Heat source layout optimization for two-dimensional heat conduction using iterative reweighted L1-norm convex minimization

Optimization of heat source distribution in two dimensional heat conduction for electronic cooling problem is considered. Convex optimization is applied to this problem for the first time by reformulating the objective function and the non-convex constraints. Mathematical analysis is performed to describe the heat source equation and the combinatorial optimization problem. A sparsity based convex optimization technique is used to solve the problem approximately. The performance of the algorithm is tested by several cases with various boundary conditions and the results are compared with a uniformly distributed layout. These results indicate that through proper selection of the number of grid cells for placing the heat sources and a minimum inter-source spacing, the maximum temperature and temperature non-uniformity in the domain can be significantly reduced. To further assess the capabilities of the method, comparisons to the results available in the literature are also performed. Compared to the existing heat source layout optimization methods, the proposed algorithm can be implemented more easily using available convex programming tools and reduces the number of input control parameters and thus computation time and resources while achieving a similar or better cooling performance.