Stefan's Problem in a Finite Domain with Constant Boundary and Initial Conditions Analysis

摘要

Stefan's problem in a finite domain is solved under constant boundary and initial conditions. Starting in a semi-infinite domain, the solution passes infinitely many stages of lead times in a finite domain and finally becomes stationary. The singularity at the finite terminal necessitates introduction of lead times. Including lead times, parameters defining the solution vary with time. Only the analytical result is reported in this paper. Partial contents: Mathematical preliminaries- Elemental functions, Integral formulas, Functions of a series; and Stefan's problem in a finite domain-Problem, Widder's solution of heat conduction, Temperature with embedding unknowns, Lead times, The Nth stage, and The final stage.