Thermal analysis of an internally finned tube using a porous medium approach

Abstract

The present work investigates the fluid flow and heat transfer characteristics of a laminar fully-developed forced convection in an internally finned tube with axially uniform heat flux and peripherally uniform wall temperature. The physical domain is divided into two regions separated by a circular arc of radius $r_i$ : one is the central circular region of the fluid extending to the tips of the fins and the other constitutes the remainder of the flow area. The latter region including the fins is modeled as a fluid-saturated porous medium. The Brinkman-extended Darcy equation for fluid flow and two equations for heat transfer are used in the porous region, while the averaged Navier-Stokes and energy equations are used in the regular fluid region. The analytical solutions for the velocity and temperature distributions are obtained from these equations. In order to validate the porous medium approach and the analytical solutions based on it, the numerical solutions are also obtained for a conjugate heat transfer problem comprising the fluid and the fins. The analytical solutions obtained by the porous medium approach are shown to be in close agreement with the numerical solutions. Based on the analytical solutions, parameters of engineering importance are identified to be the angle of the circular sector α, porosity ε, fin height ι, and effective conductivity ratio $k_{fe}/k_{se}$, and their effects on fluid flow and heat transfer are studied.