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

Abstract

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.

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

“…The role of radiation and convection on heat transmission of the longitudinal fin was studied by Gouran et al [12] with production of internal heat. Sowmya et al [13] described the thermal dissipation of a straight rectangular fin with the effect of radiation and magnetic strength using the Pade approximant based differential transform method (DTM-Pade). Thermal distribution in an extended surface is a significant topic in the research area due to its numerous engineering and industrial applications.…”