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.

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 and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful 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 surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

Open ended microwave oven for packaging

A novel open waveguide cavity resonator is presented for the combined variable frequency microwave curing of bumps, underfills and encapsulants, as well as the alignment of devices for fast flip-chip assembly, direct chip attach (DCA) or wafer-scale level packaging (WSLP). This technology achieves radio frequency (RF) curing of adhesives used in microelectronics, optoelectronics and medical devices with potential simultaneous micron-scale alignment accuracy and bonding of devices. In principle, the open oven cavity can be fitted directly onto a flip-chip or wafer scale bonder and, as such, will allow for the bonding of devices through localised heating thus reducing the risk to thermally sensitive devices. Variable frequency microwave (VFM) heating and curing of an idealised polymer load is numerically simulated using a multi-physics approach. Electro-magnetic fields within a novel open ended microwave oven developed for use in micro-electronics manufacturing applications are solved using a dedicated Yee scheme finite-difference time-domain (FDTD) solver. Temperature distribution, degree of cure and thermal stresses are analysed using an Unstructured Finite Volume method (UFVM) multi-physics package. The polymer load was meshed for thermophysical analysis, whilst the microwave cavity - encompassing the polymer load - was meshed for microwave irradiation. The two solution domains are linked using a cross mapping routine. The principle of heating using the evanescent fringing fields within the open-end of the cavity is demonstrated. A closed loop feedback routine is established allowing the temperature within a lossy sample to be controlled. A distribution of the temperature within the lossy sample is obtained by using a thermal imaging camera.