A New Modified Hamilton-Crosser and Nan Models for Thermal ‎Conductivity of Different Lengths Carbon Nanotubes Water-‎based Nanofluids

Document Type : Research Paper


Physic Department, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, I.R. Iran


In order to investigate the shape effect of nanoadditives on thermal conductivity of nanofluids, different length carbon nanotubes (CNTs) are made and using a two-step method, different nanofluids are prepared. The CNTs are cut into different lengths by functionalization at different refluxing times of 1, 2 and 4 hours. To probe the effect of aspect ratio of CNTs on the obtained experimental data, modified Hamilton-Crosser and Nan models are developed. It is found that the original Hamilton-Crosser and Nan models could not predict the experimental thermal conductivities. By replacing n = 6 + xL/D instead of the shape factor of n=6 in the Hamilton- Crosser, where L and D were length and diameter of CNTs and also by replacing φ (xL/D) instead of φ (volume fraction) in the Nan model, the prediction of modified equations show very good accordance with the experimental data which means the shape of nanoadditives has high impact on nanofluids’ properties.


Main Subjects

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[1] Choi, S.U.S., Enhancing thermal conductivity of fluids with nano-particles, ASME Journal of Fluids Engineering, 231, 1995, 99-105.
[2] Munkhbayara, B., Tanshena, M.R., Jeouna, J., Chungb, H., Jeong, H., Surfactant-free dispersion of silver nanoparticles into MWCNT-aqueous nanofluids prepared by one-step technique and their thermal characteristics, Ceramics International, 39, 2013, 6415–6425.
[3] Munkhbayar, B., Nine, M.J., Jeoun, J., Erdene, M.B., Chung, H., Jeong, H., Influence of dry and wet ball milling on dispersion characteristics of the multi-walled carbon nanotubes in aqueous solution with and without surfactant, Powder Technology, 234, 2013, 132–140.
[4] Beck, M.P., Yuan, Y., Warrier, P., Teja, A.S., The effect of particle size on the thermal conductivity of alumina nanofluids, Journal of Nanoparticle Research, 11, 2009, 1129-36.
[5] Hamzah, M.H., Che Sidik, N.A., Tan Lit Ken, T.L., Mamat, R., Najafi, G., Factors affecting the performance of hybrid nanofluids: A comprehensive review, International Journal of Heat and Mass Transfer, 115, 2017, 630–646.
[6] Leong, K.Y., Ku Ahmad, K.Z., Ong, H.C., Ghazalic, M.J., Baharumd, A., Synthesis and thermal conductivity characteristic of hybrid nanofluids – A review, Renewable and Sustainable Energy Reviews, 75, 2017, 868-878.
[7] Muhammad, U.S., Hafiz, M.A., Thermal conductivity of hybrid nanofluids: A critical review, International Journal of Heat and Mass Transfer, 126, 2018, 211–234.
[8] Tayyab, R.S., Hafiz, M.A., Applications of hybrid nanofluids in solar energy, practical limitations and challenges: A critical review, Solar Energy, 183, 2019, 173-203.
[9] Farbod, M., Kouhpeymani Asl, R., Noghrehabadi, A.R., Morphology dependence of thermal and rheological properties of oil-based nanofluids of CuO nanostructures, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 474, 2015, 71–75.
[10] Farbod, M., Ahangarpour, A., Improved thermal conductivity of Ag decorated carbon nanotubes water based nanofluids. Physics Letters A, 380, 2016, 4044–4048.
[11] Lyu, Z., Asadi, A., Alarifi, I.M., Ali, V., Foong, L.K., Thermal and Fluid Dynamics Performance of MWCNT-Water Nanofluid Based on Thermophysical Properties: An Experimental and Theoretical Study, Scientific Reports, 10, 2020, 5185.
[12] Choi, S.U.S., Yu, W., The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Maxwell model, Journal of Nanoparticle Research, 5, 2003, 167–171.
[13] Xue, Q., Xu, W.M., A model of thermal conductivity of nanofluids with interfacial shells, Materials Chemistry and Physics, 90, 2005, 298–301.
