Vacuum Arc Remelting (VAR) process is employed in the production of Nickel-based
alloys, including Alloy 718. However, challenges arise during the process due to solidification
shrinkage, leading to the loss of contact between the ingot and the mold. This phenomenon
diminishes the cooling efficiency of the system, resulting in a deeper melt pool and a decline in
ingot quality as heat removal becomes less effective. To comprehensively investigate the
implications of solidification shrinkage, we introduce a sophisticated 2D axisymmetric
Magnetohydrodynamics (MHD) model. This model incorporates calculations for electromagnetic,
thermal, and flow fields. Also, the MHD model is fully coupled with a thermal stress-strain model,
enabling the computation of solid mechanical parameters like stress, strain, and deformation
within the ingot. Our coupled model provides essential insights, including the width of the air gap
along the ingot, the precise position of contact between the ingot and mold, and the profile of the
melt pool, among other critical parameters.