Stefan problems for the diffusion–convection equation with temperature-dependent thermal coefficients

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Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative–convective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion–convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved through a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.