Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

2009 ◽  
Vol 30 (1) ◽  
pp. 63-72 ◽  
Author(s):  
Fang-fang Li ◽  
Jing Liu ◽  
Kai Yue
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Phase Change ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Phase Change Heat Transfer ◽  
Transfer Problems

Three-Dimensional Numerical Study on Freezing Phase Change Heat Transfer in Biological Tissue Embedded With Two Cryoprobes

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Fang Zhao ◽  
Zhenqian Chen
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Biological Tissue ◽  
Clinical Medicine ◽  
Numerical Study ◽  
Biological Tissues ◽  
Freezing Process ◽  
Ice Crystal ◽  
Obvious Effect ◽  
Phase Change Heat Transfer

Biological tissues undergo complex phase change heat transfer processes during cryosurgery, and a theoretical model is preferable to forecast this heat experience. A mathematical model for phase change heat transfer in cryosurgery was established. In this model, a fractal treelike branched network was used to describe the complicated geometrical frame of blood vessels. The temperature distribution and ice crystal growth process in biological tissue including normal tissue and tumor embedded with two cryoprobes were numerically simulated. The effects of cooling rate, initial temperature, and distance of two cryoprobes on freezing process of tissue were also studied. The results show that the ice crystal grows more rapidly in the initial freezing stage (<600 s) and then slows down in the following process, and the precooling of cryoprobes has no obvious effect on freezing rate of tissue. It also can be seen that the distance of 10 mm between two cryoprobes produces an optimal freezing effect for the tumor size (20 mm × 10 mm) in the present study compared with the distances of 6 mm and 14 mm. The numerical results are significant in providing technical reference for application of cryosurgery in clinical medicine.

Solution of the Phase Change Stefan Problem With Time-Dependent Heat Flux Using Perturbation Method

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mohammad Parhizi ◽  
Ankur Jain
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Phase Change ◽  
Perturbation Method ◽  
Time Dependent ◽  
Engineering Applications ◽  
Theoretical Understanding ◽  
Present Solution ◽  
Phase Change Heat Transfer ◽  
Transfer Problems

Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for phase change heat transfer problems are often not available, and approximate analytical methods are needed to be used. This paper presents a solution for a one-dimensional (1D) phase change problem with time-dependent heat flux boundary condition using the perturbation method. Two different expressions for propagation of the phase change front are derived. For the special case of constant heat flux, the present solution is shown to offer key advantages over past papers. Specifically, the present solution results in greater accuracy and does not diverge at large times unlike past results. The theoretical result is used for understanding the nature of phase change propagation for linear and periodic heat flux boundary conditions. In addition to improving the theoretical understanding of phase change heat transfer problems, these results may contribute toward design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.

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