An Analysis of the One-Phase Stefan Problem with Variable Thermal Coefficients of Order <i>p</i>

Abstract

Approximate solutions are obtained in implicit forms for the following general form of the nonlinear Stefan problem ddx(1+δ1yp)dydx+2x(1+δ2yp)dydx=4Steβ(x),0xλ, with y(0)=1,y(λ)=0, where λ>0 is a solution to the nonlinear equation y′(λ)=−2λSte, where δi>−1,i=1,2,p>0, and Ste is the Stefan number, which represents a phase-change problem with a nonlinear temperature-dependent thermal parameters (i.e., thermal conductivity and specific heat) on (0,λ).

Keywords

• nonclassical Stefan problem
• nonlinear thermal conductivity
• approximate solutions