Abstract
This paper presents an approximate mathematical technique utilizing the energy-integral method for solving the planar solidification problem of a pure liquid metal occupying the infinite half-space. Assuming a time-dependent relaxation model for the energy flux results in a hyperbolic differential equation for the thermal field which is solved under suitable conditions of both local thermodynamic equilibrium and thermal dynamical compatibility on the interface displacement. In fact, analytical expressions are derived when (a) surface temperature is prescribed; or (b) heat flux at the surface boundary is given. Comparisons of these expressions with corresponding results pertinent to parabolic Stefan problems are made; and finally all the solutions are presented in graphical form.
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