Scaling analysis of unsteady natural convection boundary layer for instantaneous heating

Natural convection thermal boundary layer adjacent to an instantaneous heated inclined flat plate is investigated through a scaling analysis and verified by direct numerical simulations. It is revealed from the analysis that the development of the boundary layer may be characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady state stage. These three stages can be clearly identified from the numerical simulations. Major scales including the flow velocity, flow development time, and the thermal and viscous boundary layer thicknesses are established to quantify the flow development at different stages and over a wide range of flow parameters. Details of the scaling analysis are described in this paper.

Scaling of thermo-magnetic convection

The scaling to characterize unsteady boundary layer development for thermo-magnetic convection of paramagnetic fluids with the Prandtl number greater than one is developed. Under the consideration is a square cavity with initially quiescent isothermal fluid placed in microgravity condition (g = 0) and subject to a uniform, vertical gradient magnetic field. A distinct magnetic thermal-boundary layer is produced by sudden imposing of a higher temperature on the vertical sidewall and as an effect of magnetic body force generated on paramagnetic fluid. The transient flow behavior of the resulting boundary layer is shown to be described by three stages: the start-up stage, the transitional stage and the steady state. The scaling is verified by numerical simulations with the magnetic momentum parameter m variation and the parameter γRa variation.

Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Obligatory dangerousness criteria in the involuntary commitment and treatment provisions of Australian mental health legislation

Abstract Objective Involuntary commitment and treatment (IC&T) of people affected by mental illness may have reference to considerations of dangerousness and/or need for care. While attempts have been made to classify mental health legislation according to whether IC&T has obligatory dangerousness criteria, there is no standardised procedure for making classification decisions. The aim of this study was to develop and trial a classification procedure and apply it to Australia's mental health legislation. Method We developed benchmarks for ‘need for care’ and ‘dangerousness’ and applied these benchmarks to classify the mental health legislation of Australia's 8 states and territories. Our focus was on civil commitment legislation rather than criminal commitment legislation. Results One state changed its legislation during the course of the study resulting in two classificatory exercises. In our initial classification, we were able to classify IC&T provisions in legislation from 6 of the 8 jurisdictions as being based on either ‘need for care’ or ‘dangerousness’. Two jurisdictions used a terminology that was outside the established benchmarks. In our second classification, we were also able to successfully classify IC&T provisions in 6 of the 8 jurisdictions. Of the 6 Acts that could be classified, all based IC&T on ‘need for care’ and none contained mandatory ‘dangerousness’ criteria. Conclusions The classification system developed for this study provided a transparent and probably reliable means of classifying 75% of Australia's mental health legislation. The inherent ambiguity of the terminology used in two jurisdictions means that further development of classification may not be possible until the meaning of the terms used has been addressed in case law. With respect to the 6 jurisdictions for which classification was possible, the findings suggest that Australia's mental health legislation relies on ‘need for care’ and not on ‘dangerousness’ as the guiding principle for IC&T. Keywords: Involuntary commitment; Mental health legislation; Dangerousness; Australia

Scaling digital radiographs for templating in total hip arthroplasty using conventional acetate templates independent of calibration markers

We describe a scaling method for templating digital radiographs using conventional acetate templates independent of template magnification without the need for a calibration marker. The mean magnification factor for the radiology department was determined (119.8%, range117%-123.4%). This fixed magnification factor was used to scale the radiographs by the method described. 32 femoral heads on postoperative THR radiographs were then measured and compared to the actual size. The mean absolute accuracy was within 0.5% of actual head size (range 0 to 3%) with a mean absolute difference of 0.16mm (range 0-1mm, SD 0.26mm). Intraclass Correlation Coefficient (ICC) showed excellent reliability for both inter and intraobserver measurements with ICC scores of 0.993 (95% CI 0.988-0.996) for interobserver measurements and intraobserver measurements ranging between 0.990-0.993 (95% CI 0.980-0.997).

Prandtl number scaling of natural convection of an inclined flat plate due to uniform surface heat flux

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a new Prandtl number scaling has been developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the friction pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71, and 9.81 m/s2 corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly-slug and slug-annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of dropset entrainment, higher superficial gas velocity was obtained at higher gravity level.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Scaling analysis of natural convection boundary layers : Application to attic space

The natural convection thermal boundary layer adjacent to an inclined flat plate and inclined walls of an attic space subject to instantaneous and ramp heating and cooling is investigated. A scaling analysis has been performed to describe the flow behaviour and heat transfer. Major scales quantifying the flow velocity, flow development time, heat transfer and the thermal and viscous boundary layer thicknesses at different stages of the flow development are established. Scaling relations of heating-up and cooling-down times and heat transfer rates have also been reported for the case of attic space. The scaling relations have been verified by numerical simulations over a wide range of parameters. Further, a periodic temperature boundary condition is also considered to show the flow features in the attic space over diurnal cycles.