Abstract
An optimal shape design problem for a melting furnace in phosphate production is discussed. To model this high temperature process, radiation effects need to be included. We employ here the convective SP\(_1\) model for radiative heat transfer, which is coupled with a nonlinear heat equation. The convective flow field is computed from the incompressible Navier–Stokes equation. The design objective is a desired temperature distribution on the bottom of the furnace, which ensures that certain chemical processes take place. To solve this shape design problem numerically we calculate the shape derivative based on a formal Lagrangian approach. This information is then used in a descent algorithm. The numerical results and optimized shapes underline the feasibility of our approach.
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This project has been supported by the German Federal Ministry of Education and Research (BMBF) under grant number 05M18UKA.
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Marx, T., Dietrich, N., Pinnau, R. (2022). Shape Optimization for the \(\text {SP}_1\)-Model for Convective Radiative Heat Transfer. In: Pinnau, R., Gauger, N.R., Klar, A. (eds) Modeling, Simulation and Optimization in the Health- and Energy-Sector. SEMA SIMAI Springer Series(), vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-99983-4_5
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