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.

Considering the application of the polymer electrolyte membrane fuel cell (PEMFC), the separator thickness plays a significant role in determining the weight, volume, and costs of the PEMFC. In addition, thermal management, i.e., temperature distribution is also important for the PEMFC system to obtain higher performance. However, there were few reports investigating the relation between the temperature profile and the power generation characteristics e.g., the current density distribution of PEMFC operated at higher temperatures (HT-PEMFC). This paper aims to study the impact of separator thickness on the temperature profile and the current density profile of HT-PEMFC. The impact of separator thickness on the gases i.e., H₂, O₂ profile of HT-PEMFC numerically was also studied using CFD software COMSOL Multiphysics in the paper. In the study, the operating temperature and the relative humidity (RH) of the supply gas were varied with the separator thickness of 2.0 mm, 1.5 mm, and 1.0 mm, respectively. The study revealed that the optimum thickness was 2.0 mm to realize higher power generation of HT-PEMFC. The heat capacity of the separator thickness of 2.0 mm was the biggest among the separators investigated in this study, resulting in the dry-up of PEM and catalyst layer was lower compared to the thinner separator thickness. It also clarified the effects of separator thickness of profile gases, e.g., O₂, H₂O, and current density profile became larger under the higher temperature and the lower RH conditions.