An experimental study has been done into the effects of vertical mechanical vibrating, vertical eccentricity, and the Rayleigh number on natural convection heat transferring out of a horizontally enclosed, ending cylindrical annulus with a radius rate of 2.6 and an aspect ratio of (2:1). The annulus produced between two concentric and vertically eccentric circular cylinders is positioned horizontally, and its internal wall is uniformly heated while isothermally cooling the external wall. The range of present conditions for Rayleigh number is 5×10^4 ≤ Ra≤ 6.48×10^6, and Pr = 0.703, the frequency of vibration is 0 ≤ f ≤ 20Hz; and the amplitude is b mm), with possible exclusion of the highest positive and negative eccentricities. Plots of the average Nusselt number variation against the Rayleigh number showed a significant increase in negative vertical eccentricity. It was found that the average Nusselt decreased as the internal cylinder changed its location vertically from negative to positive through the center, which is normally a desirable effect, but has no advantage over the concentric on the positive side. The Rayleigh number was found to be relatively sensitive to eccentricity. However, an increase of Rayleigh number leads to a nearly proportional increase in the average Nusselt number and a smaller yet still substantial increase in positive eccentricity. This study concluded that the vibration under the current experimental setup significantly affects the concentric position of the internal cylinder, whether the effect is positive or negative. The vibrational average Nusselt number increased in varying proportions, depending on the location of the heated inner cylinder.
The present paper deals with the problem of an incompressible axisymmetric creeping flow caused by a porous spherical particle in a spherical cavity filled with micropolar fluid. Depending on the kind of cell model, appropriate boundary conditions are used on the surface of sphere and spherical cavity. Drag force on the porous particle in the presence of a cavity is calculated to determine the correction factor to the Stokes law. A general expression for the hydrodynamic force acting on the porous sphere and, hence, for the wall correction factor of the sphere are obtained. The special cases of the porous sphere in viscous fluid, zero permeability solid sphere in micropolar fluid and viscous fluid are obtained in open and closed cavity respectively.
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