Performance analysis of a longitudinal fin under the influence of magnetic field using differential transform method with Pade approximant

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 power‐law 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. 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 power‐law temperature‐dependent heat transfer coefficient.…