Abstract
The thermal distribution within a rectangular profiled annular fin in the presence of a magnetic field and internal heat generation is examined in the present inspection. Furthermore, the linear and nonlinear temperature-dependent thermal conductivity and heat transfer coefficient are considered. The heat transfer equation is nondimensionalized using dimensionless terms, which results in a nonlinear ordinary differential equation (ODE) with related boundary conditions, which is then solved analytically and numerically using the DTM-Pade approximant and Runge-Kutta Fehlberg's fourth-fifth order (RKF-45) approach respectively. Moreover, the effect of several non-dimensional parameters on temperature gradient, radial, and tangential thermal stresses is explained with the assistance of graphs. The significant outcomes of the investigation reveal that enhancing the heat generation parameter strengthens temperature distribution significantly, but increasing the magnitude of the thermo-geometric parameter and magnetic field parameter leads to the lessening of thermal distribution through the fin.