Mathematical model of heat transfer in the “frozen casting mold – anti-adhesive coating – metal” system based on cellular automata
DOI:
https://doi.org/10.15276/opu.1.71.2025.21Keywords:
frozen casting mold, cellular automata, heat exchange processes, anti-adhesive coatingAbstract
A mathematical model for heat transfer in a “frozen casting mold – anti-adhesive coating – metal” system has been developed based on cellular automata. The modeling of thermal energy transfer is carried out using a special modification of the Stochastic Excitable Cellular Automata (SECA) method. Based on this mathematical model, heat transfer calculations were performed for the “frozen casting mold – anti-adhesive coating – metal” system. To determine the temperatures of the cellular automata at the initial step of the numerical experiment, each automaton is assigned initial values for temperature, thermal conductiv-ity, and heat capacity. Then, at each subsequent n-th time step, a new automaton temperature value is calculated, considering thermal fluxes from each neighboring automaton. When analyzing heat and mass transfer, it is crucial to account for heat consumption during the melting and evaporation of water, as well as heat release during moisture condensation. The heat of ice melting and water evaporation was consid-ered by increasing the specific heat capacity of the mold within the melting temperature range. The conducted research experimentally con-firmed the adequacy of the mathematical model for heat transfer in the “frozen casting mold – anti-adhesive coating – metal” system based on cellular automata. The investigations were performed using an AK5M2 alloy cast into frozen molds with an anti-adhesive coating. A nomogram is presented for determining the minimum thickness of the frozen core depending on the casting wall thickness and the mold cooling temperature. A method for selecting parameters using this nomogram is described. A mathematical dependency of the mold (core) heating depth to −5.0 °C on the casting wall thickness was derived. At this temperature, the strength of the frozen mold (core) is comparable to that of a sand-clay mold.
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References
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