This lecture delves into the thermal analysis of foundry processes, focusing on Chvorinov's theory. It covers the analytical expressions for position and temperature profiles, energy balances at interfaces, and the interpretation of key parameters. The lecture also explores the relationship between temperature, speed, and position of the solidification front, as predicted by Chvorinov's model. Additionally, it discusses heat flow, equilibrium equations, and the determination of parameters for successful solidification. The lecture concludes with a detailed examination of the solid-liquid interface, energy balances, and the control of solidification rates in foundry processes.