The problem of convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus (angular frequency, ) in the presence of a homogeneous magnetic field (B) in the azimuthal direction is considered. The small gap approximation is used together with rigid cylindrical boundaries. The onset of convection occurs in the form of axial, axisymmetric or oblique rolls. The angle between the roll axis and the axis of rotation depends of the ratio between the Chandrasekhar number, QB2, and the Coriolis number, . Fully three-dimensional numerical simulations as well as Galerkin representations for roll patterns including the subsequent stability analysis are used in the theoretical investigation. At finite amplitudes, secondary transitions to 3D-hexarolls and to spatio-temporal chaos are found. Overlapping regions of pattern stability exist such that the asymptotically realized state may depend on the initial conditions. PACS 47.27.-i, 47.65.+a 相似文献
In this paper, a numerical investigation of natural convection in a porous medium confined by two horizontal eccentric cylinders is presented. The cylinders are impermeable to fluid motion and retained at uniform different temperatures. While, the annular porous layer is packed with glass spheres and fully-saturated with air, and the cylindrical packed bed is under the condition of local thermal non-equilibrium. The mathematical model describing the thermal and hydrodynamic phenomena consists of the two-phase energy model coupled by the Brinkman-Forchheimer-extended Darcy model under the Boussinesq approximation. The non-dimensional derived system of formulations is numerically discretised and solved using the spectral-element method. The investigation is conducted for a constant cylinder/particle diameter ratio () = 30, porosity () = 0.5, and solid/fluid thermal conductivity ratio () = 38.6. The effects of the vertical, horizontal and diagonal heat source eccentricity (−0.8 0.8) and the annulus radius ratio (1.5 5.0) on the temperature and velocity distributions as well as the overall heat dissipation within both the fluid and solid phases, for a broad range of Rayleigh number (104 Ra 8 ). The results show that uni-cellular, bi-cellular and tri-cellular flow regimes appear in the vertical eccentric annulus at the higher positive eccentricity e = 0.8 as Rayleigh number increases. However, in the diagonal eccentric annulus, the multi-cellular flow regimes are shown to be deformed and the isotherms are particularly distorted when Rayleigh number increases. In contrast, in the horizontal eccentric annulus, it is found that whatever the Rayleigh number is only an uni-cellular flow regime is seen. In addition, it is shown that the fluid flow is always unstable in the diagonal eccentric geometry at e = 0.8 for moderate and higher Rayleigh numbers. However, it loses its stability in the vertical eccentric geometry only at two particular cases, while it is always stable in the horizontal eccentric geometry, for all eccentricities and Rayleigh numbers. 相似文献
In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid in a vertical porous annular region between two concentric tubes. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large in comparison with the radius of the tube) is used to linearise the governing equations. Using the perturbation method, the solutions are obtained for the velocity and the temperature fields. Also, the closed form expressions are derived for the pressure-flow relationship and the heat transfer at the wall. The effect of pressure drop on flux is observed to be almost negligible for peristaltic waves of large amplitude; however, the mean flux is found to increase by 10-12% as the free convection parameter increases from 1 to 2. Also, the heat transfer at the wall is affected significantly by the amplitude of the peristaltic wave. This warrants further study on the effects of peristalsis on the flow and heat transfer characteristics. 相似文献
Direct contact heat transfer between water and a heat transfer oil was investigated under non-boiling conditions in co-current turbulent flow through a horizontal concentric annulus. The ratio of the inner pipe diameter to the outer pipe diameter (aspect ratio) κ = 0.730−0.816; total liquid velocity (mixture velocity) VT = 0.42−1.1 m/s; inlet oil temperature Toi = 38−94°C; oil volume fraction in the flowing mixture φo = 0.25−0.75 were varied and their effects on the overall volumetric heat transfer coefficient Uv were determined at constant interfacial tension of 48 dynes/cm.
It was found that, in each concentric pipe set, the overall volumetric heat transfer coefficient increased with increasing dispersed phase volume fraction at each constant mixture velocity and reached a maximum at around φo = φw ≈ 0.5. The maximum Uv values increased with increasing total liquid velocity and decreasing aspect ratio of the annulus. The volumetric heat transfer coefficient was also found to increase with increasing inlet oil temperature and increasing total liquid velocity but to decrease with length along the test section keeping all other parameters constant. Empirical expressions for the volumetric heat transfer coefficient were obtained within the ranges of the experimental parameters. 相似文献
Let be a homeomorphism of the open annulus isotopic to the identity and let be a lift of to the universal cover without fixed point. Then we show that admits a Brouwer line which is a lift of a properly imbedded line joining one end to the other in the annulus or admits a free essential simple closed curve.
We give the solutions to the Liouville equation in an annulus A of R2 that satisfy a certain Neumann condition on each component of ∂A. As a consequence, we classify all the metrics of constant curvature in A that have constant geodesic curvature on ∂A. 相似文献