Heat Conduction and Characteristic Size of Fractal Porous Media

Based on fractal theory, two types of random Sierpinski carpets （RSCs） and their periodic structures are generated to model the structures of natural porous media, and the heat conduction in these structures is simulated by the finite volume method. The calculated results indicate that in a certain range of length scales, the size and spatial arrangement of pores have significant influence on the effective thermal conductivity, and the heat conduction presents the aeolotropic characteristic. Above the length scale, however, the influence of size and spatial arrangement of pores on the effective thermal conductivity reduces gradually with the increasing characteristic size of porous media, the aeolotropic characteristic is weakened gradually. It is concluded that the periodicity in structures of porous media is not equal to the periodicity in heat conduction.     

Depth profiling the thermal reflection coefficient of an opaque solid via an inverse thermal wave scattering theory based on the Method of Images

A new formulation of the inverse problem of depth profiling the thermal properties of an opaque solid based on one-dimensional photo-generated thermal waves is presented. The inverse problem as posed is linear in a set of lumped thermal reflection coefficients which account for the return of energy to the surface by all significant heat conduction channels. An analysis based on the Method of Images relates these coefficients to individual values of the interface thermal reflection coefficients in the material. No weak backscattering assumption is invoked to linearize the problem. The method yields a unique solution subject to a given condition of regularization. Solutions recovered by the method are stable at experimentally feasible error levels. Received: 27 September 1999 / Published online: 16 June 2000     

Transient thermal gratings at surfaces for thermal characterization of bulk materials and thin films

Transient Thermal Gratings (TTGs) at surfaces of absorbing materials have been utilized for investigating heat diffusion in bulk materials and thin films. In this report, we describe the theoretical background of the technique and present experimental data. TTGs were excited in the surface plane by interference of two pulsed laser beams and monitored by a cw probe beam, either via temperature dependence of the reflectivity or by deflection from the displacement pattern. A theoretical model describing the thermal and thermoelastic surface response was developed, both for a homogeneous material and a multilayer structure. The potential of the technique will be demonstrated by experimental results on (i) thermal diffusivities of bulk materials, (ii) anisotropic lateral heat transport, and (iii) thermal diffusivities of metal and diamond films. Furthermore, we will show that TTGs allow thermal depth profiling of inhomogeneous materials whenever there is a vertical gradient in thermal conductivity.     

Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry

This work introduces the concept of edge-field regularization into photothermal inverse depth profilometry problems. An edge field allows prior information concerning the depth location of material interfaces in a sample to be introduced into a Tikhonov regularization problem by a simple binary encoding. The edge-field regularization allows Nth-order Tikhonov stabilization constraints to be applied independently to multiple zones or segments of a depth profile between defined interface positions. This allows the reconstruction of continuous depth-profile information within known layers, without the globally imposed smoothing and edge oscillations of the classical regularization methods. This method successfully reconstructs both the amplitude of the interface discontinuities and the photothermal depth-contrast variations within the bounding edges, to a resolution limited by the resolving kernel for the underlying Nth-order Tikhonov constraint. The edge-field regularization dramatically reduces the errors associated with profiling photothermal contrast in bounded zones that are depth-displaced in the sample. Received: 19 September 2002 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-514/398-3797, E-mail: joan.power@mcgill.ca     

Linearization of Systems of Nonlinear Diffusion Equations

We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.     

Unusual thermal conductivity of the negative thermal expansion material, ZrW2O8

In order to investigate the relationship between negative thermal expansion and other thermal properties, the thermal conductivity of the α-phase of ZrW₂O₈ has been determined from 1.9 to 390 K. In addition, the heat capacity was measured from 1.9 to 300 K. The thermal conductivity of ZrW₂O₈ is low, glass-like and close to its theoretical minimum value. The phonon-phonon coupling of the highly anharmonic low-frequency modes which are responsible for negative thermal expansion in ZrW₂O₈ appears to be highly efficient, leading to short phonon mean free paths and exceptionally low thermal conductivity.     

Macroscopic properties of fractured porous media

The macroscopic properties of fractured porous media locally governed by a Laplace equation are determined by several methods. The first one consists in discretizing the porous medium and the fractures and in solving the Laplace equation in the discretized structure. The other methods consist in successive upscalings. The first upscaling replaces the porous medium by a continuum with a given transport property. The second upscaling replaces the fractures by surfaces with equivalent properties. The results of the various methods give very close results. They suggest a simple approximation which is successful when the properties of the fluid and of the continuous porous medium are not too different.     

Photoacoustic measurements of the thermal properties of AlyGa1-yAs alloys in the region 0<y<0.5

y Ga_1-yAs alloys grown by liquid phase epitaxy on GaAs substrates, by means of the open photoacoustic cell detection technique and the temperature-rise method under continuous light illumination. The values of the thermal conductivity, diffusivity and specific heat were obtained in the 0<y<0.5 region, where the Al_yGa_1-yAs band gap is mainly direct. The technique presented here is based upon an effective sample model which is shown to be suitable for the determination of the thermal properties of two layer semiconductor specimens. Received: 15 November 1996/Accepted: 5 March 1997     

Thermal conductivity in 3D NJL model under external magnetic field

The thermal conductivity of the (2+1)-dimensional NJL model in the presence of a constant magnetic field is calculated in the mean-field approximation and its different asymptotic regimes are analyzed. Taking into account the dynamical generation of a fermion mass due to the magnetic catalysis phenomenon, it is shown that for certain relations among the theory's parameters (particle width, temperature and magnetic field), the profile of the thermal conductivity versus the applied field exhibits kink- and plateau-like behaviors. We point out possible applications to planar condensed matter.     

