On identifying optimal heat conduction topologies from heat transfer paths analysis

Making clear how thermal loads are equilibrated and transferred through a structure is of importance for identifying optimal heat conduction topologies in problems of cooling scheme design. This paper proposes a new method for computing the orientations and locations of heat transfer paths from a standard finite element analysis. First, a non-dimensional parameter (C^⁎) is introduced, based on the variation in thermal compliance of the structure, to quantify the contribution of an arbitrary point in the structure to heat conduction performance. Then, a plotting algorithm is presented to search for the ridge lines of the calculated C^⁎ curved surface, which provide the steepest ascent in C^⁎ values from the points of heat sink to the points of heat source. Based on this, mathematical conditions (termed uniformity and continuity requirements) are discussed in detail and utilized as new criteria for tailoring the layouts of heat transfer paths in order for conductive cooling to be more effective. Finally, the derived criteria are incorporated into a commonly used topology optimization algorithm (SIMP algorithm), and validated though several benchmark cases. Unlike the conventional methods, the suggested approach optimizes only the orientations and locations of heat transfer paths and does not intentionally concern the overall temperature distribution, the application of which can potentially lead to worthwhile improvements at the conceptual stage of cooling design processes.