Worked Out Problem 9: A Thermal Conduction Problem Through an Extended Surface

In this chapter, we consider a scalar elliptic PDE modeling the steady-state heat transfer problem through a two-dimensional geometrically parametrized fin. The aim is to obtain efficient evaluations of the thermal field and the output of interest, defined as a measure of its dissipative capabilities. The solution is approximated using reduced order modeling techniques based on the POD-Galerkin method. The problem is described by presenting the physical domain, the goal, the parametrization, the boundary conditions, the governing PDE, and the corresponding weak formulation with its affine decomposition. Numerical results show the performance of the reduced approach with respect to the high-fidelity discretization, the quantity of interest, and the speedup. We provide the links to the source code, to the Jupyter notebook, and to the web-server ARGOS.