Un modèle simple de la pénétration couplée de chaleur et de matière dans l'absorption gaz-liquide en film ruisselant laminaire

In this paper we present a simple model based on the coupled penetration of heat and mass fronts for the study of the absorption kinetics of vapor in a concentrated salt solution falling in laminar flow down an adiabatic wall. Though this model is very simple, it permits a concrete and intuitive comprehension of the numerical integration of differential equations. The forecasts of this model, in the case of the absorption of water vapor in the lithium bromide solution, are presented and compared to the results of the numerical solution.     

Mesure de coefficients de convection par méthode impulsionnelle—influence de la perturbation de la couche limite

We present here some elements in order to improve the non-destructive procedures for the measurement of the local heat transfer coefficient between a plate uniformly heated and an air-flow. We use the pulsed photothermal method which consists of analysing the transient temperature on the front face of a wall, initially subjected to a convective flow, after a sudden deposit of luminous energy. For the examination of the experimental thermograms, two models are used: in the first one the heat coefficient is assumed to remain constant during the pulsed experiment, and we take into account its variation in time in the second one. The temporal variation law of the heat transfer coefficient used in the second model is obtained by extension of the differential method to the unsteady laminar boundary-layer due to a finite duration excitation. We compare the results of the two models in transient state with those given in steady state by multi-layered heat flux sensor.     

Transferts couples de chaleur et de masse dans des matériaux consolides utilises en génie civil

The method of measuring the humidity in the materials based on the determination of the thermal conductivity is presented and the principal characteristics are analysed. The water diffusion coefficients due to the water content and temperature gradients are measured and utilized in the numerical calculation of a drying process. These results are compared to an experiment and discussed. We note the difficulty of describing the superficial mass transfer with a single coefficient function of the heat transfer coefficient. We present some enthalpic balance which proves of interest in taking into account the presence of humidity in walls of buildings.     

Version étendue du filtre de Kalman discret appliquée à un problème inverse de conduction de chaleur non linéaire

An extended version of the discrete Kalman filter applied to a nonlinear inverse heat conduction problem. A nonlinear inverse heat conduction problem is resolved by using a formulation of the Kalman filter based on a statistical approach and extended to nonlinear systems. The time evolution of a surface heat flux density is reconstructed from a numerical simulation which allowed us to analyse the influence of some parameters, that condition the running of the filter, on the estimation result. A suitable choice of these parameters, guided by the filter behaviour observations, leads to a solution that remains stable when using noisy data, but that is slightly time-lagged compared to the exact function. This time-lag depends on the location of the interior temperature measurement needed for the inversion and on the model error caused by the approximation of the heat flux with a piece-wise constant function. The application of the extended Kalman filter with real measurements recorded from an experimental set-up, shows that this technique fits the stochastic structure of experimental measurements. The provided results are validated by using the Raynaud's and Bransier's inverse method and are in good agreement with the heat flux density estimated with this method.     

Conductivité thermique de matériaux poreux humides: évaluation théorique et possibilité de mesure

We develop here a mathematical model of simultaneous heat and mass transfer in unsaturated porous media. We put forward the influence of the total pressure gradient in the gaseous phase on the mass transfer contrary to the classical models where only two driving forces are taken into account: a temperature and a moisture gradient. We use this model on the one hand to investigate the theoretical notion of the apparent thermal conductivity of a wet porous medium and on the other hand to simulate a hot plate measurement and an unsteady state one (“flash” method). We show the great importance of both the total pressure gradient and the boundary conditions, that is to say of the measurement technique on the results.     

Prevision numérique de la convection forcée turbulente dans une cavité bidimensionnelle entrainée

Turbulent flow and associated heat transfer in confined geometry (driven closed cavity flow in two dimensions) has been studied using a finite-difference numerical method in primitive variables. Turbulence modelling is based on one point closures derived from the classicalk-ε model. Calculated mean velocity and turbulent kinetic energy are compared with available experimental data. In spite of its limitations, the k-ε model proved to be a useful tool for prediction of global quantities. The case of forced heat convection with fixed wall temperature is considered. Mean temperature field and overall thermal properties of the cavity flow are studied. Correlations giving Nusselt numbers at each face of the cavity versus Reynolds number are deduced from numerical results, they sum up mean transfer properties of such a flow configuration.     

La réanalyse du transfert instationnaire de la chaleur

This paper presents a new method to solve the thermal diffusion with, in a first step, the formulation of the general solution of the linear equations, and in a second step the particular solution of the study by introducing the boundary conditions which specialize the system of equations. This method enables to reanalyse easily the problem for various modified boundary conditions and applied thermal loads.     

