Modelling of Phase Change Heat Transfer System for Micro-channel and Chaos Simulation

The dynamic properties for the micro-channel phase change heat transfer system are studied by theoretical method combined with experiment. Liquid-vapour interface dynamic systems are obtained by introducing disjoining pressure produced by three phase molecular interactions and Lie algebra analysis. Experiments for 0.6 mm×2 mm rectangular micro-channel are carried out to obtain the pressure time serials. Power spectrum density analysis for these serials shows that the system is in chaotic state if the frequency is above 7.39 Hz. The result indicates that the high heat transfer performance of the micro channel phase change system may relate to the characteristics of chaos, The chaos attractor is drawn by the simulation of the obtained differential dynamic system under the conditions of our experiment.     

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 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.     

From compact point defects to extended structures in silicon

We show that in contrast to the 1d Frenkel-Kontorova (FK) chain known to obey the Fourier law of heat conduction and several 2d models which show logarithmic dependence of conductivity on system size, a scalar 2d FK lattice with commensurate structure exhibits anomalous heat conduction, whose thermal conductivity displays a power law behavior. The dependence of thermal gradient on bulk temperature and noise correlation is critically analyzed. A dynamical contribution to conductivity when the system attains a nonequilibrium steady state of thermal conduction has been identified.     

Theory of the photoacoustic effect of semiconductor quantum wells

We develop a theory of the photoacoustic effect of semiconductor quantum wells. Assuming a multilayer system of optically uniaxial media with dissipation we describe the generation of heat and the conduction of the heat through the system by a generalized transfer-matrix method. It is shown by applying this theory to a semiconductor quantum well that the photoacoustic signal is very sensitive on the quantum-size effect and the longitudinal and transverse relaxation times. Our theory predicts that photoacoustics should be a profitable method for the investigation of semiconductor micro- and nanostructures.     

Influence of heat bath on the heat conductivity in disordered anharmonic chain

We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼N^α. As a special case we give the expression that κ∼N^1/2 for free boundaries, and κ∼ N^-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.     

Role of thermal conduction in single-bubble cavitation

Effect of thermal conduction on radiation from a single cavitating bubble has been studied in a hydrochemical framework including variation of heat conductivity of noble gases up to 2500 K. Results of numerical simulation show that thermal conductivity plays an important role in determining ultimate cavitation temperature. Higher thermal conductivity of lighter noble gases causes to more thermal dissipation during the bubble collapse, leading to a lower peak temperature. Moreover, at the same driving conditions, radius of light emitting region is greater for heavier noble bubbles. Therefore, sonoluminescence radiation is more intensive from heavier noble gases. Phase diagrams of single-bubble sonoluminescence have also been calculated and in comparison with available experimental data, there is a relatively good agreement between the theory and experiment for noble gases.     

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.     

Thermodynamic properties of small amorphous and crystalline Silica particles at low temperatures

We have measured the low-temperature (K) specific heat and heat release of small amorphous and crystalline SiO₂ particles embedded in Teflon and of Vycor. The temperature and time dependence of these properties have been interpreted in terms of the tunneling model. We found that the particle size influences the density of states of tunneling systems of the composite. The smaller the size of the particles the larger is the density of states of tunneling systems P₀. Quartz grains with dimensions in the micrometer range show similar glass-like properties as vitreous silica. In comparison with bulk vitreous silica, Vycor shows a much larger P₀ in agreement with the behavior we found for small SiO₂ particles. We discuss the implication of our results on the origin of the universal low-temperature properties of glasses. Received 9 April 1998     

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     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Thermoelastic wave induced by pulsed laser heating

In this work, a generalized solution for the thermoelastic plane wave in a semi-infinite solid induced by pulsed laser heating is developed. The solution takes into account the non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, which play significant roles in ultrashort pulsed laser heating. Based on this solution, calculations are conducted to study stress waves induced by nano-, pico-, and femtosecond laser pulses. It is found that with the same maximum surface temperature increase, a shorter pulsed laser induces a much stronger stress wave. The non-Fourier effect causes a higher surface temperature increase, but a weaker stress wave. Also, for the first time, it is found that a second stress wave is formed and propagates with the same speed as the thermal wave. The surface displacement accompanying thermal expansion shows a substantial time delay to the femtosecond laser pulse. On the contrary, surface displacement and heating occur simultaneously in nano- and picosecond laser heating. In femtosecond laser heating, results show that the coupling effect strongly attenuates the stress wave and extends the duration of the stress wave. This may explain the minimal damage in ultrashort laser materials processing. Received: 23 May 2000 / Accepted: 26 May 2000 / Published online: 20 September 2000     

