The solar silicon production chain involves multiple stages, among which directional solidification stands out as the pivotal step that transitions silicon from its liquid form into ingots. This particular phase holds paramount importance in enhancing the quality of the resulting ingots. High-quality crystals can lead to improved performance and higher conversion efficiencies of solar cells. This study explores a comprehensive numerical simulation, employing the finite element method, to analyze the directional solidification crystal growth furnace utilized for multi-crystalline silicon production. The model encompasses various heat transfer mechanisms, including conduction within solid components, convection in molten silicon, and surface-to-surface radiation between all opaque diffuse gray surfaces. Additionally, it incorporates phase change phenomena to determine the shape of the melt-crystal interface and von Mises thermal stresses. The study illustrates a relationship between horizontal temperature gradients and the behavior of liquid silicon flow. It identifies two distinct zones within the molten silicon: a lower zone characterized by concave isothermal lines, concentrating highest temperatures at the center and lower temperatures along the crucible sides, and an upper zone featuring a lateral melt region with notably elevated temperatures compared to the central portion. The von Mises stresses near the solidification front and at the crucible's bottom were observed to be elevated due to the combined influence of temperature gradients and the attachment of the ingot to the crucible. So, controlling the temperature distribution and flow within the furnace is crucial for a deeper understanding of the complex crystal growth mechanisms and cultivating crystals of good quality, as these factors significantly influence impurity transport and defect generation during the growth process.