The contact angle of nanofluids as thermophysical property

Droplet volume and temperature affect contact angle significantly. Phase change heat transfer processes of nanofluids – suspensions containing nanometre-sized particles – can only be modelled properly by understanding these effects. The approach proposed here considers the limiting contact angle of a droplet asymptotically approaching zero-volume as a thermophysical property to characterise nanofluids positioned on a certain substrate under a certain atmosphere. Graphene oxide, alumina, and gold nanoparticles are suspended in deionised water. Within the framework of a round robin test carried out by nine independent European institutes the contact angle of these suspensions on a stainless steel solid substrate is measured with high accuracy. No dependence of nanofluids contact angle of sessile droplets on the measurement device is found. However, the measurements reveal clear differences of the contact angle of nanofluids compared to the pure base fluid. Physically founded correlations of the contact angle in dependency of droplet temperature and volume are obtained from the data. Extrapolating these functions to zero droplet volume delivers the searched limiting contact angle depending only on the temperature. It is for the first time, that this specific parameter, is understood as a characteristic material property of nanofluid droplets placed on a certain substrate under a certain atmosphere. Together with the surface tension it provides the foundation of proper modelling phase change heat transfer processes of nanofluids

"Real world" problems

We consider it important that pre-service teachers master both mathematical problem solving and the choice and analysis of problems, together with the way of posing them in the classroom, so that pupils’ thinking processes may be better stimulated. The teacher must make several decisions about the organisation of their own teaching: these relate to the choice and systematisation of ‘good’ problems, the management of pupils’ personal solutions in the sharing phases (discussion), the possible ways for making these personal solutions evolve towards expert solutions, which are the main goal. In this context, a priori analysis becomes one of the professional tools helping teachers to formulate their choices and decisions (Charnay, 2003). The “Real world” problems proposal sits within a set of activities that stimulate work with problems starting from a suitable a priori analysis, in order to identify the mathematical concepts at stake and to determine whether, how and with what aims they can be used in teaching

3D numerical simulation of a novel ventilated roof: thermal performance analysis and fluid flow behavior

This paper presents a numerical simulation of a ventilated roof based on a novel plastic support especially designed to reduce the solar heat gains by improving the airflow distribution as compared to a traditional one. In order to evaluate the benefits of the new configuration, a 3 D numerical model was developed allowing for a deep understanding of the airflow distribution inside the ventilated roof channels. The simulations were performed by varying the solar irradiance from 600 to 1000 W m−2 assuming buoyancy-driven airflow. The investigation was conducted by comparing the new proposed ventilated roof assembly to the traditional layouts. In particular, two roof types were considered as benchmarks: an insulated roof and a non-insulated one. When compared to the traditional ones, the results revealed that the innovative ventilated roof led to a great reduction (up to 70%) of the total amount of solar heat gains for all the simulated scenarios

Costruzione del concetto di equazione: dalla messa in formula alla risoluzione di equazioni e sistemi lineari

Nel presente articolo si continua il lavoro sulla costruzione dei concetti di equazione e di sistema lineare iniziato nel 2005 durante l'Incontro internazionale di studio sul RMT ad Arco di Trento. Si sono selezionati ulteriori problemi e il confronto tra le analisi a priori e a posteriori dopo la gara, ha permesso di effettuare alcune modifiche dei testi in vista delle nuove sperimentazioni. Si riportano qui i resoconti di alcune di tali sperimentazioni che hanno coinvolto classi di scuola secondaria di primo e secondo grado. La sperimentazione nella secondaria di primo grado si prefigge di far emergere eventuali strategie spontanee di tipo pre-algebrico. Nella secondaria di secondo grado, l’attività ha avuto lo scopo di introdurre il concetto di sistema lineare e le relative procedure risolutive

Costruzione del concetto di equazione:un possibile percorso con i problemi del RMT

Nel presente articolo si riportano le esperienze di alcune insegnanti di scuola secondaria di primo grado svoltesi nell’anno scolastico 2006/2007, sulla base delle scelte di problemi del RMT ritenuti significativi ai fini di un'introduzione al concetto di equazione. Si riportano inoltre alcune significative osservazioni emerse a seguito delle attività nelle classi. Le sperimentazioni effettuate e le analisi a priori e a posteriori dei problemi hanno permesso l’elaborazione di un percorso per la costruzione del concetto di equazione, proponibile nella scuola secondaria di primo grado, illustrato nell’ultima parte del presente lavoro. Il percorso si articola in tre fasi, per ognuna delle quali sono stati individuati problemi idonei alla costruzione graduale del concetto di equazione. Per la prima fase sono stati scelti problemi per i quali la soluzione dell’equazione risolvente è ottenibile anche con modalità “non esperte”. Per la seconda i problemi sono stati scelti per far emergere l’esigenza di acquisizione di nuovi strumenti (quali il calcolo letterale e i principi di equivalenza delle equazioni). Infine per la terza fase sono stati scelti problemi idonei al consolidamento del concetto di equazione

Water Pool boiling on Aluminum Metal Foams

With current growth in electronic systems, their physical sizes decrease, and the spacing between components decreases, both the total amount of heat generated and the power density increase significantly. There is a general agreement in the scientific community that current air-cooling technologies are asymptotically approaching their intrinsic limits. Pool boiling is widely used in many different engineering systems, but most of these applications have a common limitation: the maximum heat flux that can be rejected by the cooling systems under safe, reliable, and efficient operation. In this paper experimental data pertinent to deionized water pool boiling across 10 mm thick aluminum foams are presented. Three foam samples with different pore densities, 5, 10, and 40 PPI, yet with an identical mean porosity of 0.92 are tested. Compared to a heated flat plate, the foams offer higher heat transfer area albeit at induced bubble escaping resistance. The tradeoff between these two effects is investigated. Through the use of high speed video camera recording, bubble generation, trajectory and growth rate were analyzed and critically discussed