An Analytical Model for Determining the Effective Thermal Conductivity Coefficient in a Honeycomb Network with Heat Dissipation from the Central Cylindrical Axis

Document Type : Research Note

Author

Faculty of Photonic and Quantum Technology Research School, Nuclear Science and Technology Research Institute, AEOI.

Abstract

This paper presents an analytical model based on the thermal resistance network method to determine the effective thermal conductivity of a porous cylindrical lattice with a honeycomb structure, where heat flows radially outward from the central axis. The model offers a simple, software-independent solution for thermal analysis in applications like heat exchangers and photonic crystal fibers. The methodology involves a three-stage calculation: determining the thermal resistance of the unit cells (accounting for two types: with and without a fluid-filled hole), calculating the effective conductivity for each concentric layer by considering parallel resistances, and finally summing the series resistances of all layers to find the overall effective thermal conductivity. Applied to common materials like copper, aluminum, and stainless steel with water as the filler fluid, the model reveals that the unit cell's orientation to the heat flux has a negligible impact. Furthermore, the overall effective thermal conductivity stabilizes significantly with more than five layers, providing a key design insight for optimizing thermal performance and material usage.

Keywords

Main Subjects

References

1. Yuki, K., 2021. Heat transfer enhancement using unidirectional porous media under high heat flux conditions. In Porous Fluids, Advances in Fluid Flow and Transport Phenomena in Porous Media. IntechOpen) https://doi.org/10.5772/intechopen.96594).
2. Hales, T.C., 2001. The honeycomb conjectures. Discrete Comput Geom., 25, pp. 1–22 (https://doi.org/10.1007/s004540010071).
3. Lecuit, T. and Lenne, P.F., 2007. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nature Reviews Molecular Cell Biology, 8, pp. 633–644 (https://doi.org/10.1038/nrm2222).
4. Pawi, G., Wong, K.L., Kwon, K.Y., and Bartels, L., 2006. A homo-molecular porous network at a Cu (111) surface. Science, 313, pp. 961–962.
5. Masuda, H. and Fukuda, K., 1995. Ordered metal nanohole arrays made by a 2-step replication of honeycomb structures of anodic alumina. Science, 268, pp. 1466–1468 (https://doi.org/10.1126/science.1129309).
6. Innocenti, P. and Scarpa, F., 2009. Thermal conductivity properties and heat transfer analysis of multi-re-entrant auxetic honeycomb structures. Journal of Composite Materials, 43, pp. 2419–2439 (https://doi.org/10.1177/0021998309344636).
7.  Gadkaree, K.P., 1998. Carbon honeycomb structures for adsorption applications. Carbon, 36, pp. 981–989 (https://doi.org/10.1016/S0008-6223(97)00230-3).
8. Bardhan, P., 1997. Ceramic honeycomb filters and catalysts. Current Opinion in Solid State and Materials Science, 2, pp. 577–583.
9. Huang, H., Ning, Z.Y., Kariyado, T., Amemiya, T., and Hu, X., 2023. Topological photonic crystal fiber with honeycomb structure. Optics Express, 31, 27006 (https://doi.org/10.1364/OE.496046).
10. Zhang, Q., Yang, X., Li, P., Huang, G., Feng, S., Shen, C., Han, B., Zhang, X., Jin, F., Xu, F., and Lu, T.J., 2015. Bio-inspired engineering of honeycomb structure: Using nature to inspire human innovation. Progress in Materials Science, 74, pp. 332–400 (https://doi.org/10.1016/j.pmatsci.2015.05.001).
11. Chang, B., Wang, Z., and Bi, G., 2024. Study on the energy absorption characteristics of different composite honeycomb sandwich structures under impact energy. Applied Sciences, 14, 2832 https://doi.org/10.3390/app14072832
12. Ghosh, S., Senthilkumar, S., Deep, D., and Bharanitharan, K.J., 2020. A numerical approach to study the steady state heat transfer characteristics of an annular porous heat exchanger. In 3rd International Conference on Advances in Mechanical Engineering (ICAME 2020), IOP Conf. Series: Materials Science and Engineering, 912, 042030 (Doi:10.1088/1757-899X/912/4/042030. https://doi.org/10.1088/1757-899X/912/4/042030
13. Boomsma, K. and Poulikakos, D., 2001. On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam. International Journal of Heat and Mass Transfer, 44, pp. 827–836 (https://doi.org/10.1016/j.ijheatmasstransfer.2010.08.023).
14. Liu, H., Yu, Q.N., Zhang, Z.C., Qu, Z.G., and Wang, C.Z., 2016. Two-equation method for heat transfer efficiency in metal honeycombs: An analytical solution. International Journal of Heat and Mass Transfer, 97, pp. 201–210 (https://doi.org/10.1016/j.ijheatmasstransfer.2016.01.020)
15. Lu, T.J., 1999. Heat transfer efficiency of metal honeycombs. International Journal of Heat and Mass Transfer, 31, pp. 1920–1939 (https://doi.org/10.1016/S0017-9310(98)00306-8.).
16. Yuan, R. and Lu, S. 2020. Experimental and numerical study for effective thermal conductivity of metallic honeycomb sandwich structures. Journal of Sandwich Structures and Materials, pp. 1–18 https://doi.org/10.1177/1099636220933534
17. Gajić, R., Meisels, R., Kuchar, F., and Hingerl, K., 2006. All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals. Physical Review B, 73, 165310 (https://doi.org/10.1103/PhysRevB.73.165310).
18. Mortensen, N.A., Nielsen, M.D., Folkenberg, J.R., Jakobsen, C., and Simonsen, H.R., 2004. Photonic crystal fiber with a hybrid honeycomb cladding. Optics Express, 12, pp. 468–472 https://doi.org/10.1364/OPEX.12.000468).
19. Xu, G., Zhang, W., Huang, Y., and Peng, J., 2006. Optical properties of solid core honeycomb photonic crystal fiber with different doping levels. In Proceedings of SPIE ICO20: Optical Communication, 6025, 602505-1 https://doi.org/10.1117/12.666985.
20. Karimi, M., 2023. Theoretical study of hole structure and core size on the gap-map of hollow core photonic crystal fiber. Scientific Journal of Applied Electromagnetics, 11, pp. 95–105.
21. Karimi, M., 2020. Theoretical model to determine the effective thermal conductivity coefficient of the first clad region in photonic crystal fiber with a hexagonal structure. Thermal Science and Engineering Progress, 19, 100574https://doi.org/10.1016/j.tsep.2020.100574.
22. Holman, J.P., 1989. Heat Transfer. McGraw-Hill.

Files

Share

How to cite

Statistics