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Close-contact melting on an isothermal surface with the inclusion of non-Newtonian effects

Published online by Cambridge University Press:  22 February 2019

Y. Kozak Open the ORCID record for Y. Kozak [Opens in a new window] ,
Yi Zeng ,
Rabih M. Al Ghossein ,
J. M. Khodadadi  and
G. Ziskind
Y. Kozak*
Affiliation:
Heat Transfer Laboratory, Department of Mechanical Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel
Yi Zeng
Affiliation:
Mechanical Engineering Department, Auburn University, 1418 Wiggins Hall, Auburn, AL 36849-5341, USA
Rabih M. Al Ghossein
Affiliation:
Mechanical Engineering Department, Auburn University, 1418 Wiggins Hall, Auburn, AL 36849-5341, USA
J. M. Khodadadi
Affiliation:
Mechanical Engineering Department, Auburn University, 1418 Wiggins Hall, Auburn, AL 36849-5341, USA
G. Ziskind
Affiliation:
Heat Transfer Laboratory, Department of Mechanical Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel
*
†Email address for correspondence: [email protected]
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Abstract

The present study deals with a theoretical investigation of a close-contact melting (CCM) process involving a vertical cylinder on a horizontal isothermal surface, where the liquid phase is a non-Newtonian viscoplastic fluid that behaves according to the Bingham model. Accordingly, a new approach is formulated based on the thin layer approximation and different quasi-steady process assumptions. By analytical derivation, an algebraic equation that relates the molten layer thickness and the solid bulk height is developed. The problem is then solved numerically, coupled with another equation for the melting rate. The new model shows that as the yield stress increases the melting rate decreases and the molten layer thickness increases. It is found that under certain conditions, the model can be reduced to a form that allows an analytical solution. The approximate model predicts an exponential dependence of both the melt fraction and the molten layer thickness. Comparison between the numerical and analytical solutions shows that the analytical approximation provides an excellent estimation for sufficiently large values of the yield stress. Dimensional analysis, which is supported by the analytical model results, reveals the dimensionless groups that govern the problem. For the general case, the melt fraction is a function of two dimensionless groups. For the analytical approximation, it is shown that the melt fraction is governed by a single dimensionless group and that the molten layer thickness is governed by two dimensionless groups.

JFM classification

Phase change: Solidification/melting Non-Newtonian Flows: Non-Newtonian Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 720 - 742
Copyright
© 2019 Cambridge University Press 

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