Ultrafast relaxation dynamics of electronic excitations in noble-metal clusters

We investigate non-equilibrium relaxation processes in optically excited large gold and silver clusters. Time-resolved pump-probe experiments and model calculations show that optical excitation of the clusters by femtosecond laser pulses results in a heating of the electron system, which is followed by electron cooling via phonon emission. The electron heating leads to an enhanced damping of the surface-plasmon resonance in the clusters. This enhanced damping is caused by an enhancement of the Landau damping and electron scattering rates at high electron temperatures. Furthermore, we find that the rate of electron cooling in the clusters changes with electron temperature; this is a consequence of the temperature-dependent specific heat of the conduction electrons. Finally, pump-probe experiments on ellipsoidal silver clusters show that the thermal expansion of the heated clusters triggers mechanical vibrations at the acoustic eigenfrequencies of the clusters. Received: 6 December 1999 / Published online: 7 August 2000     

Effect of elastic anisotropy on the strain fields and band edges in stacked InAs/GaAs quantum dot nanostructures

The effect of elastic anisotropy on the strain fields and confinement potentials in InAs/GaAs quantum dot (QD) nanostructures was investigated for an isolated dot and a stacked multi-layer dots using finite element analysis and model solid theory. The assumption of isotropy tends to underestimate especially hydrostatic strain that is known to modify confinement potentials in conduction band. Consideration of anisotropy results in a wider band gap and shallower potential well as compared with the isotropic model. Since the band gap and potential well depth would be related to opto-electronic properties of quantum dot systems via quantum mechanical effects, it is suggested that consideration of elastic anisotropy in the calculation of strains and band structures is necessary for the design of QD-based opto-electronic devices.     

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     

One-dimensional statistical mechanics models with application to peapods

Quasi one-dimensional systems of molecules of C₆₀ encapsulated in (10/10) nanotubes were studied by both lattice-gas and Takashi–Gursey configurational integral methods of statistical mechanics for both open and capped finite nanotubes as well as infinite nanotubes. From well-established potentials, the energy, heat capacity compressibility, equation of state and absorption isotherms were computed as a function of temperature and molecular density. The existing theories were extended to include the calculation of clustering, and the number of clusters as a function of size was computed for a variety of temperatures and densities. For both models, all molecules are frozen into a single cluster, and increasing the temperature results in a break-up into smaller clusters. The corresponding heat capacity has a broad maximum, which is lower for the T–G model than for the lattice-gas model. The equations of state have a similar form in both models and are identical at low temperatures. The absorption isotherms show that filling of the tubes can take place at all temperatures of practical interest. Peapods are nearly ideal realizations of one-dimensional systems whose thermodynamic and structural properties can be accurately obtained by statistical mechanics. Received: 15 November 2001 / Accepted: 25 October 2002 / Published online: 10 March 2003 RID="*" ID="*"Corresponding author. Fax: +1-215/573-2128, E-mail: lag@sol1.lrsm.upenn.edu RID="**" ID="**"Present address: Dept. of Physics, North Carolina State University, Raleigh, NC 27695, USA     

Humidity effect on electrical properties of layered α-zirconium phosphate

The electrical properties of alkali ions exchanged zirconium hydrogen phosphate Zr(HPO₄)₂·H₂O (α-ZrP) are investigated by impedance spectroscopy technique. Cole-cole plots are used to describe the characteristic changes of electrical properties with relative humidity. The evaluated bulk resistance from the equivalent circuit shows exponential dependence of relative humidity. The surface protons of layered (α-ZrP) contribute to electrical conduction. The largest sensitivity is obtained for K ion exchanged systems.