Numerical investigation of a non-linear moving boundary problem describing solidification of a phase change material with temperature dependent thermal conductivity and convection

Abstract

Problems related to the change in state of a PCM offer a great contribution in the field of heat transfer, describing melting, freezing, and sublimation. While most articles already exist on the mathematical aspects of this type of problem that account for constant thermal conductivity, there is still insufficient modeling and solutions involving convection driven by heated fluid and temperature-dependent thermal conductivity, which are presently being considered. In connection with this, the moving boundary problems become highly non-linear and their exact treatments are restricted. To deal with non-linearity, the numerical solution of the problem is obtained via the LWC technique. Convergence analysis of the non-linear model is extensively presented. Numerical codes are validated against analytical results and found to be in strong agreement. Numerical data of the solidification of the $Al-Cu$ alloy is presented for the validation of the current model. It is found that the rate of freezing increases as the value of the dimensionless parameter b increases. The impact of other parameters on freezing is discussed in detail. Furthermore, in the Stefan problem with convection and temperature-dependent thermal conductivity, the rate of freezing is faster than the standard problem, and in the Stefan problem with convection and fixed thermal conductivity.

Keywords:

• PCM
• Péclet number
• phase change front
• solidification
• Stefan number
• temperature-dependent thermal conductivity

Additional information

Funding

Vikas Chaurasiya is grateful to DST (INSPIRE)-New Delhi (India) for the Senior Research Fellowship vide Ref. No. DST/INSPIRE/03/2017/000184 (i) Ref. no/Math/2017-18/March 18/347.