Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

The interaction of zinc oxide-based dental cements with aqueous solutions of potassium fluoride

The ability of zinc oxide-based dental cements (zinc phosphate and zinc polycarboxylate) to take up fluoride from aqueous solution has been studied. Only zinc phosphate cement was found to take up any measurable fluoride after 5 h exposure to the solutions. The zinc oxide filler of the zinc phosphate also failed to take up fluoride from solution. The key interaction for this uptake was thus shown to involve the phosphate groups of the set cement. However, whether this took the form of phosphate/fluoride exchange, or the formation of oxyfluoro-phosphate groups was not clear. Fluoride uptake followed radicaltime kinetics for about 2 h in some cases, but was generally better modelled by the Elovich equation, dq(t)/dt = alpha exp(-beta q(t)). Values for alpha varied from 3.80 to 2.48 x 10(4), and for beta from 7.19 x 10(-3) to 0.1946, though only beta showed any sort of trend, becoming smaller with increasing fluoride concentration. Fluoride was released from the zinc phosphate cements in processes that were diffusion based up to M(t)/M(infinity) of about 0.4. No further release occurred when specimens were placed in fresh volumes of deionised water. Only a fraction of the fluoride taken up was re-released, demonstrating that most of the fluoride taken up becomes irreversibly bound within the cement.

Convection-diffusion in MHD: Comparison of primitive variable and vector potential solutions of the magnetic induction equation

Abstract not available