This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. By modeling directional variability in thermal conductivity using both uniform and Von Mises distributions, the study highlights the superiority of the Von Mises distribution in providing consistent and efficient thermal performance. The Von Mises distribution, known for its concentration around a mean direction, demonstrates a significant advantage over the uniform distribution, resulting in higher mean efficiency and lower variability. The findings underscore the importance of considering both stochastic effects and directional consistency in thermal systems, paving the way for more robust and reliable design strategies.
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