Propagation of temperature waves in phase-transition regions
E.I. Narygin1,2, A.V. Pyatkova1,2
1Tyumen Branch of the S.A. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Tyumen, Russia
2Tyumen State University, Tyumen, Russia
Keywords: phase transition, Stefan problem, enthalpy method, temperature waves, numerical solution
Abstract
This paper numerically studies the propagation of temperature waves during a phase transition in a substance completely filling a plate, cylinder, or sphere. At the boundaries of the regions, the temperature varies harmonically. The phase transition temperature lies within the temperature variation range of the boundaries. The enthalpy method was used to model the phase transition. To validate the results, they were compared with analytical solutions and the results of other authors. The influence of dimensionless parameters and geometric characteristics on the temperature behavior at the center of the region and the penetrating power of temperature waves was studied. A correlation between the temperature extremum at the center of the region and the thermophysical parameters was determined. When this extremum is reached, the difference between the average temperature at the center of the region and at the boundaries is greatest. It was found that at the extremum point, the average temperature at the center of the region is equal to the phase transition temperature. The type of extremum depends on the ratio of the thermal conductivities of the phases. A qualitative dependence of the heat wave attenuation coefficient on thermophysical parameters was established. Conditions under which the penetrating power of the temperature wave is minimal were determined.
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