Analytical and Numerical Solution of Heat Transfer Equation in Rectangular Composite Fins

Abstract

Today, the use of composites has received widespread attention due to their special properties that cannot be found in alloys. Kevlar-Epoxy composite is one of the most widely used materials. In this paper, we analyze the heat transfer in rectangular fin and present an exact, Differential Transform Method and FEM solution for steady-state conduction heat transfer in rectangular composite laminates. The differential Transformation Method (DTM), is applied for predicting the temperature distribution in a rectangular composite fin. Laminate with fiber orientations of 0° is considered for the analysis. By validating the results in one composite layer, the temperature changes and heat flux in several composite layers were finally simulated in ABAQUS software and the effect of the number of composite layers and time on these parameters have been investigated. The selected composite fin’s material is Kevlar-epoxy. The results show that the exact solution and DTM predict the same trend compared to the FEM result and are very accurate and there is a good match between FEM results with DTM method and the exact solution. The thermo-geometric fin parameter (µ), the number of composite layers, and time have a significant effect on temperature distribution and heat flux. By increasing of thermo-geometric fin parameter (µ), heat flux and dimensionless variable for temperature distribution increase. When the number of layers increases, the dimensionless variable for temperature distribution and heat flux decrease along the fin. With increasing time, the temperature distribution and heat flux become more uniform and the ratio of heat flux changes decreases along the fin.

Keywords

• differential transform method
• numerical solution
• exact solution
• fem solution