Design and Optimization of Internal Longitudinal Fins of a Tube Using Constructal Theory

Abstract

This research is devoted to geometrical optimization of internal longitudinal fins based on constructal theory. These fins are extended inward from the pipe perimeter to a prescribed radius and would have an optimal length, determined analytically by means of constructal theory. The effective parameters of the current study are the ratio of high conductivity to low conductivity, volume fraction of the fins, and the number of the fins. For a round tube with two thermal boundary conditions, i.e., constant heat flux and constant temperature, the optimization length and also the corresponding thickness of fins for a known material ratio are determined parametrically ensuring maximum heat transfer and thermal efficiency In addition, dominancy of conduction heat transfer between fins and convection in the core of pipe are the main assumptions of this research. Finally, our analytical results are verified with their corresponding numerical counterparts.