Effect of the Inclination Angle and Eccentricity on Free Convection Heat Transfer in Elliptical-Triangular Annuli: A Lattice Boltzmann Approach

In this study, a Lattice Boltzmann method is used to simulation steady-state, laminar, free convection in two-dimensional annuli between a heated triangular inner cylinder and elliptical outer cylinder. The gap is filled with air as the working fluid. A constant temperature boundary condition is imposed on both the inner and outer surfaces. The study is performed for different inclination angles of inner triangular and outer elliptical cylinders at Ra=10(4). The inclination angle is varied from 0 degrees to 120 degrees for the triangular cylinder and from 0 degrees to 90 degrees for the elliptical cylinder. Furthermore, the vertical and horizontal eccentricity of the inner cylinder is investigated. The results for the inner and outer cylinders are presented in the form of isotherms, streamlines, and local and average Nusselt numbers. The results indicated that overall average Nusselt number has a type of nonlinear polynomial function with the triangular inclination angles and an approximately linear relation with the elliptical inclination angles. Also, the overall average Nusselt number decreases with the inclination of the outer elliptical cylinder. In addition, the results show that maximum heat transfer rate is reached when the inner cylinder is located at the center of the elliptical cylinder and at the lowest possible location vertically.