Constructal optimization of a rectangular non-uniform heat generation area with irregular high thermal conductivity material

Heat conduction models with three non-uniform heat generation conditions in a rectangular heat generation area (RHGA) are set up in this paper. Under given areas of the irregular high thermal conductivity material (HTCM) and RHGA, constructal optimization of the RHGA is conducted by changing the distribution of the HTCM and aspect ratio of the RHGA. The minimum dimensionless average temperature difference (DATD) of the RHGA is gained. It is found that the DATDs of the RHGA with linear heat generation distribution are abated by 82.43% and 82.65% after twice optimizations for boundary and central heat sinks, respectively. For the heat generation in one local area of the RHGA, the two decrements are 36.30% and 52.20%, respectively. For the heat generation in multiple local areas of the RHGA, the two decrements are 35.60% and 71.60%, respectively. The optimal structure of the RHGA with heat generation in multiple local areas and heat sink in the center exhibits the best cooling performance compared with the other models discussed in this paper. Moreover, the best cooling performance of the RHGA is at least augmented by 29.49% than those of the previous studies discussed in this paper.