Optimization of heat source distribution for two-dimensional heat conduction using bionic method

The volume-to-point problem is a fundamental problem for electronic cooling. The existing studies mainly focus on the heat conduction optimization through designing the distribution of the high thermal conductivity material. Actually, the heat source distribution also affects the heat conduction performance significantly. In this paper, the heat source distribution optimizations in the two-dimensional volume-to-point and volume-to-boundary problems are studied. The Lagrange function is constructed for the optimization problem and variational principle is used to optimize the heat source distribution. The result shows that the heat source is located on boundaries for optimum when there is no constraint on the heat source intensity. For the situation of the heat sources with discretized size and finite intensity, the bionic optimization (BO) method is introduced to optimize the heat source layout. Further mathematical analysis is conducted to deduce the optimization criterion that the heat source is suggested to be located at the position with the lowest temperature during the process of BO. Three typical cases with various boundary conditions are used to verify the proposed method for distribution of heat sources with discretized size and finite intensity. Compared to random distribution and uniform distribution, bionic method can reduce the maximum temperature rise and improve the temperature uniformity of the solution effectively. The improvement ratios of the two indices are at least 23% and 54% averagely compared to the two other methods for each test case, respectively. Results of the cases with different calculation parameters are presented, through analyzing which the influences of the parameters on the performance of solutions by the bionic optimization are investigated. It is revealed that the heat source distribution affects the heat conduction process significantly, and the proposed bionic method is an effective method to optimize the heat source distribution and improve the heat conduction performance.