In this study, an analytical approach is used to find expressions for the closure time in freezing processes for spheres and cylindrical tubes. The starting point is the well-known two-phase Stefan problem. A new characteristic solution is established for extending the theory of constant heat flux ratio. Next, temperature profiles are assumed and substituted into the interface equation, which are then solved for the inward freezing process to get the closure time. Plots are generated to compare the new expressions to previously published experimental results of closure time. The new analytical approximations give reasonable outcomes as discussed in this paper. This paper demonstrates a general approach that can be further applied to different types of phase-change problems.
Analytical Approximations for the Closure Time of Freezing Processes in Spheres and Cylindrical Tubes
Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received May 16, 2018; final manuscript received January 21, 2019; published online March 21, 2019. Assoc. Editor: Yit Fatt Yap.
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Al-Hamed, K. H. M., Sahin, A. Z., Laoui, T., and Bokhari, A. H. (March 21, 2019). "Analytical Approximations for the Closure Time of Freezing Processes in Spheres and Cylindrical Tubes." ASME. J. Thermal Sci. Eng. Appl. October 2019; 11(5): 054501. https://doi.org/10.1115/1.4042854
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