Annulus, conduction

Liu, Z. Sun, X., and Ma, C., 2005, Experimental study of the characteristics of solidification of satiric acid in an annulus and its thermal conductivity enhancement, Energy Comers. Mgmt. 46 971—984. 

The space between inner and outer cylinders forms the annulus. The column bottom plate is made of stainless steel and typically contains 90 exit holes below the annulus. The holes are covered by a filter plate to keep the stationary phase in place. Three different column sizes are available for the laboratory P-CAC unit the physical characteristics of the different annular columns are summarized in Table 1. The collection of the different fractions at the lower end of the annular column is regulated by a fixed glide ring system. Each chamber in the fixed glidering corresponds to an exit holes in the bottom plate of the column. The number of exit holes equals the number of chambers. The fixed glide ring system allows the continuous and controlled recovery of the separated fractions at the end of the column. Thus cross contamination is avoided and precise fraction collection is ensured. The whole process of collecting the fractions is conducted in a closed system. Unused eluent can be easily recycled. 

It is now essential to write the mass and energy balance equations for the two dimensions z and r. For the sake of completeness, we will include the effect of longitudinal dispersion and heat conduction and deduce the material and energy balances for one component in an elementary annulus of radius Sr and length Sz. We assume that equimolar counterdiffusion occurs and by reference to Fig. 3.25 write down, in turn, the components of mass which are entering the element in unit time longitudinally and radially ... 

Based on the assumption that much of the flow restriction was due to plugging of the upgradient barrier screen, the sand in the barrier frame annulus was removed and an attempt made to flush the screen with high-pressure water jets. Additional tracer tests conducted after the jetting showed that a hydraulic restriction was still present. Since the cause of the hydraulic restriction could not be unambiguously determined or ameliorated, the decision was made to replace the 14-40 SMZ with the higher hydraulic conductivity 8-14 SMZ, and at the same time to remove the 100-mesh screen from the barrier frame. 

Gu, W.Y., Justiz, M.A. and Yao, H. (2002) Electrical conductivity of lumbar annulus fibrosis Effects of porosity and fixed charge density. Spine 27, 2390-2395... 

Taking the heat transfer coefficient, h, as a function of the fluid velocity, density, viscosity, specific heat and thermal conductivity, u, p, p, Cp and k, respectively, and of the inside and outside diameters of the annulus, di and do respectively, then ... 

Nevertheless, it was clearly demonstrated that bras-sinosteroids, like the other steroids investigated here, interact with the plasmalemma thereby showing short-term effects on the membrane potential and/or medium acidification. In some cases these effects correlate with stomata 1 movement and solute uptake into leaves or conducting tissue. The results are compatible with an effect of these substances on the membrane-embedded moiety of the plasmalemma H -ATPase yielding a modified proton pump rate. They support, therefore, the "Annulus Hypothesis" according to which sterol effects are caused by direct lipid-protein binding. 

General Expression for Arbitrary Flux. The spreading resistance of a circular annulus of inner and outer radii a and b, respectively, on one end of a semi-infinite circular flux tube of radius c and thermal conductivity k is considered here. 

For example, to determine Nu, for the case where the body is a very long horizontal isothermal circular cylinder of diameter D, the relevant heat transfer would then be that by heat conduction across a cylindrical annulus of inner diameter D, inner temperature T , outer diameter D + 2A, and outer temperature 7U (assumed constant). Calculating this heat transfer by standard methods, substituting Eq. 4.16, and converting to a Nusselt number yields... 

For problems where convection and/or conduction within a medium are coupled with radiative transfer, a number of methods and solutions are available in the literature. Most such solutions are for simple geometries (e.g., free convection in the annulus between two concentric horizontal cylinders at different temperatures). 

The measured power decreases steadily with tintie for the first 400 days after the beginning of the automatic operation. This is consistent with the progressive drying of the inner annulus of the barrier and the associated decrease of thermal conductivity of the bentonite. The slight increase in power in the second part of the period represented is attributed to the progressive hydration of the barrier due to the incoming water. Some predictions reproduce accurately the observed behavior. 

The considered radial process in the bentonite annulus is a complicated one with coupled, highly nonlinear flows that involve many things. There are liquid flow and vapor flow as well as conductive and convective heat flow depending on gradients in pressure, water vapor density and temperature. The flow coefficients depend on water properties such as saturation water vapor pressure and dynamic viscosity of water. They also depend on the properties of bentonite water retention curve, hydraulic conductivity and water vapor diffusion coefficient, and thermal conductivity, all of which are functions of degree of water saturation. 

Abramowitz M. Stegun 1., 1972. Handbook of Mathematical Functions. Dover Publ. N.Y. Carslaw H.S. Jaeger J.C. 1965. Conduction of Heat in Solids. Oxford Sc. Publ., Oxford. Claesson J. 2003. Drying and Resaturation of a Bentonite Annulus. An Analytical Solution. Report, Building Physics, Chalmers, Sweden. Rutqvist J., Noorishad J. Tsang C-F. 1999. Coupled Termohydromechanical Analysis of a Heater Test in Unsaturated Clay and Fractured Rock at the Kamaishi Mine. SKI report 99 50, the Swedish Nuclear Power Inspectorate. 

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