Flux-Freezing

Any attempt to maintain an internal electric field in a perfectly conducting medium will be thwarted by the mobility of the charges, which immediately move to cancel any potential difference. The timescale for this cancellation is very short in comparison with the timescales for the field to begin building in the medium that is, they take place on times short in comparison with the actual fluid motions. 

To see this, assume that a is the value usually quoted for the conductivity of stellar plasma, 10 s This conductivity is large enough to ensure that the magnetic diffusion term effectively vanishes. Then, 

we have used the convective, or co-moving, derivative d/dt = 9/9t -I- v V. The magnetic flux is therefore simply a scalar multiple/of the mass density, or 5 fp. Thus, if the density is locally increased, so is the magnetic field strength. The magnetic field seems to move with the fluid, hence the appellation frozen.  

The characteristic timescale for the decay of the field depends on the scale length for the field generation and the dissipation scale for the currents. To see this, look at the dimensionless form of the dynamo equation, but now ignore the effects of the fluid motions. The equation is linear in the field strength, which means that we can scale 

notice that in the case of an infinitely conducting medium the time for the decay is infinitely long. We have used only one possible representation for the magnetic diffusion coefficient, however, and we shall shortly see that this is one of the longer estimates. 

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Flux freezing High conductivity condition which transports magnetic energy as if the material were frozen to field lines. 

White dwarfs are the remnant of the evolution of low and intermediate (<5 Mq) mass stars, formed by core contraction during the last stages of nuclear burning. Since they reach densities in excess of 10 g cm and typically have radii of order 0.01 R they were expected, by simple theory, to be able to possess very strong surface fields. Any weak field remnant in the core at the time of contraction, should the field be able to survive this stage of evolution, would be amplified by flux-freezing to very large values, of... 

Individual HI clouds having temperatures of order 100 K display internal fields of order 10 /xG, larger than that inferred for the low-density gas and consistent with flux-freezing in the clouds. OH transitions, which are col-lisionally excited and arise from masers that are pumped in the presence of strong infrared sources, provide similar field measurements. 

In either case the Pb contains numerous undesirable metal impurities, notably Cu, Ag, Au, Zn, Sn, As and Sb, some of which are clearly valuable in themselves. Copper is first removed by liquation the Pb bullion is melted and held just above its freezing point when Cu rises to the surface as an insoluble solid which is skimmed off. Tin, As and Sb are next removed by preferential oxidation in a reverberatory furnace and skimming off the oxides alternatively, the molten bullion is churned with an oxidizing flux of molten NaOH/NaN03 (Harris process). The softened Pb may still contain Ag, Au and perhaps Bi. Removal of the first two depends on their preferential solubility in Zn the mixed metals are cooled slowly from 480° to below 420° when the Zn (now containing nearly all the Ag and Au) solidifies as a crust which is skimmed off the... 

Calculate the distance spanned by the habitable zone around the Sun at its current luminosity of 3.8 x 1026 W. Using Equation 7.5 for the flux at a distance corresponding to 273 K, the freezing point of water is given by ... 

Bear, 1972 1979 Freeze and Cherry, 1979), which is the negative divergence of the fluxes. This equation is a statement of the divergence principle, applied to solute... 

At later times, solar heat fluxes and convective heat transfer from the atmosphere become important. For a spill onto an insulated dike floor these fluxes may be the only energy contributions. This approach seems to work adequately for liquefied natural gas (LNG) and perhaps for ethane and ethylene. The higher hydrocarbons (C3 and above) require a more detailed heat transfer mechanism. This model also neglects possible water freezing effects in the ground, which can significantly alter the heat transfer behavior. More details on boiling pools is provided elsewhere.19... 

H. Gieseler, W.J. Kessler, M. Finson, et al.. Evaluation of tunable diode laser absorption spectroscopy for in-process water vapor mass flux measurements during freeze drying, J. Pharm. Sci., 96(7), 1776-1793 (2007). 

Stefan gave an exact solution for the constant-velocity melting of a semi-infinite slab initially at the fusion temperature. This was extended by Pekeris and Slichter (P2) to freezing on a cylinder of arbitrary surface temperature and Kreith and Romie (K6) to constant-velocity melting of cylinders and spheres by a perturbation method, in which the temperature is assumed to be expressible in terms of a convergent series of unknown functions. To make the method clear, consider the freezing of an infinite cylinder of liquid, of radius r0, at constant surface heat flux. For this geometry the heat equation is... 

As a first approximation, the stresses for the solid, ice and gel water can be formulated with the help of a linearized Hookean type law, where the depression of the gel water below the macroscopic freezing point of water must be considered. This can be done by including the micro-ice-lens model of Set-zer [1] in the constitutive relations for the aforementioned stress tensor. The gas phase can be described as an ideal gas. Concerning the constitutive assumptions for the liquid stresses, the heat flux and the interactions, the reader is referred to de Boer et al. [4], There a ternary model for the numerical simulation of freezing and thawing processes is discussed. 

Cold "Burns" (8). Direct contact of body tissue with liquid hydrogen for a short time may result in no damage because the boiling liquid will be separated from the skin by a layer of vapor and because hydrogen has a relatively low heat of vaporization. Cold gas jetting onto the skin can result in a high heat flux sufficient to cause freezing. The body can tolerate heat fluxes of 30 Btu/hr-ft without discomfort a flux of 740 Btu/hr-ft will freeze facial tissue in about 10 seconds. A... 

Membrane modules should always be stored in a cool, dark place out of direct sunlight and kept from freezing. Wet-tested membranes should be stored at no lower than about 5°C to prevent freezing of the sodium metabisulfite preservative solution (FilmTec membranes can go to -4°C).6 Dry membranes will not be affected by freezing temperatures. (Note that once wetted, membranes should not be allowed to dry out, as irreversible loss of flux may occur.)... 

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