Effect of aspect ratio and eccentricity on heat transfer from a cylinder in a cavity

This paper presents hydrodynamic and thermal behavior of fluid surrounds an isothermal circular cylinder in a square cavity. Simulations were carried out for four aspect ratios (defined by L/D) 2.0,3.0,4.0,5.0.Effect of eccentric positions (ε =-0.5 and 0.5) of cylinder with respect to the cavity was carried out at L/D=2.0. Predicted results for eccentric cases are compared with concentric (ε = 0.0) case for a fluid having Prandtl number 1.0. Grashof number based on diameter of the cylinder, ranging 10 to 10 6. The control volume based finite volume method is used to discretize the governing equations in cylindrical coordinate. SIMPLE algorithm is used. A collocated variable arrangement is considered and TDMA solver is employed to solve the system of equations. Parametric results are presented in the form of streamlines and isothermal lines for both eccentric and concentric positions. Heat transfer distribution along the perimeter of the cylinder is presented in the form of local Nusselt number. Predicted results show good agreement with experimental results described in reference (see Cesini et.al. (1999)) Nomenclature A = coefficient matrix Greek symbols C p = specific heat β = thermal expansion coefficient D = diameter of the cylinder ε = eccentricity g = gravity acceleration ϕ = any variable Gr = Grashof number Φ = total mass flux h = heat transfer coefficient Ω = convective or diffusive flux k = thermal conductivity of fluid µ = dynamic viscosity of fluid L = length & width of walls ρ = density of fluid Nu = Nusselt number ψ = stream function n = surface normal σ = an index defined by equation (14) Pr = Prandtl number θ = tangential coordinate r = radial coordinate Θ = dimensionless temperature R = dimensionless radial coordinate Subscripts/superscripts P = pressure av = average value P * = modified pressure , (eqn.4) D = based on diameter T = temperature C = at cylinder wall u = radial velocity component L = local value v = tangential velocity component ref = reference value U r = dimensionless radial velocity W = at cavity wall U θ = dimensionless tangential velocity ∞ = ambient condition