K., Wang, X. H., Wang, F., Li, Y. B., Huang, D. J., Liu, H., ... ., & Zhang, H. (2018). Largely enhanced thermal conductivity of graphene/copper composites with highly aligned graphene network. Carbon, 127, 102-112. https://doi.org/10.1016/j.carbon.2017.10.099
  40. [40] Chu, K., Li, W., & Dong, H. (2013). Role of graphene waviness on the thermal conductivity of graphene composites. Applied physics a, 111(1), 221–225. https://doi.org/10.1007/s00339-012-7497-y
  41. [41] Ramanathan, T., Abdala, A. A., Stankovich, S., Dikin, D. A., Herrera-Alonso, M., Piner, R. D., ... ., & Brinson, L. C. (2008). Functionalized graphene sheets for polymer nanocomposites. Nature nanotechnology, 3(6), 327-331. https://doi.org/10.1038/nnano.2008.96
  42. [42] Reif, J., Rafiee, J., Wang, Z., Song, H., Yu, Z. Z., & Koratkar, N. (2009). Enhanced mechanical properties of nanocomposites at low graphene content. ACS nano, 3(12), 3884-3890. https://doi.org/10.1021/nn9010472
  43. [43] Zhang, L., Hou, G., Zhai, W., Ai, Q., Feng, J., Zhang, L., ... ., & Ci, L. (2018). Aluminum/graphene composites with enhanced heat-dissipation properties by in-situ reduction of graphene oxide on aluminum particles. Journal of alloys and compounds, 748, 854-860. https://doi.org/10.1016/j.jallcom.2018.03.237
  44. [44] Tang, L. C., Wan, Y. J., Yan, D., Pei, Y. B., Zhao, L., Li, Y. B., ... ., & Lai, G. Q. (2013). The effect of graphene dispersion on the mechanical properties of graphene/epoxy composites. Carbon, 60, 16-27. https://doi.org/10.1016/j.carbon.2013.03.050
  45. [45] Shi, D. L., Feng, X. Q., Huang, Y. Y., Hwang, K. C., & Gao, H. (2004). The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. Journal of engineering materials and technology, 126(3), 250-257. https://doi.org/10.1115/1.1751182
  46. [46] Yang, Q. S., He, X. Q., Liu, X., Leng, F. F., & Mai, Y. W. (2012). The effective properties and local aggregation effect of CNT/SMP composites. Composites part b: Engineering, 43(1), 33-38. https://doi.org/10.1016/j.compositesb.2011.04.027
  47. [47] Hassanzadeh-Aghdam, M. K., & Mahmoodi, M. J. (2018). Micromechanical modeling of thermal conducting behavior of general carbon nanotube-polymer nanocomposites. Materials science and engineering: B, 229, 173-183. https://doi.org/10.1016/j.mseb.2017.12.039
  48. [48] ElSherbiny, S. M., Raithby, G. D., & Hollands, K. G. T. (1982). Heat transfer by natural convection across vertical and inclined air layers. Journal of heat transfer, 104(1), 96-102. https://doi.org/10.1115/1.3245075

Published

2026-06-23

Issue

Vol. 2 No. 4 (2025): Mechanical Technology and Engineering Insights (MTEI)

Section

Articles

How to Cite

Daneshvar, D. . (2026). Lattice Boltzmann Simulation of Heat Transfer in a Square Cavity Coupled with Copper–Graphene Nanocomposite Wall. Mechanical Technology and Engineering Insights, 2(4), 233-256. https://doi.org/10.48313/mtei.v2i4.62

Similar Articles

11-20 of 23

You may also start an advanced similarity search for this article.