Mass transport in a partially covered fluid-filled cavity

A method of computing the concentration field of dissolved material inside an etch-hole is presented. Using a number of assumptions, approximate convection-diffusion equations are formulated, and analytical descriptions for the concentration in different parts of the domain are obtained. By coupling these descriptions the concentration field can be computed. The assumptions and the results are validated by comparison with solutions based on a finite-volume method. Results of the boundary-layer method are given for two characteristic etch-hole geometries. The described boundary-layer method is efficient in terms of computational time and memory, because it does not require the construction of a computational grid in the interior of the domain. This advantage will be exploited in a future paper where the method will be used to simulate wet-chemical etching

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Laminar natural convection over a slender vertical frustrum of a cone with constant wall heat flux

The problem of laminar natural convection flow over a slender frustrum of a cone with constant wall heat flux is treated in this paper. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for Prandtl numbers from 0.1 to 100 for a range of values of transverse curvature parameter. It is found that the effect of transverse curvature is of great significance in such flows. In dieser Arbeit wird das Problem der laminaren, natürlichen Konvektionsströmung öber einem dünnen Kegelstumpf mit konstantem Wandwärmestrom behandelt. Die maßgeblichen Differentialgleichungen werden mit Hilfe einer Kombination von Quasilinearisierung und Differenzenverfahren gelöst. Numerische Lösungen werden für die Prandtl ' sehen Zahlen zwischen 0. l und 100 innerhalb eines Bereiches von Querkrüm mungswerten erhalten. Es wird gezeigt, daß der Einfluß der Querkrümmung in solchen Strömungen von großer Bedeutung ist.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46650/1/231_2005_Article_BF00997635.pd

Practical asymptotics (Introduction to Special Issue)

The term practical asymptotics is explained. It is argued that many practical problems are amenable to and will benefit from the asymptotic approach. Fifteen papers by authors who are active in a wide range of disciplines demonstrate this. It is argued that the teaching of asymptotic methods should remain an integral part of any sophisticated numerics curriculum, raising it far above the level of mere number crunching

Fin methods of higher order

The classical method which describes heat conduction in elongated bodies, e.g., fins, is extended to methods of higher order. Numerical examples are put forward to show that these higher order methods are capable of yielding accurate results with relatively little effort. A comparison with a classical method of the finite-difference variety shows that these methods may sometimes be superior. It is expected that they may be applied with the same accuracy to fields other than heat transfer. Fluid mechanics and elasticity are likely candidates. It is shown that higher order fin methods can easily be applied to nonlinear problems. On the other hand, a successful application of the methods requires smooth boundary conditions. Any feature in the problem definition that would lead to local singularities, such as sharp corners or abrupt changes in the boundary conditions, renders these methods less effective. Therefore, paradoxically, these higher order "fin methods" do not lend themselves very well for the derivation of more accurate solutions in the case of actual cooling fins. Nevertheless, since the methods are based on the original treatment of heat transfer in fins, and for want of a better terminology, it would seem appropriate to call then fin methods

A class of backward free-convective boundary-layer similarity solutions

This paper presents a class of backward free-convective boundary-layer similarity solutions. It is shown that these boundary layers can be produced along slender downward-projecting slabs of prescribed thickness variation, which are infinitely long. It is pointed out that these solutions can be used to describe free convective flows along vertical fins which have received attention in the literature before. An important result is that the temperature along a downward-projecting fin of constant thickness varies in proportion to the inverse of the seventh power of the shifted longitudinal coordinate

The effect of normal blowing on the flow near a rotating disk of infinite extent

The effect of blowing through a porous rotating disk on the flow induced by this disk is studied. For strong blowing the flow is almost wholly inviscid. First-order viscous effects are encountered only in a thin layer at some distance from the disk. The results of an asymptotic analysis are compared with numerical integrations of the full equations and complete agreement is found

Higher approximations to the solution of a problem concerning a high-pressure gas-discharge arc

AbstractThe method of matched asymptotic expansions is applied to a problem which is of importance in the modelling of high-pressure gas-discharge arcs. In the solution domain, three different regions are distinguished, in each of which an asymptotic solution can be given. These match smoothly in two regions of common validity. The results are used in a companion paper [1]