Sensitivity analysis of thermal performances of flat plate solar air heaters

Sensitivity analysis is a mathematical tool, first developed for optimization methods, which aim is to characterize a system response through the variations of its output parameters following modifications imposed on the input parameters of the system. Such an analysis may quickly become laborious when the thermal model under consideration is complex or the number of input parameters is high. In this paper, we develop a mathematical model to analyse the heat exchanges in four different types of solar air collectors. When building this thermal model we show that for each collector, at quasi-steady state, the energy balance equations of the components of the collector cascade into a single first-order non-linear differential equation that is able to predict the thermal behaviour of the collector. Our heat transfer model clearly demonstrates the existence of an important dimensionless parameter, referred to as the thermal performance factor of the collector, that compares the useful thermal energy which can be extracted from the heater to the overall thermal losses of that collector for a given set of input parameters. A sensitivity analysis of our thermal model has been performed for the most significant input parameters such as the incident solar irradiation, the inlet fluid temperature, the air mass flow rate, the depth of the fluid channel, the number and nature of the transparent covers in order to measure the impact of each of these parameters on our model. An important result which can be drawn from this study is that the heat transfer model developed is robust enough to be used for thermal design studies of most known flat plate solar air heaters, but also of flat plate solar water collectors and linear solar concentrators.     

Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.     

Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys

Abstract In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. * Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”.     

Uniform bounds under increment conditions

We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.

     

Randomized greedy matching

We consider a randomized version of the greedy algorithm for finding a large matching in a graph. We assume that the next edge is always randomly chosen from those remaining. We analyze the performance of this algorithm when the input graph is fixed. We show that there are graphs for which this Randomized Greedy Algorithm (RGA) usually only obtains a matching close in size to that guaranteed by worst-case analysis (i.e., half the size of the maximum). For some classes of sparse graphs (e.g., planar graphs and forests) we show that the RGA performs significantly better than the worst-case. Our main theorem concerns forests. We prove that the ratio to maximum here is at least 0.7690…, and that this bound is tight.