Flow of second-order fluids over an enclosed rotating disc

Summary This paper is devoted to a study of the flow of a second-order fluid (flowing with a small mass rate of symmetrical radial outflow m, taken negative for a net radial inflow) over a finite rotating disc enclosed within a coaxial cylinderical casing. The effects of the second-order terms are observed to depend upon two dimensionless parameters ₁ and ₂. Maximum values ₁ and ₂ of the dimensionless radial distances at which there is no recirculation, for the cases of net radial outflow (m>0) and net radial inflow (m<0) respectively, decrease with an increase in the second-order effects [represented by T(=₁+₂)]. The velocities at ₁ and ₂ as well as at some other fixed radii have been calculated for different T and the associated phenomena of no-recirculation/recirculation discussed. The change in flow phenomena due to a reversal of the direction of net radial flow has also been studied. The moment on the rotating disc increases with T.Nomenclature , , z coordinates in a cylindrical polar system - z₀ distance between rotor and stator (gap length) - =/z₀, dimensionless radial distance - =z/z₀, dimensionless axial distance - _s =_s/z₀, dimensionless disc radius - V =(u, v, w), velocity vector - dimensionless velocity components - uniform angular velocity of the rotor - , p fluid density and pressure - P =p/(₂z₀₂², dimensionless pressure - ₁, ₂, ₃ kinematic coefficients of Newtonian viscosity, elastico-viscosity and cross-viscosity respectively - ₁, _{2 2}/z₀², resp. ₃/z₀², dimensionless parameters representing the ratio of second-order and inertial effects - m =, mass rate of symmetrical radial outflow - l a number associated with induced circulatory flow - Rm =m/(z₀₁), Reynolds number of radial outflow - R_l =l/(z₀₁), Reynolds number of induced circulatory flow - Rz =z₀²/₁, Reynolds number based on the gap - ₁, ₂ maximum radii at which there is no recirculation for the cases Rm>0 and Rm<0 respectively - ₁(T), ₂(T) ₁ and ₂ for different T - U_1(T)⁽⁺⁾ = dimensionless radial velocity, Rm>0 - V_1(T)⁽⁺⁾ =, dimensionless transverse velocity, Rm>0 - U_2(T)^(–) =, dimensionless radial velocity, Rm=–Rn<0, m=–n - V_2(T)^(–) =, dimensionless transverse velocity, Rm<0 - C_m moment coefficient