One-dimensional phase change with periodic boundary conditions

Using a recently proposed semianalytical numerical scheme, we investigated the one-dimensional phase change problem with periodic Dirichlet boundary condition. We analyzed the molting boundary and the temperature distribution for different materials (Stefan number) and for several oscillation amplitudes and oscillation frequencies of the periodically oscillating surface temperature. The effect of the oscillating surface temperature on the evolution of the moving boundary is most pronounced when the domain is small and diminishes as the domain grows. Comparison of temperature distributions at different domain sizes suggests the increasing size of the domain to be the dominant factor that determines the temperature distribution. Numerical experiments show that, for given frequency, the surface temperature variation only impacts the temperature in a region near the surface. For example, for frequency of pi/2 once the domain has grown larger than approximately 5 units of length, the temperature for x' > 5 essentially remains constant.