[14] Prasher, R., Bhattacharya, P., Phelan, P.E., Brownian-motion-based convective-conductive model for the effective thermal conductivity of nanofluids, Journal of Heat Transfer, 128, 2006, 588–595.
[15] Zhang, P., Hong, W., Wu, J.F., Liu, G.Z., Xiao, J., Chen, Z.B., Cheng, H.B., Effects of surface modification on the suspension stability and thermal conductivity of carbon nanotubes nanofluids, Energy Procedia, 69, 2015, 699 – 705.
[16] Mohamad, A.A., Thermal contact theory for estimating the thermal conductivity of nanofluids and composite materials, Applied Thermal Engineering, 120, 2017, 179-186.
[17] Ambreen, T., Kim, M.H., Influence of particle size on the effective thermal conductivity of nanofluids: A critical review, Applied Energy, 264, 2020, 114684.
[18] Tahmooressi, H., Kasaeian, A., Tarokh, A., Rezaei, R., Hoorfar, M., Numerical simulation of aggregation effect on nanofluids thermal conductivity using the lattice Boltzmann method, International Communications in Heat and Mass Transfer, 110, 2020, 104408.
[19] Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford University Press, Cambridge, UK, 1904.
[20] Hamilton, R.L., Crosser, O.K., Thermal conductivity of heterogeneous two-component systems, Journal of Industrial and Engineering Chemistry, 1, 1962, 187–191.
[21] Jeffrey, D.J., Conduction through a random suspension of spheres, Proceedings of the Royal Society of London: Series A, Mathematical and Physical Sciences, 335, 1973, 355-367.
[22] Lamas, B., Abreu, B., Fonseca, A., Martins, N., Oliveira, M., Critical analysis of the thermal conductivity models for CNT based nanofluids, International Journal of Thermal Sciences, 78, 2014, 65-76.
[23] Xing, M., Yu, J., Wang, R., Experimental investigation and modelling on the thermal conductivity of CNTs based nanofluids, International Journal of Thermal Sciences, 104, 2016, 404-411.
[24] Hayat, T., Ahmed, B., Abbasi, F.M., Ahmad, B., Mixed convective peristaltic flow of carbon nanotubes submerged in water using different thermal conductivity models, Computer Methods and Programs in Biomedicine, 135, 2016, 141-150.
[25] Yang, L., Xu, X., A renovated Hamilton–Crosser model for the effective thermal conductivity of CNTs nanofluids, International Communications in Heat and Mass Transfer, 81, 2017, 42–50.
[26] Yang, L., Du, K., Zhang, X., A theoretical investigation of thermal conductivity of nanofluids with particles in cylindrical shape by anisotropy analysis, Powder Technology, 314, 2017, 328-338.
[27] Yang, L., Xu, X., Jiang, W., Du, K., A new thermal conductivity model for nanorod-based nanofluids, Applied Thermal Engineering, 114, 2017, 287-299.
[28] Mousavi, N.S.S., Kumar, S., Effective in-field thermal conductivity of ferrofluids, Journal of Applied Physics, 123, 2018, 043902–043909.
[29] Bunoiu, O.M., Matu, G., Marin, C.N., Malaescu, I., Investigation of some thermal parameters of ferrofluids in the presence of a static magnetic field, Journal of Magnetism and Magnetic Materials, 498, 2020, 166132.
[30] Amani, M., Amani, P., Kasaeian, A., Mahian, O., Pop. I., Wongwises, S., Modeling and optimization of thermal conductivity and viscosity of MnFe2O4 nanofluid under magnetic field using an ANN, Scientific Reports, 7, 2017, 17369.
[31] Farbod, M., Ahangarpour, A., Etemad, S.G.H., Stability and thermal conductivity of water-based carbon nanotube nanofluids, Particuology, 22, 2015, 59-65.
[32] Huxtable, S.T., Cahill, D.G., Shenogin, S., Xue, L., Ozisik, R., Barone, P., Usrey, M., Strano, M.S., Siddons, G., Shim, M., Kebunski, P., Interfacial Heat Flow in Carbon Nanotube Suspensions, Nature Materials, 2, 2003, 731–734.
[33] Das, S.K., Choi, S.U.S., Yu, W., Pradeep, T., Nanofluids: Science and Technology, John Wiley & Sons, New Jersey, 2008.
[34] Nan, C.W., Shi, Z., Lin, Y., A simple model for thermal conductivity of carbon nanotube-based composites, Chemical Physics Letters, 375, 2003, 666–669.