A simplified approach to the transient conduction in a two-dimensional fin

In this study, after applying an averaging technique in the transverse direction, the problem of transient conduction in a two-dimensional rectangular fin is reduced to that of a one-dimensional fin problem. The averaging method used in the improved one-dimensional formulation takes into account in an approximate manner the temperature variations across the fin. The classical formulation of the one-dimensional fin problem neglects the transversal temperature gradients. The resulting partial differential equation is analyzed using Laplace transforms when fin base is subjected to a step change in base temperature. Results of averaging technique are compared to one-dimensional transient solutions. These results indicate that accuracy on heat transfer at the fin base and average temperature profiles along the fin is significantly improved. The present analysis extends the range of applicability of one-dimensional formulation to larger values of Plot number based upon the lateral fin surface. Typical results are presented in graphical form for various values of pertinent parameters.