Thermal design optimization by geometric parameterization of heat sources

In this master thesis, a thermal design optimization has been performed. By solvingthe two dimensional steady state conduction convection equation using the finiteelement method in a unit square domain with a source term corresponding tocomponents heated by resistive heating, the objective functional was formulated as aminimization of the combination of a low temperature and small temperaturedifferences inside the domain. The design parameters are based on geometricproperties such as length, width, angle or position of the heat sources. The heatsources were parameterized by combining two smooth exponential functions thatexplicitly depended on the position and size of the heat source. The problem wasthen solved as a PDE constrained optimization problem using MATLAB's built infunction fmincon. Three different 1D test cases were implemented to investigate how the solverbehaved and that the parameterization was correctly implemented. Then the solverwas extended to 2D and three heat sources were placed in the domain. The optimalangle of rotation of the sources where the heat transfer was governed by conductionand convection were found. This was followed by an optimal placement of two heatsources in the domain. Three cases with a different convective field in each case wereinvestigated. In the last examples, four heat sources were placed inside the domain.One geometric property of each heat source was allowed to change. The fourdifferent parameters were length, width, angle of rotation and position. Themotivation was to test the functionality of the solver using different design parameterswith different sensitivities. The results showed that the derived objective functional fullfilled the purpose tominimize the temperature and temperature deviation from the mean temperature,respectively. In the 1D cases it was concluded that there exist several local minimawhen adding a heat source and a heat sink of unequal magnitude. Optimal angles ofthree heat sources in 2D showed a trivial solution and fast convergence. The optimalplacement of two heat sources converged rapidly when the forced convection was setto zero. When adding convection the number of iterations increased and the optimalplacement was highly dependent of the type of convective field and boundaryconditions. When constructing a non symmetric problem the optimization loopedover several random initial positions in order to find the best optimal solution. Forthe last examples, narrow bounds were used and the solver converged rapidly. Evenhere, the type of convective field highly affected the optimal solution