Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

“…Explicit solutions are given in (Briozzo et al, 2007(Briozzo et al, & 2010Briozzo & Tarzia, 2002;Natale & Tarzia, 2006;Rogers & Broadbridge, 1988;Tirskii, 1959;Tritscher & Broadbridge, 1994) where nonlinear thermal coefficients are considered and in (Natale & Tarzia, 2000;Rogers, 1986) for Storm's materials.…”

Exact solution for Stefan problem with general power-type latent heat using Kummer function

“…Similar to Lombardi and Tarzia [16] and Natale and Tarzia [17], time-dependent surface flux is considered in the above Stefan problem so that the similarity transformation technique can be applied.…”

One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

“…The partial differential equation of heat conduction is a nonlinear equation when the temperature dependence of the thermal parameters is taken into account. We assume that the metal exhibits nonlinear thermal characteristics, such that the heat capacity, c p (T ), and the thermal conductivity, k(T ) ,satisfy a Storm's condition [4][5][6][7][8]:…”

“…There, the validity of the approximation (6) was examined for aluminum, silver, sodium, cadmium, zinc, copper and lead. In [7], the free boundary problems (1)-(5) (fusion case) for the particular case k(T ) = ρc/ (a + bT ) 2 and s(T ) = ρc = constant was studied. The explicit solution of this problem was obtained through the unique solution of an integral equation with time as a parameter.…”