Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while the Navier–Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity, and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.
Flow fields in an annulus between two rotating cylinders with a porous lining have been numerically examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The effects of porous sleeve thickness and its properties on the flows and their stability in the annulus are numerically investigated. Three-dimensional momentum equations for the porous and fluid layers are formulated separately and solved simultaneously in terms of velocity and vorticity. The solutions have covered a wide range of the governing parameters (10−5≤Da≤10−2, 2000≤Ta≤5000, 0.8≤b¯≤0.95). The results obtained show that the presence of a porous sleeve generally has a stabilizing effect on the flows in the annulus.
The effects of porous sleeve properties on the flow stability in rotating cylinders are numerically investigated in this study. To this end, three-dimensional momentum equations for the porous and fluid layers are formulated separately in terms of velocity and vorticity. These equations are then numerically solved over a wide range of parameters (10−2 ≤ Da ≤ 10−5, 2000 ≤ Ta ≤ 5000) to determine the critical Taylor number for the onset of flow instability for various porous sleeve properties. The results obtained show that the presence of a porous sleeve in general has a stabilizing effect on the flow in the annulus.
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