3-D Air Flow in a Toroidal Natural Convection Loop

Heat transfer characteristics of air flows in concentric toroidal annular tubes filled with porous media were numerically investigated. The toroidal annulus is constant walls temperature where the outer wall temperature is lower than the inlet temperature. The numerical methodology was based on the finite difference approximation method. The computations were performed for vertical and horizontal toroidal ring, four toroidal length and four radius ratios cases for a modified Rayleigh number range (10 ≤ Ra ≤ 5000). The inner tube radius ranged from 0.15 to 0.4 m with the radius ratios Rr 0.333, 0.555, 0.777 and 0.888 and a length of 0.05, 0.1, 0.15 and 0.2m. The local Nusselt number in the angular direction for both walls and the average Nusselt number in concentric toroidal annular tubes were obtained. In addition the isothermal lines and the streamlines were investigated. The results show that The vertical toroidal loop is more suitable than the horizontal one because the heat transfer is less so the temperature values will be higher and remain high for a longer time which is required in such devices The best design of such devices is to take L=0.05 with inner radius of 0.15 m and to use it at δ =0 (vertical) General Terms Cp: Specific heat at constant pressure (kJ/kg o C), g: Acceleration due to gravity (m/s), kf: Thermal conductivity of the fluid (W/m K), ks: Thermal conductivity of the solid (W/m K), keff.: Effective thermal conductivity of the porous media (W/m K), K: Permeability (m), l: toroidal gap length (m), L: Dimensionless toroidal gap length, NuLocal 1 : Local Nusselt number on the inner surface, NuLocal 2: Local Nusselt number on the outer surface, Nu 1: Mean Nusselt number on the inner surface, Nu 2: Mean Nusselt number on the outer surface, p: Pressure (N/m2), q: Local heat flux (m), r: Radial coordinate (m), R: Dimensionless radial coordinate, Ra*: Modified Rayleigh number, Rr: Radius ratio, T: Temperature (K), ur,uφ, uz: velocity component in r,φ and z direction (m/s), Ur, Uφ, Uz: Dimensionless velocity component in R, φ and Z direction, x, y, z: Cartesian coordinate system (m), Z: Dimensionless axial coordinate, αf : Fluid thermal diffusivity (m/s), αs : Solid thermal diffusivity, αeff. : Effective thermal diffusivity (m/s), β: Volumetric thermal expansion coefficient (1/K), θ: Dimensionless temperature, ψr, ψφ, ψz: Vector potential component in R,φ and Z – direction, μf : Dynamic viscosity of fluid (Pa.s), FAI: angular direction.