Abstract
UDC 541.124/128
A mathematical model of the process of transfer that occurs 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 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 temperatures solidus and liquidus) has been introduced. The exact solutions for the liquid and solid phases are expressed in terms of a number of integrals and effective values of the heat capacities.
Keywords: casting, heat flow, thermal conductivity, thermal diffusivity, heat capacity, thermal diffusion ratio.