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

In this work, Boltzmann transform has been used to analyze the problem of freezing of pure Aluminum in semi-infinite domain. The uniqueness of solution (solidification front location) has been proved using the characteristics of the functions appeared in solution. The effect of density change on temperature distribution and errors resulting from ignoring this change have been investigated. The ...

We investigate the interface dynamics in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation obtained by B.Shraiman and D.Bensimon, we derive intergro-differential evolution equation of interphase dynamics. It is shown that such representation of the conformal mapping technique is convenient for computer simulations of the quasi-stationary Stefan ...

We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L(1) data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L(∞) data; this is done by regularization of the nonlinearity. The regulari...