Fracture behaviors induced by thermal stress in an anisotropic half plane superconductor

This Letter presents a theoretical analysis to the fracture behavior of a large single domain YBCO superconductor under thermal stress based on the two-dimensional theory of anisotropic thermoelasticity, the coupled finite element and infinite element numerical method. The thermal stress intensity factors are obtained due to a uniform heat flux by a line crack in a generally half plane superconductor. It is found that the thermal stress intensity factors decrease with the decrease of temperature, and while the longer the crack length is, the larger the stress intensity factors. Additionally, the J-integral at the crack tip is also investigated, a similar behavior to the thermal stress intensity factors is found. These results are benefit for us to understand the fracture mechanism of superconductor both in theory and application.     

On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium

The effect of elasticity of the flexible walls on the MHD peristaltic flow of a Newtonian fluid in a two-dimensional porous channel with heat transfer has been studied under the assumptions of long-wavelength and low-Reynolds number. The analytical solution has been obtained for the stream function, temperature and heat transfer coefficient. The effect of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The numerical results show that the trapped bolus increases in size and more trapped bolus appears with increasing permeability parameter, elastic tension and mass characterizing parameters but decreases for large values of Hartmann number.     

Fourier and Wavelet Transform Analysis of Pressure Signals during Explosive Boiling

The transient pressure in a liquid-pool during explosive boiling of acetone is measured by a micro-pressure-measuring system. The Fast Fourier transform and continuous wavelet transform methods are applied to investigate the frequency characteristics. The results show that the dominant frequency of the explosive boiling is 0-2 MHz, and the bubble cluster formed by numerous tiny bubbles departs twice. Analysis and discussions are also conducted to explain the bubble evolution during the explosive boiling.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Numerical modeling of the thermal lensing effect in a grazing-incidence laser

The numerical modeling of thermal lensing effect is investigated in a grazing-incidence laser. The deformation of the bounce face is introduced into the modeling for the first time, and the Gaussian distribution of the pump light and the anisotropic heat conduction are considered. The results indicate that the proportion of the deformation on the bounce face to the thermal lensing effect is as high as 80% for small grazing-incident angle of 5°. The thermal lensing effect sensitively depends on the pump power, grazing-incident angle and the pump distribution in a grazing-incidence bounce geometry laser.     

Thermal Conductivity Measurement of Submicron-Thick Aluminium Oxide Thin Films by a Transient Thermo-Reflectance Technique

Thermal conductivity of submicron-thick aluminium oxide thin films prepared by middle frequency magnetron sputtering is measured using a transient thermo-reflectance technique. A three-layer model based on transmission line theory and the genetic algorithm optimization method are employed to obtain the thermal conductivity of thin films and the interracial thermal resistance. The results show that the average thermal conductivity of 330- 1000nm aluminium oxide thin films is 3.3 Wm^-1K^-1 at room temperature. No significant thickness dependence is found. The uncertainty of the measurement is less than 10%.     

Calculation of the temperature and thermal expansion of a STM tip heated by a short laser pulse

A mathematical model for the calculation of the temperature field in a scanning tunneling microscope (STM) tip under laser illumination is developed. The duration of the laser pulse is a few nanoseconds or shorter. A Gaussian distribution of the laser light intensity in time and space is assumed. Two different mechanisms of tip heating are taken into account: 1. due to an enhanced electric field on the tip; 2. due to heating of the side surface of the tip by the focused spot of laser light. An average tip temperature is calculated using the heat conductivity equation. The enhanced electric field on the tip is calculated by the method of boundary integral equations. Received: 20 August 2002 / Revised version: 4 December 2002 / Published online: 19 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-2551/962-490, E-mail: sklein@fh-muenster.de     

Determination of Thermal Conductivity of Liquids by a Multi-Point Laser Pump Method

As an advanced optical method, a multi-point pump method is presented for measurements of thermo-physical properties of liquids. Meanwhile, based on the laser-induced thermal grating method, a new theory model is presented and used to analyse the thermal effects caused by the multi-point laser pump, by which the thermal conductivity of liquids can be obtained. The results of some typical liquids, such as water, ethanol and acetone, are presented and are consistent with those of acknowledged values, demonstrating that the multi-point method is simple and useful for characterizing thermal properties of liquids.     

Local Heating Effect of Flow Past a Circular Cylinder

Heating effects of air flows past a two-dimensional circular cylinder at low Reynolds numbers and low Mach numbers are investigated by numerical simulation. The cylinder wall is heated partially rather than heated on the whole surface as with previous researches. The heating effects are completely different for various heating locations on the cylinder surface. Heating either windward or leeward side stabilizes the flow and reduces or completely suppresses vortex shedding from the cylinder at supercritical Reynolds numbers, which is consistent with previous results of heating on the whole surface of the cylinder. However, as the lateral sides of the cylinder （perpendicular to the stream-wise direction） are heated, an adverse effect is found for the first time in that the flow is destabilized and vortex shedding can be excited at subcritical Reynolds numbers. As the lateral sides of the cylinder are cooled, the flow is stabilized.     

Measurement of rotational temperature in CO2 waveguide laser medium

A small-signal gain in CO₂ waveguide laser medium has been measured on rotational-vibrational transitions in the P-branch of the (0, 0, 1)-(0, 2⁰, 0) band. It has been found that the rotational temperature is well defined in the waveguide laser system where high excitation power is injected and a large amount of energy is flowing through vibrational, rotational, and translational degrees of freedom. The rotational temperature is slightly higher than the translational temperature.