Modèles de transferts thermiques lors de la fusion d'une solution binaire dispersée

Heat transfer models during the melting of a dispersed binary solution. In this paper, we present a model for heat transfers occurring during the melting of crystallized droplets of a binary solution dispersed within an oil. This model takes into account the heat conduction within the emulsion associated with a heat source (sink) due to the eutectic melting of droplets followed by the progressive melting. The model has been applied to the differential scanning calorimetry in the case of aqueous solutions of ammonium chloride dispersed in a motor oil. The investigated cell containing the emulsion is a cylinder a few mm ³ in volume. By simulation, we could replicate the shape of the experimental thermogramms. The validation of the model permits determining some parameters which are experimentally inaccessible due to the small size of the cell, like the space–time evolution of the temperature inside the DSC sample or the concentration of every droplet as well as the melted proportion.     

Étude numérique de l'ébullition en convection mixte dans une couche poreuse verticale

By using an enthalpic method (two-phase mixture model), we have studied numerically boiling with mixed convection in a vertical porous layer with a discrete heating. Liquid is injected at the top face. Finite volume method is used for numerical resolution of equations of volumetric enthalpy and pressure. Results giving time–space evolution of temperature, pressure, velocities of the fluids and evaporated volume are presented and analyzed. Parametric studies to assess the effects of inlet velocity, imposed heat flux and permeability, were performed. Results show that boiling is important if the effects of both, natural and forced convections are similar. The evaporated volume will decrease at high values of intrinsic permeability of porous medium or at high values of inlet velocity.     

Séchage superficiel d'un matériau poreux humide par convection forcée d'air chaud: couplage entre les équations de transfert dans le matériau et celles de la couche limite

The authors considered drying of a thick slab of humid porous material immersed in a laminar steady flow of hot air parallel to its surface. They wrote the boundary layer equations in air (continuity, momentum, energy and mass), those describing humidity and heat transfer in the porous medium deduced from Luikov's theory. Then, they coupled them at the air-product interface by expressing the continuity of the thermal and mass fluxes taking into account the evaporation. They solved numerically the resulting system of differential equations using an implicit finite-difference method. They determined the instantaneous evaluation of the spatial distributions of heat and humidity, the local values of the Nusselt and Sherwood numbers. They also studied the influences of principal parameters of the system.     

Convection thermique pour l'écoulement de couette avec débit axial; cas d'un fluide pseudo-plastique

The different patterns of psuedo-plastic fluid flow between two coaxial cylinders, with an axial component of velocity, have been determined. A new mode on stability was set obviousness. The incidence of the flow's structure and heat flux on the Nusselt number has been examined. The variation of rheological properties has been accounted for in the correlation between the mean Nusselt number and the usual dimensionless parameters.     

Étude expérimentale d'une interaction de jets obliques avec un écoulement transversal compressible. I. Effets de la compressibilité en régime subsonique sur les champs aérothermiques

Experimental study of inclined jets cross flow interaction in compressible regime. I. Effect of compressibility in subsonic regime on velocity and temperature fields. The results of the investigation of the interaction of a row of jets with a compressible cross flow are compared with their counterpart obtained in incompressible regime. The comparison reported here focuses on the flow field resulting from the interaction above and at the wall. The velocity and temperature fields are measured respectively by laser Doppler velocimetry and thermocouple probes. The wall temperature distributions are measured using an infrared camera. The experiments are performed for cross flow Mach numbers of 0.72 and 0.1 for respectively the compressible and incompressible regimes with almost the same injection rate (R=0.50 and 0.6). Significant differences are noticed between the two flow fields in particular on the vertical development of the jets in the cross flow and on the turbulent diffusion. The jet penetration is found to be higher in the compressible regime with less interaction between the jets. The comparison also shows that the wall heat transfer modifications induced by the jets are less pronounced in the compressible case as a result of the higher penetration of the jets. These results show that neither the mass flux ratio nor the momentum ratio are good candidates for extrapolation of the cooling efficiency from the incompressible case to the real compressible case as encountered in the practical applications.     

