Cold Hearth Melting (CHM) is a metallurgical process used for melting, purification, and alloying of metals. In this process, an electron beam melts feedstock within a water-cooled hearth, after which the molten material is intermittently poured into a chilled crucible to form an ingot layer by layer. While CHM is widely used in industrial production, predictive understanding of how process parameters influence ingot quality remains limited. This work presents a computational framework for modeling and optimizing the CHM process for binary alloys, with a focus on titanium–niobium systems. The approach accounts for coupled fluid flow, heat transfer, solidification, and solute transport during each pour. The model simulates the transient pour into the crucible, capturing the evolving free surface and the effects of beam heating on quality metrics such as alloy homogeneity and layer height uniformity. Flow dynamics are modeled using an incremental pressure-correction scheme [1], while scalar transport equations describe solute redistribution. Energy transport is treated with a coupled enthalpy–temperature formulation incorporating latent heat effects and a lever-rule-based solidification model [2]. Microscale segregation behavior is informed through thermodynamic relations and solidification models that link continuum-scale temperature and composition fields to phase evolution. Electron beam heating is represented as a parametrized volumetric heat source, allowing systematic variation of thermal input and spatial uniformity. The simulation is implemented in a differentiable finite-element setting, enabling the use of automatic differentiation to compute sensitivities of the quality metrics with respect to process parameters describing the heat source. This capability supports gradient-based optimization strategies for exploring tradeoffs between beam heating and segregation.