Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

A lattice Boltzmann equation (LBE) for axisymmetric thermal flows is proposed. The model is derived from the kinetic theory which exhibits several features that distinguish it from other previous LBE models. First, the present thermal LBE model is derived from the continuous Boltzmann equation, which has a solid foundation and clear physical significance; Second, the model can recover the energy equation with the viscous dissipation term and work of pressure which are usually ignored by traditional methods and the existing thermal LBE models; Finally, unlike the existing thermal LBE models, no velocity and temperature gradients appear in the force terms which are easy to realize in the present model. The model is validated by thermal flow in a pipe, thermal buoyancy-driven flow, and swirling flow in vertical cylinder by rotating the top and bottom walls. It is found that the numerical results agreed excellently with analytical solution or other numerical results.     

Dynamics of heat and mass transfer through a water-air interface based on measurements of thermal radio emission at a frequency of 60 GHz

We study the dynamics of heat and mass transfer through a water-air interface on the basis of laboratory radiometric measurements of the time dependence of thermal radio emission of water at a frequency of 60 GHz, which is related to air turbulization above its surface by a fan. We recover the dynamics for the temperature profile in water and in a viscous sublayer of air as well as for the heat flux through the water-air interface. The flux components related to evaporation and heat exchange and the rate of evaporation from a unit surface are determined. An equation for determining the thickness of the viscous sublayer in the air from the heat flux value is obtained;this thickness is about 2 mm under the experimental conditions. The process dependence on the water turbulence is established and methods for determining the thermal film thickness are proposed. In the absence of turbulence in unstable stratified water we observed the development of a periodic convective process from the time the critical value of the Rayleigh number was reached. The heat exchange dependence on the presence of petroleum film on the water surface is studied. It is found that for a film thickness of 5 μm the heat exchange rate decreases by a factor of 3 because of the petroleum presence. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 3, pp. 351–369, March, 1997.     

Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet

This Letter endeavours to complete an earlier numerical analysis for flow and heat transfer in a viscous fluid over a sheet nonlinearly stretched by extending the investigation in two directions. On one side, the effects of thermal radiation are included in the energy equation, and, on the other hand, the prescribed wall heat flux case (PHF case) is also analyzed. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The variations of dimensionless surface temperature as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include a nonlinearly stretching sheet, thermal radiation, viscous dissipation and power-law index of the wall temperature parameters, are graphed and tabulated.     

基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法

双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略.     

Energetic and thermal performance of high-gain diode-side-pumped Nd:YAG rods

We investigated the energetic and thermal performance of a diode-side-pumped Nd:YAG rod laser with up to 50 W power deposited as excess heat into a 3-mm-diameter, 10-cm-length rod. The rod design produces an extremely flat gain profile resulting in “textbook” expressions of thermal lensing and birefringence. Thermal and energetic measurements are compared to corresponding “textbook” theoretical expressions. Discrepancies between various published thermo-mechanical YAG parameters are resolved by a self-consistent set of measured and calculated data for rod thermal lens focal lengths, birefringence depolarization and ratio of heat to stored energy (χ). Measured thermal and energetic performance under lasing and nonlasing conditions are presented, which agree with published theoretical expressions and measurements. Compensation of rod thermal lensing with simple spherical concave lenses is demonstrated. In addition various methods for compensating birefringence depolarization are theoretically and experimentally analyzed and compared. Received: 19 July 1999 / Revised version: 22 October 1999 / Published online: 23 February 2000     

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution α, so that the only free parameter is the (reduced) thermal gradient ϵ. It turns out that the reduced moments of order k are polynomials of degree k−2 in ϵ, with coefficients that are nonlinear functions of α. In particular, the rheological properties (k = 2) are independent of ϵ and coincide exactly with those of the simple shear flow. The heat flux (k = 3) is linear in the thermal gradient (generalized Fourier’s law), but with an effective thermal conductivity differing from the Navier–Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.     

On a class of three-dimensional corner eddies

Consider Stokes flow in a viscous fluid filling a corner, of angle 2α, bounded by two infinite plane walls. Assume that the flow is symmetrical about some plane which is normal to the walls bounding the corner. Since superposition is valid we may consider flows that are symmetrical about the plane bisecting the comer and those that are antisymmetrical about this plane. In either case it is shown that for a class of corner eddies, the corner flow is made up of an infinite sequence of eddies asr → 0, wherer is the radial distance from the corner. Moreover, the eigenvalues λ which determine the structure of the corner eddy fields satisfy the same equation, sin λα = ± λ sin 2α, that arises in the corresponding plane case. The three-dimensional velocity fields are, however, quite different from those seen in the plane case. In particular, in the symmetric case the streamlines are not closed and foci, rather than elliptic stagnation points, are the centres of the eddies in the plane of symmetry. These results represent, in this special context, a generalization to three-dimensions of Moffatt’s classical result for planar corner eddies.     

Klein-Gordon thermal equation for a planck gas

In this paper the quantum hyperbolic equation formulated in our earlier paper [Found. Phys. Lett. 10, 599 (1997)] is applied to the study of the propagation of the initial thermal state of the universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced,V _P = ħ/8t_P = 1.125 10¹⁸ GeV, wheret _P is a Planck time. For the barrier heightV <V _P , the master thermal equation isthe modified telegrapher’sequation, and for barrier heightV >V _P the master equation is theKlein- Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed.     

Lattice thermal expansion of silver indium disulphide

Lattice parameters of chalcopyrite type compound silver indium disulphide (AgInS₂) were determined as a function of temperature by the x-ray method in the temperature range 28 to 685°C. Using these data, the coefficients of thermal expansion,a _⊥ anda _‖, were evaluated by a graphical method. The temperature dependence ofa _⊥ anda _‖ is represented by a suitable equation. The anisotropic thermal expansion of AgInS₂ is explained in terms of the thermal expansion of the Ag-S and In-S bonds of the AgInS₂ lattice.     

