Differential transformation method to determine heat transfer in annular fins

Abstract

AbstractFins are the extended surfaces that are utilized to afford a significant increase in the surface area for heat transference between a heated source and a colder ambient liquid. To enhance the heat transference rate from the exterior surface of a circular conduit, radial, or concentric annular fins are used. Fins are utilized in heat exchanging devices like superheaters, electrical equipment, computer CPU heat sinks, car radiators, refrigeration, and heat exchangers. Motivated by these applications, the current paper explores the thermal attribute of an annular fin with variable thermal conductivity. The framed equations are articulated in terms of nonlinear ordinary differential equations. One of the most effective techniques, the differential transformation method has been implemented to find the analytical solution. The domination of nondimensional parameters on the thermal gradient of the fin has been analyzed graphically. Furthermore, the variation in radial and tangential stress in an annular fin for various dimensionless parameters has been examined with a graphical explanation. Results reveal that the thermal gradient of fin increases for improved values of variable thermal conductivity parameters. The greater values of thermogeometric parameters result in a higher heat transfer.