To analyse and optimize industrial melting and heating furnaces for metallurgical processes a knowledge of internal heat transfers is necessary. Computer-aided simulations of heat transmission processes for specified operating points give good results but are time-consuming and associated with cost-intensive software. However, an analytical model gives a faster and simpler alternative. Moreover only standard software is needed. There exist different convection and radiation models to calculate heat transmission processes. The present thesis should give an overview of some relevant models and their practical applicability. This assessment is based on the generation of a mass and energy balance of a shaft furnace.