| Abstract Scope |
Additive manufacturing processes are highly sensitive to heat dissipation, with inaccurate thermal control leading to residual stresses, distortion, cracking, and degradation of material performance. Classical analytical heat-transfer models provide valuable physical insight but are typically restricted by assumptions that neglect much of the geometry, rely on simplified boundary conditions, and only partially account for thermal dynamics. These restrictions limit their ability to accurately represent realistic manufacturing processes. In this work, we take a step toward a more general analytical framework for fast, physics-based thermal prediction in finite three-dimensional domains.
The framework is designed to systematically incorporate finite-geometry effects, transient dynamics, realistic heat-loss mechanisms, and flexible spatial and temporal heat-source descriptions. Using two complementary analytical approaches based on Laplace transforms and Fourier-series expansions, we derive closed-form and semi-analytical expressions for transient and steady-state temperature fields under several commonly used heat-source representations, including Gaussian, ellipsoidal, double-ellipsoidal, and time-dependent on/off sources. The resulting analytical predictions are compared with numerical implementations and demonstrate strong agreement while retaining direct physical interpretability. More importantly, the framework provides a computationally efficient alternative to repeatedly solving the full governing equations numerically, which is particularly important for real-time process control where conventional finite-element or finite-difference simulations can become computationally prohibitive. |