Analytical Approximations for the Closure Time of Freezing Processes in Spheres and Cylindrical Tubes with a Nanofluid Case Study

[+] Author and Article Information
Khaled Al-Hamed

P.O. Box 6616 Student Housing at KFUPM, Dhahran, Saudi Arabia 31261 Dhahran, 31261 Saudi Arabia kld.hamed.9@gmail.com

Ahmet Z. Sahin

KFUPM Box 1461 KFUPM Box 1461 Dhahran, 31261 Saudi Arabia azsahin@kfupm.edu.sa

Tahar Laoui

Building 63 Room-254, KFUPM campus Dhahran, 31261 Saudi Arabia tlaoui@kfupm.edu.sa

Ashfaque Bokhari

Building 5 Office: 5-509, KFUPM campus Dhahran, 31261 Saudi Arabia abokhari@kfupm.edu.sa

1Corresponding author.

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 xx xx, xxxx. Assoc. Editor: Yit Fatt Yap.

ASME doi:10.1115/1.4042854 History: Received May 16, 2018; Accepted January 21, 2019


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 is 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.

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