Computational heat transfer with spectral graph theory: Quantitative verification

The objective of this paper is to quantify the precision of a novel approach for computational heat transfer modeling based on spectral graph theory. Two benchmark heat transfer problems with planar boundaries, for which exact analytical solutions are available, are used to determine the precision of temperature predictions obtained from spectral graph, finite difference (one-dimensional), and finite element (three-dimensional) methods. These studies show that the spectral graph approach captures the temperature trends in the benchmark case studies with error in the range of 2% to 10% depending on the location in the body. These verification studies also provide an approach to calibrate the numerical parameters in the new method. The spectral graph approach is applied for predicting the thermal history of a complex three-dimensional additive manufactured (3D printed) part. The temperature trends in a 50-layer part are computed 2.3 times faster than a commercial finite-element software package, and the results differ by less than 7.5%. Further improvements in the computational speed of the spectral graph approach are expected through code optimization and parallelization. This work has far-reaching practical implications for predicting thermal-induced defects in a variety of manufacturing processes including casting and additive manufacturing.