Fractional-order energy equation of a fully wet longitudinal fin with convective-radiative heat exchange through Sumudu transform analysis

The Adomian Decomposition Sumudu Transform Method (ADSTM) is applied to solve a fractional-order problem that involves temperature variations in a fully wet convective-radiative longitudinal fin. Darcy's law is used in formulating the energy balance equation to take into account the porous nature of the fin. The fractional-order energy balance equation for the fin is solved under two situations: a constant convective heat transfer coefficient and a temperature-dependent convective heat transfer coefficient. The ADSTM solution is compared with numerical results, obtained using the Runge-Kutta-Fehlberg approach. A series solution is obtained, and the roles of various parameters of the fractional-order differential equation are analyzed. It is found that the solution to the fractional-order differential equation outperforms the integer-order solution in modeling the temperature profile of the fin. Furthermore, it is observed that improvements in the wet porous characteristics of the fin lead to a reduction in its temperature.