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Close-contact melting of shear-thinning fluids

Published online by Cambridge University Press:  28 July 2023

Nan Hu Open the ORCID record for Nan Hu [Opens in a new window]  and
Li-Wu Fan Open the ORCID record for Li-Wu Fan [Opens in a new window]
Nan Hu
Affiliation:
Key Laboratory of Clean Energy and Carbon Neutrality of Zhejiang Province, Zhejiang University, Hangzhou 310027, PR China State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China Institute of Thermal Science and Power Systems, School of Energy Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
Li-Wu Fan*
Affiliation:
Key Laboratory of Clean Energy and Carbon Neutrality of Zhejiang Province, Zhejiang University, Hangzhou 310027, PR China State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China Institute of Thermal Science and Power Systems, School of Energy Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
*
†Email address for correspondence: liwufan@zju.edu.cn
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Abstract

This study aims at establishing a model for close-contact melting (CCM) of shear-thinning fluids. We presented a theoretical framework for predicting the variation of liquid melt film thickness and motion of unmelted solid for both Carreau and power-law fluids. We identified the appropriate energy equation considering the convective effect and derived an analytical temperature profile across the liquid film. Using the lubrication approximation, force equilibrium relationships and the corresponding numerical approaches were built. By using laser interferometry and photographic recording methods, we found excellent agreement between numerical solutions and experimental results for Carreau liquids, revealing that the convective effect weakens heat transfer and melting rate. We identified the critical liquid film thickness that determines three situations of CCM in the theoretical model for Carreau fluids. Numerical prediction demonstrated that the CCM of Carreau fluids can be almost equivalent to that of power-law fluids if the initial film thickness is greater than the critical value. Finally, approximate analytical models were developed for both Carreau and power-law models. For the applicability of the approximate analytical solutions, we derived two- and three-dimensional dimensionless phase diagrams of validity range and identified a key dimensionless group $(\varLambda Re)^{4/3}{Re}\left [3\ln (Ste+1)\right ]^{1/3}{Pe}^{-1/3}$, where $\varLambda$ is dimensionless characteristic time, Re is Reynolds number, Ste is Stefan number and Pe is Peclect number. The reliability of the approximate solutions was verified by comparing with the numerical results. These approximate solutions enable convenient and low-cost computational prediction of the dynamic CCM process of shear-thinning fluids.

JFM classification

Phase change: Solidification/melting Non-Newtonian Flows: Rheology Low-Reynolds-number flows: Lubrication theory