热对流条件下固液密度比对颗粒沉降运动影响的直接数值模拟

本文应用任意拉格朗日-欧拉(ALE)算法对固液两相流流场中考虑热对流的非等温颗粒在竖直通道中的沉降运动进行了数值模拟.在牛顿流体中通过积分黏性应力和压力获得颗粒的受力跟踪颗粒运动,使用有限元方法数值求解流场的N-S方程和能量方程,模型不需经验假设.通过模拟来研究颗粒沉降的运动规律和热对流下固液密度比对固液两相流的影响作用.结果表明随着固液密度比的增加,颗粒经历了稳定沉降、周期性摆动,不规则摆动等过程;热对流使颗粒的摆动幅度和沉降速度发生变化;热对流对颗粒的影响作用随着固液密度比的增加而减小.     

The effect of particle size on the thermal conductivity of alumina nanofluids

We present new data for the thermal conductivity enhancement in seven nanofluids containing 8–282 nm diameter alumina nanoparticles in water or ethylene glycol. Our results show that the thermal conductivity enhancement in these nanofluids decreases as the particle size decreases below about 50 nm. This finding is consistent with a decrease in the thermal conductivity of alumina nanoparticles with decreasing particle size, which can be attributed to phonon scattering at the solid–liquid interface. The limiting value of the enhancement for nanofluids containing large particles is greater than that predicted by the Maxwell equation, but is predicted well by the volume fraction weighted geometric mean of the bulk thermal conductivities of the solid and liquid. This observation was used to develop a simple relationship for the thermal conductivity of alumina nanofluids in both water and ethylene glycol.     

Integro-differential equation method in the hydrodynamics of an incompressible viscous fluid

An integro-differential equation method is proposed to describe the motion of an incompressible viscous fluid. The method uses an analogy between the hydrodynamic equations for an incompressible viscous fluid and the magnetostatic equations. An analysis is made of the flow of an incompressible viscous fluid round an object as a specific application. The solution automatically satisfies the boundary conditions at the surface of the object and at infinity. Zh. éksp. Teor. Fiz. 112, 1332–1339 (October 1997)     

Composition dependence of the energy gap and thermal diffusivity in bulk As-Se glasses

We have measured the composition dependence of the optical energy gap and thermal diffusivity in bulk As _x Se_1−x (0.10⩽x⩽0.50) glasses using photoacoustic technique. The energy gap shows a threshold minimum value and thermal diffusivity has a threshold maximum value at the stoichiometric composition As₂Se₃ corresponding tox=0.40. The decrease in energy gap is explained on the basis of chemical bonding. It is argued that the threshold percolation of rigidity in the random network is responsible for the peaking of the thermal diffusivity at the stoichiometric composition.     

Superconducting resonator in strong microwave fields: Thermal domain, nonlinear thermal effects

The thermal nonlinearity of superconducting films in an electromagnetic field is investigated theoretically. It is shown that the transition of the superconductor from the superconducting to the normal state as a result of Joule heating exhibits hysteresis, corresponding to the onset of a bistable state in the film. It is shown that as a result of the nonuniformity of the amplitude of the electromagnetic field along the surface of the superconducting film, above some threshold a normal-phase domain forms in the superconductor. It is ascertained that the temporal evolution of the domain walls exhibits the character of thermal autowaves of heating or cooling. The nonlinear radio-frequency characteristics (reflection and transmission coefficients and frequency responses) of a stripline resonator under conditions of thermal nonlinearity are calculated. Zh. Tekh. Fiz. 67, 81–89 (October 1997)     

The origin of thermal hadron production

Multihadron production in high energy collisions, from e⁺e^- annihilation to heavy ion interactions, shows remarkable thermal behaviour, specified by a universal “Hagedorn” temperature. We argue that this hadronic radiation is formed by tunneling through the event horizon of colour confinement, i.e., that it is the QCD counterpart of Hawking-Unruh radiation from black holes. It is shown to be emitted at a universal temperature T_H ≃ (σ/2 π)^1/2, where σ denotes the string tension. Since the event horizon does not allow information transfer, the radiation is thermal “at birth”.     

The rates of bimolecular thermal reactions taking into account local medium fluctuations

The contribution of local medium fluctuations to the rates of thermal chemical reactions was calculated for the first time. It was shown for the “ideal gas” model that the fluctuation contribution to a rate constant was proportional to the specific volume of particles and amounted to 1–10% already at densities of about 20 atmosphere densities. For this reason, chemical kinetics calculations of reaction rates should be performed taking into account local medium fluctuations before taking into account specific volume in the equation of state.     

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) ⁷⁰Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case. Zh. éksp. Teor. Fiz. 114, 1757–1764 (November 1998)     

Characteristic features of the low-temperature thermal conductivity of highly-enriched and natural germanium

Experimental data on the thermal conductivity K(T) of natural and highly enriched (99.99%) Ge⁷⁰ crystals with ground and polished surfaces are analyzed in the temperature interval ∼2–8 K. In all samples, the boundary scattering mechanism predominates in the interval from 2 to 4.0 K. As temperature increases, in highly enriched samples N processes start to contribute to phonon transport and the behavior of K(T) corresponds to viscous Poiseuille flow of a phonon gas. The isotopic scattering mechanism plays a large role in isotopically nonideal samples. Fiz. Tverd. Tela (St. Petersburg) 40, 1604–1607 (September 1998)