Étude numérique de l'évaporation dans un courant d'air humide laminaire d'un film d'eau ruisselant sur une plaque inclinée

Numerical study of the evaporation in laminar humid air flow of a liquid film flowing over an inclined plate. By using an implicit centered finite differences method with a non-uniform grid, the authors study numerically the evaporation of a thin liquid film flowing over an inclined plate in a forced humid-air flow. They consider the existence of two-dimensional laminar boundary-layers with variable physical properties and show that the term of enthalpy diffusion is always negligible, whether the plate is adiabatic, isothermal or heated by a constant heat flux density. By using in the liquid film transfer equations which are one-dimensional, partially two-dimensional and two-dimensional, the authors additionally show the following features. If the plate is adiabatic, the liquid mass flow rate is without influence on the transfers and the gas–liquid interface behaves like an isotherm surface at rest. In this case, one may use a one-dimensional model in the film whatever liquid mass flow rate is. If the wall is isotherm or heated by a constant heat flux and when the liquid mass flow rate is less than 10⁻³ kg·m⁻¹·s⁻¹, the one-dimensional model is sufficient; if it is included in the interval [10⁻³ kg·m⁻¹·s⁻¹, 10⁻² kg·m⁻¹·s⁻¹[, the partially two-dimensional model is useful; if it is superior to 10⁻² kg·m⁻¹·s⁻¹, it is necessary to use the two-dimensional model. Generally, whatever the thermal conditions on the plate are, heat transfer is dominated by the liquid-vapor transition.     

Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction

Heat flux estimation through inverted non-integer identification models. A model of non-integer order that reproduced the transient thermal behaviour of a system is identified. This model is expressed as a linear relationship between the fractionnal derivates of the temperature at a point of the medium and those of the solicitation applied on the system. Using recursive form of the derivates lead to identify the unknows of the model applying the linear least square method from experimental data. The application concerned a semi-infinite medium submited to a single heat flux on its surface. Among the applications of this approach, the identified model is used in an inverse technique to estimate the heat flux applied on the medium.     

Convection mixte dans un écoulement de poiseuille vertical: Étude comparative de chauffage volumique et pariétal à flux constant

Numerical study of heat transfer in a laminar flow between two vertical parallel plates is reported. Two configurations are considered: the first consists of an imposed constant wall-heat-flux boundary conditions; the second corresponds to a bulk energy dissipation by direct electric-conduction (Joule effect) in the fluidIn the two cases, we have kept the same average temperature-difference between the fluid at the entrance and at the exit of the channel. The flow rate is also the same in both cases. Comparison is made between the axial evolution of Nusselt number obtained from this computation and the Nusselt number given by a classical correlation, in forced convection regime. It has been found that they are in good agreement.Heat transfer enhancement in the mixed convection regime is analysed We show particularly that the temperature distribution at the exit section of the channel is more uniform in the bulk heating case than in the constant wall-heat-flux condition.The secondary-flow induced by free convection and its contribution to the temperature uniformity is also studied We show the similarity between the two configurations from the point of view of the secondary-flow structure. In both cases we cam observe two convective cells whose centres are located closer to the exit from the channel. It is explained that this phenomenon is due to the presence, in the two cases, of the wall temperature increase along the channel in the downstream direction.     

Contact périodique en regime etabliresistances thermiques apparentes limites pour des durees de contact nulles et unfinies

The knowledge of heat transfer between periodically contacting metallic surfaces is necessary in numerous engineering applications.The analytical solution for quasi-steady state heat transfer in periodically contacting finite regions was first given by NIKHAILOV[1], and then by VICK and OZISIK [2]. These solutions are revisited. The limit cases at infinite or nul contact duration are studied. It is shown that the apparent limit resistances of the system are: These expressions are convenient physical tools easier to implement than the exact analytical solution.     

Estimation des propriétés thermiques à l'échelle millimétrique par méthodes périodiques: Résolution du problème direct et du problème inverse

Estimation of thermal properties by periodic methods: direct problem and inverse problem solving. This article presents two processes of thermal diffusivity measurement for homogeneous material. The experimental bench uses a periodic method dedicated to millimeter scale study. Simulation of this experimental method is studied in detail. The case of a homogeneous material of unknown diffusivity to be measured is studied. Sensitivity coefficient and calculus of Cramer–Rao bounds (BCR) prove the good conditioning of diffusivity estimation and illustrate the action of thermal losses. Simulations of Monte Carlo compare performances of least squares estimator to optimal performances defined by the BCR. Two experimental processes are validated by a study of the iron ARMCO chosen as material of reference.     

Représentation non locale d'un milieu hétérogène en diffusion pure

For a one-dimensional diffusive transfer through a spatially periodic heterogeneous medium, the quadrupoles method allows to obtain the exact non-local (in time) equation describing the transfer. The case of reversible (that is to say when input and output can be permuted) and non-reversible media is examined separately. Some examples are treated for illustration: degenerated media (made of pure resistances or capacitances) or real media. The obtained equation cannot be reduced to the hyperbolic Cattaneo–Vernotte equation, which is unable to describe diffusive transfer through heterogeneous media.