The temperature distribution in a longitudinal fin with magnetic field due to conductive-convective-radiative heat transfer is debriefed in this research article. Thermal properties of the fin material, such as thermal conductivity and heat transfer coefficient, have been considered to vary non-linearly with local temperature whereas surface emissivity has been taken to be constant. The main governing equation of the current model is developed with the aid of Fourier's law of heat conduction, exponentially temperature-dependent thermal conductivity, Maxwell expression for the effect of the magnetic field, and powerlaw temperature-dependent heat transfer coefficient. This equation is converted into a non-dimensional form using dimensionless variables and then traced out numerically with the assist of Runge-Kutta Fehlberg's fourth-fifth method. Also, the transformed nonlinear energy equation is solved using a DTM-Pade approximant, yielding an approximate closed-form solution. The findings of the analytical and numerical investigation are depicted graphically. The outcomes have divulged that the convective and radiative parameters significantly decrease the temperature distribution and improve convective cooling from the fin surface. The rise in the Hartmann number is responsible for the decreasing of the temperature distribution and it aids in accelerating heat transfer.

Temperature distribution, and efficiency of a rectangular profiled longitudinal fin are examined in this investigation with the impact of the magnetic field. By exploiting appropriate non‐dimensional terms, the heat transfer equation incorporating temperature‐dependent thermal conductivity, heat transfer coefficient, and Maxwell expression for the effect of the magnetic field yield a dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions (BCs). Sumudu transform method with Pade approximant (STM‐PA) has been employed to obtain an analytical solution for the temperature profile of a longitudinal rectangular fin subjected to a uniform magnetic field under multi‐boiling heat transfer. The STM‐PA results are compared to the Runge‐Kutta Fehlberg's fourth‐fifth (RKF‐45) order technique for computational verification and are observed to be in good accordance. The behavior of dimensionless temperature profile has been explicated graphically for diverse values of non‐dimensional parameters such as thermal conductivity parameter, Hartmann number, and thermogeometric parameter. The results of this study show that as the thermal conductivity parameter enriches, the temperature profile of the longitudinal fin improves, whereas it declines for the Hartmann number and thermogeometric parameter. Under multi‐boiling heat transference, fin efficiency varies significantly depending on the impact of pertinent variables.