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A9
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Agbessi, Y., Alibenyahia, B., Nouar, C., Lemaitre, C. & Choplin, L. 2015 Linear stability of Taylor–Couette flow of shear-thinning fluids: modal and non-modal approaches. J. Fluid Mech. 776, 354–389.CrossRefGoogle Scholar
Allouche, M.H., Botton, V., Millet, S., Henry, D., Dagois-Bohy, S., Guzel, B. & Ben Hadid, H. 2017 Primary instability of a shear-thinning film flow down an incline: experimental study. J. Fluid Mech. 821, R1.CrossRefGoogle Scholar
Bejan, A. 1992 Single correlation for theoretical contact melting results in various geometries. Intl Commun. Heat Mass Transfer 19 (4), 473–483.CrossRefGoogle Scholar
Boyko, E. & Stone, H.A. 2021 Flow rate-pressure drop relation for shear-thinning fluids in narrow channels: approximate solutions and comparison with experiments. J. Fluid Mech. 923, 621.CrossRefGoogle Scholar
Chekila, A., Nouar, C., Plaut, E. & Nemdili, A. 2011 Subcritical bifurcation of shear-thinning plane poiseuille flows. J. Fluid Mech. 686, 272–298.CrossRefGoogle Scholar
Chen, W.Z., Hao, J.L. & Chen, Z.Y. 2013 A study of self-burial of a radioactive waste container by deep rock melting. Sci. Technol. Nucl. Ins. 2013, 184757.Google Scholar
Chen, Z.H., Hu, X.C., Hu, K., Utaka, Y. & Mori, S. 2020 Measurement of the microlayer characteristics in the whole range of nucleate boiling for water by laser interferometry. Intl J. Heat Mass Transfer 146, 118856.CrossRefGoogle Scholar
Dong, Z.F., Chen, Z.Q., Wang, Q.J. & Ebadian, M.A. 1991 Experimental and analytical study of contact melting in a rectangular cavity. J. Therm. Heat Transfer 5 (3), 347–354.CrossRefGoogle Scholar
Emerman, S.H. & Turcotte, D.L. 1983 Stokes's problem with melting. Intl J. Heat Mass Transfer 26 (11), 1625–1630.CrossRefGoogle Scholar
Esfahani, B.R., Hirata, S.C., Berti, S. & Calzavarini, E. 2018 Basal melting driven by turbulent thermal convection. Phys. Rev. Fluids 3 (5), 053501.CrossRefGoogle Scholar
Fomin, S.A., Saitoh, T.S. & Chugunov, V.A. 1997 Contact melting materials with non-linear properties. Heat Mass Transfer 33 (3), 185–192.CrossRefGoogle Scholar
Fomin, S.A., Wei, P.S. & Chugunov, V.A. 1995 Contact melting by a nonisothermal heating surface of arbitrary shape. Intl J. Heat Mass Transfer 38 (17), 3275–3284.CrossRefGoogle Scholar
Fu, W.C., Yan, X., Gurumukhi, Y., Garimella, V.S., King, W.P. & Miljkovic, N. 2022 High power and energy density dynamic phase change materials using pressure-enhanced close contact melting. Nat. Energy 7, 270–280.CrossRefGoogle Scholar
Groulx, D. & Lacroix, M. 2007 Study of the effect of convection on close contact melting of high Prandtl number substances. Intl J. Therm. Sci. 46 (3), 213–220.CrossRefGoogle Scholar
Guo, Z.Y., Tao, W.Q. & Shah, R. 2005 The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer. Intl J. Heat Mass Transfer 48 (9), 1797–1807.CrossRefGoogle Scholar
Henot, M., Plihon, N. & Taberlet, N. 2021 Onset of glacier tables. Phys. Rev. Lett. 127 (10), 108501.CrossRefGoogle ScholarPubMed
Hu, N., Li, Z.R., Xu, Z.W. & Fan, L.W. 2022 Rapid charging for latent heat thermal energy storage: a state-of-the-art review of close-contact melting. Renew. Sust. Energy Rev. 155, 111918.CrossRefGoogle Scholar
Hu, N., Zhang, R.H., Zhang, S.T., Liu, J. & Fan, L.W. 2019 A laser interferometric measurement on the melt film thickness during close-contact melting on an isothermally-heated horizontal plate. Intl J. Heat Mass Transfer 138, 713–718.CrossRefGoogle Scholar
Hu, N., Zhu, Z.Q., Li, Z.R., Tu, J. & Fan, L.W. 2018 Close-contact melting heat transfer on a heated horizontal plate: revisited in the presence of nano-enhanced phase change materials (NePCM). Intl J. Heat Mass Transfer 124, 794–799.CrossRefGoogle Scholar
Kozak, Y. 2022 Theoretical analysis of close-contact melting on superhydrophobic surfaces. J. Fluid Mech. 943, A39.CrossRefGoogle Scholar
