L. Dresner

Some remarks on the integration of the extended Nernst-Planck equations in the hyperfiltration of multicomponent solutions

Abstract A new method is suggested for the integration of the extended Nernst-Planck equations in the hyperfiltration of multicomponent solutions through ion-exchange membranes. The method is based on the assumption of good coion exclusion. It yields the asymptotic solute rejections with comparatively little computational labor. The new method is compared with several older methods. Some circumstances, hitherto unnoticed, are described under which negative rejection of a solute may occur.

Stability of cable‐in‐conduit superconductors

The stability margin of a single triplex of NbTi/Cu strands soldered around a heater wire, sheathed in a stainless‐steel tube, and cooled by pressurized helium is found to be multivalued for certain combinations of transport current, ambient helium pressure, and externally imposed helium flow. A qualitative model based on the idea that good recovery in stagnant or slowly flowing helium is due to heating‐induced flow accounts well for the complex multivalued behavior of the stability margin.

Propagation of normal zones in composite superconductors

Propagation velocities of normal zones in a multifilamentary composite conductor were measured for a range of magnetic fields and operating currents. The degree of thermal contact of the conductor with the helium bath was varied, the conductor having been bare, insulated by a thin Formvar layer, or completely potted in wax. The measurements were compared with theory, and good agreement was achieved by suitably choosing the heat transfer coefficient. (auth)

Transient Heat Transfer in Superfluid Helium — Part II

Three classical problems associated with the ordinary diffusion equation concern the temperature in (1) a half-space with clamped heat flux at the free face, (2) a half-space with clamped temperature at the free face, and (3) an infinite medium with a pulsed plane heat source. These problems are also important for the nonlinear diffusion equation based on the Gorter-Mellink relation, which describes heat transport in superfluid helium. A similarity solution to problem (1) , the champed-flux problem, has already been found1 and compared, with goou agreement, with experimental data of van Sciver.2 [A similarity solution is one in which the profiles of temperature rise AT versus distance Z at different times t can be obtained from one another by suitable (different) stretching of the temperature and distance axes.] In this paper, I give similarity solutions in analytic form to problems (2) and (3) , the clamped-temperature and pulsed-source problems.

Stability and protection of Ag/BSCCO magnets operated in the 20–40 K range

Abstract The rate of growth of normal zones has been calculated for Ag/BSCCO composites operated in the 20–40 K range. Formulae are presented for the propagation velocity and for the normal zone voltage as a function of the hot spot temperature. These formulae take into account the strong temperature dependence of the specific heats of silver and BSCCO, as well as the temperature dependences of the thermal conductivity and resistivity of silver. In spite of very slow propagation (of the order of 1 cm s−1), normal zone voltages seem adequate to allow the detection of normal zones before the conductor overheats. Finally, a formula for estimating the minimum quench energy is proposed. Estimates based on this formula indicate that potted magnets wound with Ag/BSCCO conductors should not train.

Parametric study of the stability margin of cable-in-conduit superconductors: Theory

Recently, Lue, Miller, and Dresner reported that the stability margin of cable-in-conduit superconductors is multivalued for certain combinations of transport current, ambient helium pressure, and externally imposed helium flow. There is a limiting transport current below which the stability margin is single-valued and equal to the upper stability margin. The theory of ref. 1 is used here to determine the scaling of the limiting transport current with critical temperature, ambient helium temperature, resistivity of copper, length of the heated zone, duration of the heat pulse, hydraulic diameter of the helium-filled part of the cable, volume fraction of copper in the metal, and volume fraction of metal in the cable. Combined with experimental data, the scaling relation provides a sound basis for design.

Analytic solution for the propagation velocity in superconducting composites

The propagation velocity of normal zones in composite superconductors has been calculated analytically for the case of constant thermophysical properties, including the effects of current sharing. The solution is compared with that of a more elementary theory in which current sharing is neglected, i.e., in which there is a sharp transition from the superconducting to the normal state. The solution is also compared with experiment. This comparison demonstrates the important influence of transient heat transfer on the propagation velocity.

Quench energies of potted magnets

The quench energy of potted magnets has been studied for the following two extreme models of the winding: (1) treating it as an anisotropic three-dimensional continuum and (2) ignoring heat conduction in the epoxy and treating it as a one-dimensional continuum. For each model, we have obtained a formula for the point-source quench energy, complete up to a single undetermined constant, by applying a combination of dimensional and group-theoretic arguments to the heat balance equation. The undetermined constant has been estimated by solving the heat balance equation approximately. Correction factors are given for taking into account the sources being distributed in space and time. The formulas are compared with available experimental data; agreement is fair.

Hyperfiltration studies V. Salt rejection of membranes by a concentration polarization method

Abstract A method was developed for rapid measurement of the salt rejecting characteristics of hyperfiltration membranes based on the theory of concentration polarization in an unstirred system. A piston forces solution through a cylinder (an adapted one cc tuberculin syringe) sealed at one end by a membrane. The transmission rate of the membrane and the concentration of the effluent are measured and the concentration-flux curves compared with those computed theoretically through solution of the time-dependent diffusion equation. Results have been obtained that agree well with theory and also with other experimental observations.

Superconductor stability '90: a review☆☆☆

Abstract Superconductor stability, as a characteristic of steady states, is reviewed. Reference is made to internally cooled superconductors, metastable magnets and superfluid helium.