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The paper presents a mathematical model and simulation of resistance spot welding (RSW) of a binary alloy during the final solidification process. After analyzing the heat distribution and heat transfer process, the authors established assumptions for a planar front solidification model. Following the application of initial and boundary conditions, the model is developed numerically to describe the thermal distribution in the resistance spot welding system as a function of position and time. For each value in the time array, a heat transfer profile through the welding sheet is calculated as a piecewise function. The model is further executed with Python, which allows customized inputs of resistance spot welding parameters. Finally, the heat transfer model is simulated with COMSOL Multiphysics in the specific example of 1050 mild steel. Heat transfer module is applied to the proposed mathematical model, and simulation of temperature profile and thermal gradient of the welding zones are developed. The simulation further confirms the mathematical model and provides a demonstration that the temperature decreases through both the water-cooled welding tips and thermal diffusion to the surrounding metal sheets, leading to adjacent heat-affected zones. The model is intended for predicting the resistance spot welding nugget solidification process, as well as to help analyze the effects of welding parameters to achieve a weld nugget of optimal size.