New perturbation method for planar phase‐change processes with time‐dependent boundary conditions

1987 ◽  
Vol 62 (11) ◽  
pp. 4375-4381 ◽  
Author(s):  
Ch. Charach ◽  
Y. Zarmi ◽  
A. Zemel
Keyword(s):  
Boundary Conditions ◽  
Phase Change ◽  
Perturbation Method ◽  
Time Dependent ◽  
Change Processes ◽  
Planar Phase ◽  
New Perturbation

Numerical Modelling of Phase Change in Freezing and Thawing Unsaturated Soil

1993 ◽  
Vol 24 (2-3) ◽  
pp. 95-110 ◽  
Author(s):  
H. Engelmark ◽  
U. Svensson
Keyword(s):  
Boundary Conditions ◽  
Phase Change ◽  
Change Process ◽  
Numerical Solutions ◽  
Time Dependent ◽  
Total Water Content ◽  
Total Water ◽  
Freezing And Thawing ◽  
Water Ice ◽  
Temperature Boundary

This paper presents a new method for handling the phase change process in numerical simultations of freezing and thawing soils. Moisture and heat transfer in soils subjected to both freezing and thawing are discussed. Simulated freezing results of temperature and total water content (water + ice) are compared with experimental data reported by Jame (1977). Simulated and experimental results were similar. The effects of different time-dependent temperature boundary conditions were evaluated and discussed. The method was used both with abrupt and smooth temperature boundary conditions and both resulted in stable numerical solutions. Finally, results from a simulation of a freezing and thawing cycle are presented and discussed qualitatively.

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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