Explicit solutions for a two-phase unidimensional Lamé-Clapeyron-Stefan problem with source terms in both phases
The authors consider the classical Stefan problem with different thermal coefficients in the two phases and also different heat sources depending on the variable \(\frac{x}{ra_i\sqrt{t}}\) in the solid phase \((i=1)\) and liquid phase \((i=2)\), \(a_i\) denoting heat diffusivity. The problem is formulated for \(x>0\), \(t>0\). The initial temperature is a negative constant (phase change temperature is zero) and the same value is imposed for \(x\rightarrow +\infty\). Explicit solutions are constructed when at \(x=0\) temperature is prescribed as a positive constant and when incoming heat flux is given with an \(1/\sqrt{t}\) singularity. Conditions ensuring the equivalence of these two classes are analyzed together with other properties of the solutions.
sublimation-dehydration similarity solution
scientific article; zbMATH DE number 5129639
scientific article