Solutions of a non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition

Abstract

Solutions of similarity-type for a nonlinear non-classical Stefan problem with temperature-dependent thermal conductivity and a Robin boundary condition are obtained. The analysis of several particular cases are given when the thermal conductivity L(f) and specific heat N(f) are linear in temperature such that L(f)=α+δf with N(f)=β+γf. Existence of a similarity type solution also obtained for the general problem by proving the lower and upper bounds of the solution.

Keywords

• boundary value problem
• stefan problem
• explicit solution
• existence of solutions