Thermal analysis of an annular fin under multi-boiling heat transfer coefficient using differential transform method with Pade approximant (DTM-Pade)

Abstract

The convective heat transfer between the object and surrounding environment can be improved by increasing the surface area. This can be done by mounting an annular/radial fin to a cylindrical surface and thus enormous heat is transferred by the annular fin. Motivated by this fact, the temperature distribution and thermal stresses of an annular fin with internal heat generation under multi-boiling heat transfer are examined using the differential transform method (DTM)-Pade approximant. The governing equation and corresponding boundary conditions are transformed into a highly nonlinear ordinary differential equation (ODE) by introducing suitable non-dimensional terms. The resultant transformed ODE is solved analytically using DTM-Pade approximant. The results achieved from DTM-Pade and Runge-Kutta Fehlberg fourth-fifth (RKF-45) technique are compared for numerical validation and are found to be close to each other. The performance of the fin and aspects of dimensionless temperature profile has been elucidated graphically with the impact of dimensionless parameters. Furthermore, the results of this scrutiny manifest that the temperature profile of the fin increases with the impact of thermal conductivity parameter and heat generation parameter whereas it decreases for thermo-geometric parameter. Fin efficiency varies significantly with the impact of prescribed parameters under multi boiling heat transfer cases. The radial and tangential stress distribution are more in the case of radiation heat transfer compared to other cases.