Analysis of Transient Heat Transfer in Annular Fins of Various Shapes with a Base Subjected to a Decayed Exponential Function of Time in Heat Flux

摘要

This theoretical study of the heat flow within finned heat exchangers is of considerable practical importance because of the extensive utilization of finned surfaces for heat transfer enhancement in applications varying from air-cooled heal exchanges in the process industries to heat-rejection equipment in space vehicles. This article investigates the transient heat transfer in two-dimensional annular fins of various shapes with a base subjected to a decayed exponential function of time in heat flux. In order to obtain the solutions of the governing partial differential equation, the following procedures of analysis are performed: 1. Normalize the governing partial differential equation subject to the appropriate initial and boundary conditions. 2. Take the Laplace transform with respect to time. 3. Utilize the integral method to solve the transformed system. 4. Achieve the inverse Laplace transform by the Fourier series technique, and the transient temperature distribution of the annular fins of various shapes are obtained as a base subjected to a decayed exponential function of time in heat flux. 5. Typical results in the form of graphs are also presented.