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This is a fundamental study of the phenomenon of natural convection in the region formed by a vertical warm wall rising above a cold horizontal wall, or in the region between a cold vertical wall extending downward from a warm horizontal surface. The study consists of scale analysis, numerical simulations, and an asymptotic solution of the low Rayleigh number limit. The scale analysis predicts the persistence of a single cell in the corner region, regardless of Rayleigh number. The cell migrates toward the corner as the Rayleigh number RaH increases: the flow rate and the net heat transfer rate vary as Ra1/7H. The scale analysis is verified qualitatively and quantitatively by means of numerical experiments in the range RaH =103–107, Pr=0.7–7, H/L=1–4, where Pr is the Prandtl number and H/L is the height/length ratio of the corner region. Additional numerical simulations are presented for cases where one or both walls have uniform heat flux; in these cases, the heat transfer rate shows nearly the same behavior as when the corner walls are both isothermal. The asymptotic solution for the RaH→0 limit shows that the flow field is relatively insensitive to whether the wall temperature varies continuously or discontinuously through the corner point.
As in any medical intervention, there is either a known or an anticipated benefit to the patient from undergoing a medical imaging procedure. This benefit is generally significant, as demonstrated by the manner in which medical imaging has transformed clinical medicine. At the same time, when it comes to imaging that deploys ionising radiation, there is a potential associated risk from radiation. Radiation risk has been recognised as a key liability in the practice of medical imaging, creating a motivation for radiation dose optimisation. The level of radiation dose and risk in imaging varies but is generally low. Thus, from the epidemiological perspective, this makes the estimation of the precise level of associated risk highly uncertain. However, in spite of the low magnitude and high uncertainty of this risk, its possibility cannot easily be refuted. Therefore, given the moral obligation of healthcare providers, 'first, do no harm,' there is an ethical obligation to mitigate this risk. Precisely how to achieve this goal scientifically and practically within a coherent system has been an open question. To address this need, in 2016, the International Atomic Energy Agency (IAEA) organised a summit to clarify the role of Diagnostic Reference Levels to optimise imaging dose, summarised into an initial report (Järvinen et al 2017 Journal of Medical Imaging 4 031214). Through a consensus building exercise, the summit further concluded that the imaging optimisation goal goes beyond dose alone, and should include image quality as a means to include both the benefit and the safety of the exam. The present, second report details the deliberation of the summit on imaging optimisation.