Motivated by the phosphate production in a melting furnace we consider shape optimization as well as optimal control problems for approximations of the radiative heat transfer equation. In particular the Rosseland Approximation as well as the SP1 equation are studied. Additionally, we compare how the different models of the physical phenomena impact the different optimizations. The aim is to analyze how the shape of the furnace, as well as a simplified flame geometry, impact the resulting temperature distribution. For that, well-posedness of both models is shown and differentiability of the respective cost functionals is proven using the adjoint approach. Throughout this thesis the optical thickness is of special interest. Its impact on the respective solutions, derivatives and gradients is investigated and a framework is given in which they converge from SP1 equation to the Rosseland Approximation. The optimization problems are solved numerically using the calculated gradient to underline the theoretical results.weiterlesen