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根据Stefan问题研究物质固态和液态共存时接触面的移动变化。本文考虑这样一类问题:有两种不同的物质,分别在各自固定的区域,通过接触面交换热量。在初始时刻物质甲为固态且温度处在临界温度,物质乙为液态且温度则高于该临界温度。物质甲将出现两种状态,本文将研究这两种状态之间的接触面的变化,以及两种物质各自的温度分布。本文利用repeated erfc integral得到所求问题的形式级数解,并证明该级数一致收敛。
According to the Stefan problem, we study the change of the contact surface when the material solid and liquid coexist. This article considers such a problem: There are two different substances that exchange heat through the contact surfaces in their own fixed areas, respectively. At the initial moment, Substance A is solid and the temperature is at a critical temperature, Substance B is a liquid and the temperature is above the critical temperature. Substance A will appear in two states, this article will study the changes in the contact surface between the two states, and the temperature distribution of the two substances. In this paper, we use the repeated erfc integral to obtain the formal series solution of the desired problem and prove that the series converges uniformly.