Abstract
A mathematical model of energy transfer in metals (alloys) during their melting and crystallization has been developed with the aid of the energy conservation equation under the appropriate boundary conditions. Using a number of substitutions, exact integral solutions of a nonlinear differential heat transfer equation have been obtained for both the liquid and solid phases. The notion of the thermal diffusion ratio concerning the change in the solid state fraction with time related to the reference temperature (the effective average value between the solidus and liquidus temperatures) has been introduced. The exact solutions for the liquid and solid phases are expressed in terms of integrals based on the effective values of the heat capacities of the phases.
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