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As many industrial processes operate under pressure, information concerning the thermodynamics of equilibria between phases under pressure is essential in energetic engineering. Many models have been offered for the true representation of thermodynamic properties. New thermodynamic models, which have an even greater level of precision and which are based on molecular concept are in progress. These models, more predictive, will help reduce the number of experimental data to determine. They will allow for the dimensioning of thermodynamic systems and the improvement of the understanding of the physical phenomena involved.
The first and second principles of thermodynamics are essential "laws" for solving energy-related problems. The first principle stipulates the equality of the various forms of energy (thermal, mechanical, electrical, etc.) and leads to the examination of the energy flows to which the various systems are subjected, and then to the writing of the balance sheet that must translate the conservation of energy. However, while there is quantitative equality between the various forms of energy, the quality of the various forms of energy varies from one form to another, and even within a given form, and also varies according to the situation under consideration.
The production of low-carbon electricity is a necessity that calls for the development of new technologies. Thermophotovoltaic conversion involves the direct conversion of thermal energy using the photovoltaic effect. As with photovoltaic conversion using solar radiation, it recovers radiative heat from sources with temperatures between 500 and 2,500 °C. This article presents basic principles, science and engineering, and main applications. Powered by a wide variety of primary energy sources, coupled with energy storage in thermal form at very high temperatures (1,000 to 2,500°C), and with cell efficiencies tending towards 50 %, thermophotovoltaic systems offer new options for decarbonized electricity production.
This article, further to previous ones relative to the inverse problems in thermal conduction, deals with inverse problems in forced convection. The energy equation then contains an advection term. After a brief review of the techniques of inversion of measures, a textbook case, highlighting the influence of this transport term compared with conduction, is first studied. Four concrete examples are then given to illustrate the methodology, from numerical and experimental standpoints.
The different components of the estimation error met when seeking to solve a problem of inversion of measurements are presented. A few approaches that allow their assessment and control are reviewed. The specific case of estimation of a function that has been given a parameterized form is studied through the introduction and detailed description of several regularization techniques that provide a necessary compromise between dispersion and bias of the estimation. The study of the errors caused by the parameters that are ‘assumed to be known’, and the guiding principles and utility of Bayesian techniques, are presented at the end of the article.
The construction of a criterion to be minimized, which is the basis for solving any inverse problem, is introduced. The case of inversion of measurements using a linear model is dealt with. The study of its possibly ‘ill-posed’ character, the ordinary least square estimator and its variance-covariance matrix are detailed. The different techniques for inverting measurements using a non-linear model are then detailed. Examples of inversion in steady or unsteady conduction are presented, starting from simulated measurements that integrate some noise. Explosion of estimations, in the case of a bad conditioning of the sensitivity matrix is highlighted.
The task of constructing an appropriate model, here the solution of one of the forms of the heat equation, is tackled in the framework of inverse problems in heat diffusion. Several examples are used to introduce the notions of input, output and structural parameters of a model. The physical principles of the techniques of temperature measurement, with or without contact, are detailed together with the corresponding calibration laws, taking into account the notions of measurement noise and of sampling of the sensor signal. The sensitivity of the model output to its structural parameters or to its parameterized input is the basis of the inverse approach.
Phase change mechanisms are present in many fields: industrial drying operations, geothermal energy, exchangers, … Several macroscopic models are possible: for example Darcean or inertial for the momentum balance, local equilibrium or local non-equilibrium models for the energy balance. Equilibrium water contents depend on capillary and adsorption effects. A complete model is complex. Under certain conditions, a water transport model in the form of a non-linear diffusion equation can be a good approximation. However, the saturation, temperature, concentration, pressure and velocity fields are often complex, reflecting the various mechanisms affecting water transport.
Porous media are ubiquitous in many fields concerning natural, manufactured, or biological media. Modeling heat transfer in these media requires taking into account the multi-scale aspect, which, in this article will be limited to the passage from the pore scale to a macroscopic or Darcy scale. The macroscopic or effective properties (permeability, effective diffusion, etc.) are described in the text for the main heat transfer mechanisms: conduction, convection and natural convection, radiative transfer.
This article presents the basics of radiative transfer in media that alters thermal radiation passing through them. Such media are called semi-transparent, or (radiatively) participants. They are found, in particular, in high-temperature industrial processes, fire safety, combustion chamber thermics, atmospheric science, solar energy harvesting, etc. The different mechanisms of interaction of radiation with matter are detailed. They lead to a transport equation whose solution gives access to the fundamental energy quantities for the heat transfer engineer (flux, radiant sources).
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