A new approach to the transient conduction in a 2-D rectangular fin

Abstract

The purpose of this work is to develop a method that enables one to reduce the problem of transient conduction in a 2-D rectangular fin to that of a 1-D problem. After applying the perturbation technique and an averaging method, the problem of transient conduction in a 2-D rectangular fin is reduced to that of a 1-D problem. A linear operator method can then be applied to solve the resulting partial differential equation if the associated Sturm-Liouville problem is manageable. Actual calculation of transient temperature profiles in a 2-D rectangular fin confirms the validity of the method developed in this work.