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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
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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