A constrained variational principle for heat conduction

The heat equation is re-studied in this Letter in view of variational theory. By the semi-inverse method, a variational principle for the heat conduction is obtained, which is first appeared in the literature. The physical understanding of the obtained variational principle still needs further explanation.     

Temperature Dependence of Thermal Conductivity of Nanofluids

Mechanism of thermal conductivity of nanofluids is analysed and calculated, including Brownian motion effects, particle agglomeration and viscosity, together influenced by temperature. The results show that only Brown- Jan motion as reported is not enough to describe the temperature dependence of the thermal conductivity of nanofluids. The change of particle agglomeration and viscosity with temperature are also important factors. As temperature increases, the reduction of the particle surface energy would decrease the agglomeration of nanopartieles, and the reduction of viscosity would improve the Brownish motion. The results egree well with the experimental data reported.     

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.     

A fractal model for heat transfer of nanofluids by convection in a pool

Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.     

A Novel Kinetic Model of Liquid Nitrogen＇s Explosive Boiling at the Initial Stage

The liquid nitrogen＇s explosive boiling characteristics under transient high heat flux have attracted increasing attentions of researchers over the world due to its wide applications. Although some experiments have been performed, the process and the characteristics at the initial stage, especially within 1 ~s, have not been described reasonably yet. Based on the related experiments and theoretical analysis, a novel kinetic model combined with quasi-fluid idea is presented to analyse the characteristics of liquid nitrogen＇s explosive boiling at the initial stage. The results indicate that the model can appropriately describe the liquid nitrogen＇s explosive boiling. The behaviour and the heat transfer characteristics of a single bubble are very different from those of the bubble cluster, thus the behaviour of individual bubbles could not be directly applied to describe the explosive boiling process at the initial stage.     

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%.     

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     

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.     

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.     

Effect of diffusion layers and defect layer on acoustic phonons transport through the structure consisting of different films

By using the continuum elastic approximation model and the transfer matrix method, we investigate the effect of diffusion layers and defect layer on acoustic phonons transport through the structure consisting of different films. Our work show that most acoustic phonons can easily pass the structure, but some only have much less transmission probabilities and form corresponding dips in the transmission spectrum. With the change of the structure parameters such as the width of diffusion layers and defect layer, the number of unit cell and the density of containing Al in diffusion layers and defect layer, the magnitude of the frequencies of acoustic phonons corresponding to the dips almost remain unchanged, but the transmission coefficients corresponding to the dips change at different degree, and the transmission probabilities of some frequencies are very sensitive to the variation of the above-mentioned structure parameters. These results can provide some references in controlling the transmission coefficients of acoustic phonons, devising parts of acoustic apparatus and theoretical investigation related.     

Thermal diffusivity and Biot number: A new experimental method

A new simple method is presented for measuring thermal diffusivity and Biot number in cylindrical samples made of relatively highly conducting materials, subjected to laminar air flow. The basic idea is a heat source in the middle section of the sample, acting also as a thermocouple; only one additional temperature sensor at the cylinder basis is required to give all information, without requiring any hypothesis about the effective time dependence of the heat source.     

Heat Conductivity of One-Dimensional Carbon Chain in an External Potential

The heat transport m a one-dimensional （ID） carbon nanowire （CNW） lying in an external potential with different amplitudes and periods is studied by the non-equilibrium molecular dynamics method. It is found that the thermal conductivity of CNW is always anomalous, increasing with the CNW length and obeying the power law k- N, in which a decreases with the increasing external potential amplitude. The thermal conductivity could be enhanced by the external potential with rather larger amplitudes, which means that an applied external potential could be an efficient tool to improve the heat conductivity of a real 1D material In addition, the effect of different periods of the external potential is studied, finding the external potential with an incommensurate period leads to the smaller a value.     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Heat transport in a four-perpendicularity-bend quantum waveguide

Using the scattering matrix method, we investigate acoustic phonon transmission and thermal conductance in a four-perpendicularity-bend quantum waveguide at low temperatures. The transmission spectrum of the quantum waveguide displays a series of resonant peaks and dips; and when one of the bend heights is larger than or equal to the minimum of the dimensions of the phonon channel in the quantum waveguide, a stop-frequency gap will appear; and some single four-perpendicularity-bend quantum waveguides with larger bend heights exhibit narrower width or smaller number of the stop-frequency gaps than that with smaller bend heights. The thermal conductivity is much sensitive to the change of the smaller heights and longitudinal lengths of the bend section; and the thermal conductivity decreases with the increasing of the temperature first, then increases after it reaches a minimum. The investigations of multiple four-perpendicularity-bend waveguides connected in series indicate that the first additional waveguide suppresses the transmission coefficient and forms the stop-frequency gap; and two additional resonance peaks will be formed when each four-perpendicularity-bend waveguide is added in the series. The results could be useful for controlling thermal conductance artificially and the design of phonon devices.     

Charge and Heat Transport in Polycrystalline Metallic Nanostructures

Metals are typically good conductors in which the abilities to transport charge and to transport heat can be related through the Wiedemann-Franz law. Here we report on an abnormal charge and heat transport in polycrystalline metallic nanostructures in which the ability to transport charge is weakened more obviously than that to transport heat. We attribute it to the influence of the internal grain boundaries and have formulated a novel relation to predict the thermal conductivity. The Wiedemann-Franz law is then modified to account for the influence of the grain boundaries on the charge and heat transport with the predictions now agreeing well with the measured results.     

Use of an open photoacoustic cell for the thermal characterisation of liquid crystals

In this paper, we describe the use of an open cell photoacoustic configuration for the evaluation of the thermal effusivity of liquid crystals. The feasibility, precision and reliability of the method are initially established by measuring the thermal effusivities of water and glycerol, for which the effusivity values are known accurately. In order to demonstrate the use of the present method in the thermal characterization of liquid crystals, we have measured the thermal effusivity values in various mesophases of 4-cyano-4^′-octyloxybiphenyl (8OCB) and 4-cyano-4^′-heptyloxybiphenyl (7OCB) liquid crystals using a variable temperature open photoacoustic cell. A comparison of the measured values for the two liquid crystals shows that the thermal effusivities of 7OCB in the nematic and isotropic phases are slightly less than those of 8OCB in the corresponding phases. Received: 28 March 2001 / Revised version: 8 June 2001 / Published online: 18 July 2001     

Memory effects and heat transport in one-dimensional insulators

We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the weakly nonlinear regime, numerical simulation on long enough chains reveal sizeable deviations from the perturbative results in the form of a slower decay of correlations in equilibrium. Their origin can be traced back to the subtle nonlinear effects described by mode-coupling theories. Measures of thermal conductivity with nonequilibrium molecular-dynamics method confirm the relevance of such effects for low-dimensional lattices even at very low temperatures. Received 20 April 2000     

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     

Thermal Diffusivity of Film/Substrate Structures Characterized by Transient Thermal Grating Method

Transient thermal grating method is used to measure the thermal diffusivity of absorbing films deposited on transparent substrates. According to periodically modulated dielectric constant variations and thermoelastic deformations of the thin films caused by the transient thermal gratings, an improved optical diffraction theory is presented. In the experiment, the probing laser beam reflectively diffracted by the thermal grating is measured by a photomultiplier at different grating fringe spaces. The thermal diffusivity of the film can be evaluated by fitting the theoretical calculations of diffraction signals to the experimental measured data. The validity of the method is tested by measuring the thermal diffusivities of absorbing ZnO films deposited on glass substrates.