The Mpemba effect is the name given to the assertion that it is quicker to cool water to a given temperature when the initial temperature is higher. This assertion seems counter-intuitive and yet references to the effect go back at least to the writings of Aristotle. Indeed, at first thought one might consider the effect to breach fundamental thermodynamic laws, but we show that this is not the case. We go on to examine the available evidence for the Mpemba effect and carry out our own experiments by cooling water in carefully controlled conditions. We conclude, somewhat sadly, that there is no evidence to support meaningful observations of the Mpemba effect.
3 January 2015 in Annual Review of Fluid Mechanics
Turbulent fountains arise when a localized flow, free to entrain fluid from its surroundings, is opposed by a buoyancy force. This review cites numerous examples to highlight their wide occurrence in nature and in industry. The breadth of the literature reviewed is significant, drawing from over half a century of progress, and we initially focus on axisymmetric, small–density difference fountains in uniform environments. Many aspects of their rich dynamical behavior, including that of their rise heights and fluctuations in height, are described and encapsulated within the fountain classification presented. Drawing from detailed experimental data sets, dimensional considerations, recent numerical studies, and numerous successful extensions to the original theoretical model for a fountain, we implicitly highlight the current predictive capability offered. The turbulent entrainment of ambient fluid, the effects of environmental stratification, and the role of confinement on a fountain are all discussed. Finally, we suggest future avenues of research.
The year 2020 has seen the world gripped by the effects of the COVID‐19 pandemic. It is not the first time, nor will it be last, that our increasingly globalized world has been significantly affected by the emergence of a new disease. In much of the Northern Hemisphere, the academic year begins in September, and for many countries, September 2020 marked the return to full schooling after some period of enforced closure due to COVID‐19. In this paper, we focus on the airborne spread of disease and investigate the likelihood of transmission in school environments. It is crucial to understand the risk airborne infection from COVID‐19 might pose to pupils, teachers, and their wider social groups. We use monitored CO2 data from 45 classrooms in 11 different schools from within the UK to estimate the likelihood of infection occurring within classrooms regularly attended by the same staff and pupils. We determine estimates of the number of secondary infections arising via the airborne route over pre/asymptomatic periods on a rolling basis. Results show that, assuming relatively quiet desk‐based work, the number of secondary infections is likely to remain reassuringly below unity; however, it can vary widely between classrooms of the same school even when the same ventilation system is present. Crucially, the data highlight significant variation with the seasons with January being nearly twice as risky as July. We show that such seasonal variations in risk due to changes in ventilation rates are robust and our results hold for wide variations in disease parameterizations, suggesting our results may be applied to a number of different airborne diseases.
We present the results of an experimental investigation across a broad range of source Froude numbers, $0. 4\leq {\mathit{Fr}}_{0} \leq 45$ , into the dynamics, morphology and rise heights of Boussinesq turbulent axisymmetric fountains in quiescent uniform environments. Typically, these fountains are thought to rise to an initial height, ${z}_{i} $ , before settling back and fluctuating about a lesser (quasi-) steady height, ${z}_{ss} $ . Our measurements show that this is not always the case and the ratio of the fountain’s initial rise height to steady rise height, $\lambda = {z}_{i} / {z}_{ss} $ , varies widely, $0. 5\lesssim \lambda \lesssim 2$ , across the range of ${\mathit{Fr}}_{0} $ investigated. As a result of near-ideal start-up conditions provided by the experimental set-up we were consistently able to form a vortex at the fountain’s front. This enabled new insights into two features of the initial rise of turbulent fountains. Firstly, for $1. 0\lesssim {\mathit{Fr}}_{0} \lesssim 1. 7$ the initial rise height islessthan the steady rise height. Secondly, for ${\mathit{Fr}}_{0} \gtrsim 5. 5$ , the vortex formed at the fountain’s front pinches off, separates from the main body and rises high above the fountain; there is thus a third rise height to consider, namely, the maximum vortex rise height, ${z}_{v} $ . From our observations we propose classifying turbulent axisymmetric fountains into five regimes (as opposed to the current three regimes) and present detailed descriptions of the flow in each. Finally, based on an analysis of the rise height fluctuations and the width of fountains in (quasi-) steady state we provide further insight into the physical cause of height fluctuations.
The risk of long range, herein ‘airborne', infection needs to be better understood and is especially urgent during the COVID-19 pandemic. We present a method to determine the relative risk of airborne transmission that can be readily deployed with either modelled or monitored CO2 data and occupancy levels within an indoor space. For spaces regularly, or consistently, occupied by the same group of people, e.g. an open-plan office or a school classroom, we establish protocols to assess the absolute risk of airborne infection of this regular attendance at work or school. We present a methodology to easily calculate the expected number of secondary infections arising from a regular attendee becoming infectious and remaining pre/asymptomatic within these spaces. We demonstrate our model by calculating risks for both a modelled open-plan office and by using monitored data recorded within a small naturally ventilated office. In addition, by inferring ventilation rates from monitored CO2, we show that estimates of airborne infection can be accurately reconstructed, thereby offering scope for more informed retrospective modelling should outbreaks occur in spaces where CO2 is monitored. Well-ventilated spaces appear unlikely to contribute significantly to airborne infection. However, even moderate changes to the conditions within the office, or new variants of the disease, typically result in more troubling predictions.