Analysis of two-dimensional freezing on the outside of a coolant-carrying tube

E. M. Sparrow, C. F. Hsu

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The solution methodology developed in the preceding paper has been amplified, adapted, and then employed to solve the conjugate phase change-convection problem which results when a coolant passes through a tube situated in a liquid phase-change medium. The axial temperature increase experienced by the coolant gives rise to two-dimensional freezing about the tube. In the first part of the paper, the procedures used to incorporate the coolant energy equation and the various boundary conditions into the solution methodology are described. A closed-form analytical solution is then derived to start the main numerical solutions. The numerical work was focused on gaseous coolants because they give rise to much larger axial variations than do liquid coolants. Results were obtained for the thickness of the frozen layer, the coolant bulk temperature, the tube wall temperature, and the energy extracted from the phase-change medium, with the coolant Stanton number, the Biot number, and the solid-phase Stefan numbers as parameters. Among the parameters, the results were not very sensitive to the Stanton and Stefan numbers but were quite responsive to the Biot number.

Original languageEnglish (US)
Pages (from-to)1345-1357
Number of pages13
JournalInternational Journal of Heat and Mass Transfer
Issue number8
StatePublished - Aug 1981

Bibliographical note

Funding Information:
Acknowledyeme-n-Tf his research was performed under the auspices of the U.S. Department of Energy (DOE,/DE-ACO2-79ER 10343) Office of Basic Energy Sciences.


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