Natural convection from horizontal isothermal elliptic disks - Models and experiments

Abstract

General models are proposed for natural convection from horizontal isothermal thin elliptic disks. The models are based on the linear superposition of the corresponding diffusive limits (shape factors) and the laminar boundary layer asymptotes. The dimensionless shape factor for the elliptic disk is based on a modification of the Smythe solution for the finite circular cylinder. A comprehensive procedure is presented that leads to a complex formulation of the body-gravity function. A simpler procedure based on the method of inscribing and circumscribing circular cylinders within the elliptic cylinder yields a simpler expression for accurate evaluations of the body-gravity function. The Nusselt and Rayleigh numbers, and the dimensionless shape factor and body-gravity function are based on the characteristic body length proposed by Yovanovich, i.e., the square root of the total surface area of the body. The proposed models are compared against air data obtained over eight decades of the Rayleigh number for three thin elliptic disks having a range of aspect ratios. The agreement between theory and experiment is shown to be excellent. (Author)