Temporal and spatial temperature model predictions

Heat conduction models relevant to applications such as additive manufacturing and medical surgery are studied. The Fourier model is well-known in the field of heat transfer, but in cases involving for example ultra-short heat pulses, the hyperbolic and dual-phase-lag models are proposed as more realistic. Several publications reported on the existence of unwanted oscillations related to the hyperbolic model. These oscillations were the result of ill-posed problems and not numerical techniques. The problem was re-formulated, divided into auxiliary problems and solved using a combination of methods, resulting in oscillation-free solutions. Modal analysis was applied to the model problems to derive series solutions, proving convergence of the solutions in terms of energy and inertia norms. It was shown that modal analysis is effective in determining reliable model parameters and investigating the properties of the solutions.