Kozak, Y., Rozenfeld, T. & Ziskind, G. 2014 Close-contact melting in vertical annular enclosures with a non-isothermal base: theoretical modeling and application to thermal storage. Intl J. Heat Mass Transfer 72, 114–127.CrossRefGoogle Scholar
Kozak, Y., Zeng, Y., Al Ghossein, R.M., Khodadadi, J.M. & Ziskind, G. 2019 Close-contact melting on an isothermal surface with the inclusion of non-Newtonian effects. J. Fluid Mech. 865, 720–742.CrossRefGoogle Scholar
Kumar, P., Zuri, S., Kogan, D., Gottlieb, M. & Sayag, R. 2021 Lubricated gravity currents of power-law fluids. J. Fluid Mech. 916, A33.CrossRefGoogle Scholar
Marsh, B.D. 1978 On the cooling of ascending andesitic magma. Phil. Trans. R. Soc. Lond. A 288 (1355), 611–625.Google Scholar
Mayer, P. & Moaveni, S. 2008 Close-contact melting as a subtractive machining process. Intl J. Advan. Manuf. Tech. 37 (9–10), 980–995.CrossRefGoogle Scholar
Moallemi, M.K. & Viskanta, R. 1985 Experiments on fluid-flow induced by melting around a migrating heat-source. J. Fluid Mech. 157, 35–51.CrossRefGoogle Scholar
Moallemi, M.K., Webb, B.W. & Viskanta, R. 1986 An experimental and analytical study of close-contact melting. Trans. ASME J. Heat Transfer 108 (4), 894–899.CrossRefGoogle Scholar
Moore, F.E. & Bayazitoglu, Y. 1982 Melting within a spherical enclosure. Trans. ASME J. Heat Transfer 104 (1), 19–23.CrossRefGoogle Scholar
Motahar, S., Nikkam, N., Alemrajabi, A.A., Khodabandeh, R., Toprak, M.S. & Muhammed, M. 2014 A novel phase change material containing mesoporous silica nanoparticles for thermal storage: a study on thermal conductivity and viscosity. Intl Commun. Heat Mass Transfer 56, 114–120.CrossRefGoogle Scholar
Nouar, C., Bottaro, A. & Brancher, J.P. 2007 Delaying transition to turbulence in channel flow: revisiting the stability of shear-thinning fluids. J. Fluid Mech. 592, 177–194.CrossRefGoogle Scholar
Saito, A., Utaka, Y., Akiyoshi, M. & Katayama, K. 1985 a On the contact heat-transfer with melting. 1. Experimental-study. Bull. JSME 28 (240), 1142–1149.CrossRefGoogle Scholar
Saito, A., Utaka, Y., Akiyoshi, M. & Katayama, K. 1985 b On the contact heat-transfer with melting. 2. Analytical study. Bull. JSME 28 (242), 1703–1709.CrossRefGoogle Scholar
Schueller, K. & Kowalski, J. 2017 Spatially varying heat flux driven close-contact melting – a Lagrangian approach. Intl J. Heat Mass Transfer 115, 1276–1287.CrossRefGoogle Scholar
Schuller, K., Kowalski, J. & Raback, P. 2016 Curvilinear melting – a preliminary experimental and numerical study. Intl J. Heat Mass Transfer 92, 884–892.CrossRefGoogle Scholar
Shao, X.F., Chen, C.L., Yang, Y.J., Ku, X.K. & Fan, L.W. 2019 Rheological behaviors of sugar alcohols for low-to-medium temperature latent heat storage: effects of temperature in both the molten and supercooled liquid states. Sol. Energy Mater Sol. Cells 195, 142–154.CrossRefGoogle Scholar
Shao, X.F., Yang, S., Chen, C.L., Fan, L.W. & Yu, Z.T. 2021 Temperature-dependent rheological behaviors of binary eutectic mixtures of sugar alcohols for latent heat storage: a comparative study with pure sugar alcohols. J. Therm. Sci. 30 (6), 2002–2014.CrossRefGoogle Scholar
Sinha, G.K., Narayan, S. & Srivastava, A. 2021 Microlayer dynamics during the growth process of a single vapour bubble under subcooled flow boiling conditions. J. Fluid Mech. 931, A23.CrossRefGoogle Scholar
Sochi, T. 2015 Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits. Rheol. Acta 54 (8), 745–756.CrossRefGoogle Scholar
Sparrow, E.M. & Geiger, G.T. 1986 Melting in a horizontal tube with the solid either constrained or free to fall under gravity. Intl J. Heat Mass Transfer 29 (7), 1007–1019.CrossRefGoogle Scholar
Wilkinson, W.L. 1972 Non-Newtonian flow and heat transfer. P. I. Mech. Engng 186 (1), 109–116.Google Scholar
Yoo, H., Hong, H. & Kim, C.J. 1998 Effects of transverse convection and solid-liquid density difference on the steady close-contact melting. Intl J. Heat Fluid Flow 19 (4), 368–373.CrossRefGoogle Scholar