Effect of Adiabatic Circular Cylinder on the Natural Convection Heat Transfer Characterizes in a Porous Enclosure

Abstract

The present work studies numerically natural convective flow between a circular adiabatic cylinder located in a square porous enclosure using finite element method. Darcy–Forchheimer model is used in solving the dimensionless governing equations including; continuity, energy and momentum of the fluid along with Bousseinesq approximation. The enclosure is heated from bottom and cooled at isothermal temperature for the vertical walls. The top wall and obstacle are assumed adiabatic. The considered parameters are 10³ = Ra = 10⁶, 10^-5 = Da = 10^-3, obstacle vertical location 0.25 = h = 0.75 and cylinder radius 0.1 = D = 0.9 with Pr = 0.7. It is obtained that as the Rayleigh and Darcy numbers increase, both streamlines; Nusselt numbers will increase leading to increase the rate of heat transfer. The results show that the heat transfer rate is significantly dependent on the diameter of the circular cylinder and the location of the cylinder. It is found the maximum heat transfer rate obtained at D=0.1 and when the cylinder moves vertically upward at