Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.

Evaluating the effectiveness of Z: The claims made about CICS and where we go from here

There have been few genuine success stories about industrial use of formal methods. Perhaps the best known and most celebrated is the use of Z by IBM (in collaboration with Oxford University's Programming Research Group) during the development of CICS/ESA (version 3.1). This work was rewarded with the prestigious Queen's Award for Technological Achievement in 1992 and is especially notable for two reasons: 1) because it is a commercial, rather than safety- or security-critical, system and 2) because the claims made about the effectiveness of Z are quantitative as well as qualitative. The most widely publicized claims are: less than half the normal number of customer-reported errors and a 9% savings in the total development costs of the release. This paper provides an independent assessment of the effectiveness of using Z on CICS based on the set of public domain documents. Using this evidence, we believe that the case study was important and valuable, but that the quantitative claims have not been substantiated. The intellectual arguments and rationale for formal methods are attractive, but their widespread commercial use is ultimately dependent upon more convincing quantitative demonstrations of effectiveness. Despite the pioneering efforts of IBM and PRG, there is still a need for rigorous, measurement-based case studies to assess when and how the methods are most effective. We describe how future similar case studies could be improved so that the results are more rigorous and conclusive.

Low Reynolds number turbulence models for accurate thermal simulations of electronic components

The electronics industry and the problems associated with the cooling of microelectronic equipment are developing rapidly. Thermal engineers now find it necessary to consider the complex area of equipment cooling at some level. This continually growing industry also faces heightened pressure from consumers to provide electronic product miniaturization, which in itself increases the demand for accurate thermal management predictions to assure product reliability. Computational fluid dynamics (CFD) is considered a powerful and almost essential tool for the design, development and optimization of engineering applications. CFD is now widely used within the electronics packaging design community to thermally characterize the performance of both the electronic component and system environment. This paper discusses CFD results for a large variety of investigated turbulence models. Comparison against experimental data illustrates the predictive accuracy of currently used models and highlights the growing demand for greater mathematical modelling accuracy with regards to thermal characterization. Also a newly formulated low Reynolds number (i.e. transitional) turbulence model is proposed with emphasis on hybrid techniques.

On Reynolds number and scaling effects in microchannel flows

This paper presents a numerical study of the Reynolds number and scaling effects in microchannel flows. The configuration includes a rectangular, high-aspect ratio microchannel with heat sinks, similar to an experimental setup. Water at ambient temperature is used as a coolant fluid and the source of heating is introduced via electronic cartridges in the solids. Two channel heights, measuring 0.3 mm and 1 mm are considered at first. The Reynolds number varies in a range of 500-2200, based on the hydraulic diameter. Simulations are focused on the Reynolds number and channel height effects on the Nusselt number. It is found that the Reynolds number has noticeable influences on the local Nusselt number distributions, which are in agreement with other studies. The numerical predictions of the dimensionless temperature of the fluid agree fairly well with experimental measurements; however the dimensionless temperature of the solid does exhibit a significant discrepancy near the channel exit, similar to those reported by other researchers. The present study demonstrates that there is a significant scaling effect at small channel height, typically 0.3 mm, in agreement with experimental observations. This scaling effect has been confirmed by three additional simulations being carried out at channel heights of 0.24 mm, 0.14 mm and 0.1 mm, respectively. A correlation between the channel height and the normalized Nusselt number is thus proposed, which agrees well with results presented.