An appropriate analysis for optimum design of wet fins based on modified 1-D and 2-D approaches

Abstract

The analysis of thin fins has generally been done by considering one-dimensional (1-D) heat conduction in fins. The condition for 1-D heat conduction for dry surfaces has been reported by many researchers. However, in the case of refrigeration and air conditioning applications, fin surface becomes wet due to the condensation of moisture on the surfaces. For the wet surface, no analysis has so far been conducted with considering two-dimensional (2-D) heat conduction in a fin. The present paper aims to determine analytically the temperature distribution for 2-D heat conduction in wet fins. Modified one-dimensional method is proposed appropriately for the solution of the two-dimensional heat conduction in the fin based on a trapezoidal rule. From the results, it can be highlighted that the modified 1-D model matches closely with the 2-D model. It has also been observed that under any design condition, 1-D classical model does not have capacity to predict the accurate result for thermal performance and local optimization parameters. In any range of Bi, modified 1-D model determines the heat transfer exactly with that by the 2-D model. This investigation also shows that there is no such condition found for the global optimization: the heat transfer rate and the fin efficiency always increase with Bi which may be extremely important aspect in a practical design to be selected Bi in an application. On the other hand, it can be demonstrated that this design condition for optimization has never been studied in the literature of fin heat transfer before.