Thermal optimization of an internally finned tube using analytical solutions based on a porous medium approach

The present work deals with thermal optimization of an internally finned tube having axial straight fins with axially uniform heat flux and peripherally uniform temperature at the wall. The physical domain was divided into two regions: One is the central cylindrical region of the fluid extending to the tips of the fins and the other constituted the remainder of the tube area. The latter region including the fins was modeled as a fluid-saturated porous medium. The Brinkman-extended Darcy equation for fluid flow and two-equation model for heat transfer were used in the porous region, while the classical Navier-Stokes and energy equations were used in the central cylindrical region. The analytical solutions for the velocity and temperature profiles were in close agreement with the corresponding numerical solution as well as with existing theoretical and experimental data. Finally, optimum conditions, where the thermal performance of the internally finned tube is maximized, were determined using the developed analytical solutions.