Thermal optimization of a circular-sectored finned tube using a porous medium approach

The present work investigates the heat transfer characteristics of a laminar fully developed forced convection in a circular-sectored finned tube with axially uniform heat flux and peripherally uniform wall temperature. The tubes with circular-sectored fins are modeled as a fluid-saturated porous medium. Using the Brinkman-extended Darcy model for fluid flow and the two-equation model for heat transfer, the analytical solutions for both velocity and temperature distributions are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer in order to validate the porous medium approach. The agreement between the solutions based on the porous medium approach and the conventional method is close within 5.3 percent. Based on the analytical solutions, parameters of engineering importance are identified to be the angle of the circular sector a and the effective conductivity ratio C, and their effects on fluid flow and heat transfer are studied. Also, the total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of a tube with circular-sectored fins.