Uncertainty analysis of temperature distribution in a thermal fin using the concept of fuzzy derivative

In the present work, by using the concept of fuzzy derivative, an effective method is presented for analyzing the uncertainty of temperature distribution in a straight thermal fin. In the present study, all sources of uncertainty are considered simultaneously by triangular fuzzy numbers. The proposed method has the advantage of involving the experiences and opinions of the expert about the input parameters through the concept of membership degree. As one of the main results, it has been shown that the use of strongly generalized Hukuhara derivative leads to invalid solutions, while the granular derivative, as a newfound fuzzy derivative, provides reasonable results that are consistent with the physics of the problem. Another result of the present work is a relation that explicitly states the effects of all uncertain parameters on the temperature distribution along the thermal fin. The effect of two parameters including fin length and fin root temperature has been studied in detail. The results of the present work have been compared with the results of the classical Monte Carlo method showing good agreement.