Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems

Thermal fluctuations around inhomogeneous nonequilibrium steady states of one-dimensional rigid heat conductors are analyzed in the framework of generalized fluctuating hydrodynamics. The effect of an external source of noise is also considered. External fluctuations come from temperature and position fluctuations of the source. Contributions of each kind of noise to the temperature correlation function are computed and compared through the study of its asymptotic behavior.

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

Information-theoretical derivation of an extended thermodynamical description of radiative systems

A radiative equation of the Cattaneo–Vernotte type is derived from information theory and the radiative transfer equation. The equation thus derived is a radiative analog of the equation that is used for the description of hyperbolic heat conduction. It is shown, without recourse to any phenomenological assumption, that radiative transfer may be included in a natural way in the framework of extendedirreversible thermodynamics

Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Design and construction of precision heat fluxmeters

The possibility of local elastic instabilities is considered in a first¿order structural phase transition, typically a thermoelastic martensitic transformation, with associated interfacial and volumic strain energy. They appear, for instance, as the result of shape change accommodation by simultaneous growth of different crystallographic variants. The treatment is phenomenological and deals with growth in both thermoelastic equilibrium and in nonequilibrium conditions produced by the elastic instability. Scaling of the transformed fraction curves against temperature is predicted only in the case of purely thermoelastic growth. The role of the transformation latent heat on the relaxation kinetics is also considered, and it is shown that it tends to increase the characteristic relaxation times as adiabatic conditions are approached, by keeping the system closer to a constant temperature. The analysis also reveals that the energy dissipated in the relaxation process has a double origin: release of elastic energy Wi and entropy production Si. The latter is shown to depend on both temperature rate and thermal conduction in the system.

Heat pulse line-source method to determine thermal conductivity of consolidated rocks

An instrument designed to measure thermal conductivity of consolidated rocks, dry or saturated, using a transient method is presented. The instrument measures relative values of the thermal conductivity, and it needs calibration to obtain absolute values. The device can be used as heat pulse line source and as continuous heat line source. Two parameters to determine thermal conductivity are proposed: TMAX, in heat pulse line source, and SLOPE, in continuous heat line source. Its performance is better, and the operation simpler, in heat pulse line-source mode with a measuring time of 170 s and a reproducibility better than 2.5%. The sample preparation is very simple on both modes. The performance has been tested with a set of ten rocks with thermal conductivity values between 1.4 and 5.2 W m¿1 K¿1 which covers the usual range for consolidated rocks.

No Major Differences Found between the Effects of Microwave-Based and Conventional Heat Treatment Methods on Two Different Liquid Foods

Extension of shelf life and preservation of products are both very important for the food industry. However, just as with other processes, speed and higher manufacturing performance are also beneficial. Although microwave heating is utilized in a number of industrial processes, there are many unanswered questions about its effects on foods. Here we analyze whether the effects of microwave heating with continuous flow are equivalent to those of traditional heat transfer methods. In our study, the effects of heating of liquid foods by conventional and continuous flow microwave heating were studied. Among other properties, we compared the stability of the liquid foods between the two heat treatments. Our goal was to determine whether the continuous flow microwave heating and the conventional heating methods have the same effects on the liquid foods, and, therefore, whether microwave heat treatment can effectively replace conventional heat treatments. We have compared the colour, separation phenomena of the samples treated by different methods. For milk, we also monitored the total viable cell count, for orange juice, vitamin C contents in addition to the taste of the product by sensory analysis. The majority of the results indicate that the circulating coil microwave method used here is equivalent to the conventional heating method based on thermal conduction and convection. However, some results in the analysis of the milk samples show clear differences between heat transfer methods. According to our results, the colour parameters (lightness, red-green and blue-yellow values) of the microwave treated samples differed not only from the untreated control, but also from the traditional heat treated samples. The differences are visually undetectable, however, they become evident through analytical measurement with spectrophotometer. This finding suggests that besides thermal effects, microwave-based food treatment can alter product properties in other ways as well.

Experimental investigation of transient natural convection cooling of high prandtl number fluid with variable viscosity

Report for the scientific sojourn at the James Cook University, Australia, between June to December 2007. Free convection in enclosed spaces is found widely in natural and industrial systems. It is a topic of primary interest because in many systems it provides the largest resistance to the heat transfer in comparison with other heat transfer modes. In such systems the convection is driven by a density gradient within the fluid, which, usually, is produced by a temperature difference between the fluid and surrounding walls. In the oil industry, the oil, which has High Prandtl, usually is stored and transported in large tanks at temperatures high enough to keep its viscosity and, thus the pumping requirements, to a reasonable level. A temperature difference between the fluid and the walls of the container may give rise to the unsteady buoyancy force and hence the unsteady natural convection. In the initial period of cooling the natural convection regime dominates over the conduction contribution. As the oil cools down it typically becomes more viscous and this increase of viscosity inhibits the convection. At this point the oil viscosity becomes very large and unloading of the tank becomes very difficult. For this reason it is of primary interest to be able to predict the cooling rate of the oil. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of high Prandtl fluid considering the variable viscosity effects.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Conduction mechanisms and charge storage in Si-nanocrystals metal-oxide-semiconductor memory devices studied with conducting atomic force microscopy

In this work, we demonstrate that conductive atomic force microscopy (C-AFM) is a very powerful tool to investigate, at the nanoscale, metal-oxide-semiconductor structures with silicon nanocrystals (Si-nc) embedded in the gate oxide as memory devices. The high lateral resolution of this technique allows us to study extremely small areas ( ~ 300nm2) and, therefore, the electrical properties of a reduced number of Si-nc. C-AFM experiments have demonstrated that Si-nc enhance the gate oxide electrical conduction due to trap-assisted tunneling. On the other hand, Si-nc can act as trapping centers. The amount of charge stored in Si-nc has been estimated through the change induced in the barrier height measured from the I-V characteristics. The results show that only ~ 20% of the Si-nc are charged, demonstrating that the electrical behavior at the nanoscale is consistent with the macroscopic characterization.

Design and construction of precision heat fluxmeters

InAlAs/InGaAs/InP based high electron mobility transistor devices have been structurally and electrically characterized, using transmission electron microscopy and Raman spectroscopy and measuring Hall mobilities. The InGaAs lattice matched channels, with an In molar fraction of 53%, grown at temperatures lower than 530¿°C exhibit alloy decomposition driving an anisotropic InGaAs surface roughness oriented along [1math0]. Conversely, lattice mismatched channels with an In molar fraction of 75% do not present this lateral decomposition but a strain induced roughness, with higher strength as the channel growth temperature increases beyond 490¿°C. In both cases the presence of the roughness implies low and anisotropic Hall mobilities of the two dimensional electron gas.