Signal propagation in the general theory of relativity with viscosity and thermal conductivity: Linear theory

The Eckart-Landau-Lifshitz classical relativistic models of a viscous, heat-conducting fluid are known to lead to an infinite signal propagation velocity. This infinite value contradicts the postulate of a limiting signal velocity, equal to the velocity of light in vacuum. It is suggested that this paradox might be resolved by incorporating internal relaxation processes in the particles of the medium. It has been shown previously that in the special theory of relativity the velocity of a signal in a viscous, heat-conducting fluid with inheritance turns out to be finite. That assertion is proved in the present paper within the framework of the general theory of relativity in the approximation of a weak gravitational field.Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–18, May, 1993.     

On the one-dimensional acoustic propagation in conical ducts with stationary mean flow

This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.     

A comparison of experiment and theory for sound propagation in variable area ducts

An experimental and analytical program has been carried out to evaluate sound suppression techniques in ducts that produce refraction effects due to axial velocity gradients. The analytical program employs a computer code based on the method of multiple scales to calculate the influence of axial variations due to slow changes in the cross-sectional area as well as transverse gradients due to the wall boundary layers. Detailed comparisons between the analytical predictions and the experimental measurements have been made. The circumferential variations of pressure amplitudes and phases at several axial positions have been examined in straight and variable area ducts, with hard walls and lined sections, and with and without a mean flow. Reasonable agreement between the theoretical and experimental results has been found.     

具有声激波的跨音流管道中声传播的数值方法

本文采用四阶MacCormack格式和附加四阶粘性项方法,求解具有声激波的跨音流变差分格壁管中的声传播问题,比前人结果有明显改善。本文详细介绍了这种差分方法,特别是关于截面硬式,人工粘性项和计算可靠性判据。这种方法省内存,省机时,可以在微机上实现计算。     

On the viscosity and thermal conductivity of dense gases

The modified Enskog theory (MET) of transport in dense gases can be used to predict the density dependence of transport coefficients provided the function y, which is a product of a dimensionless density and a pair correlation function, is known as a function of density. In this communication we consider the inverse problem, extracting information on the y function from measured transport property data, both to resolve some peculiarities found by others, and to provide the basis for improved MET predictions.     

Many-atom interactions in the theory of higher order elastic moduli: A general theory

The total potential energy of a crystal U({r _ik }) as a function of the vectors r _ik connecting centers of equilibrium positions of the ith and kth atoms is assumed to be represented as a sum of irreducible interaction energies in clusters containing pairs, triples, and quadruples of atoms located in sites of the crystal lattice A2: U({r _ik }) ≡ Σ _N=1 ⁴ E _N ({r _ik }). The curly brackets denote the “entire set.” A complete set of invariants {I _j ({r _ik })} _N , which determine the energy of each individual cluster as a function of the vectors connecting centers of equilibrium positions of atoms in the cluster E _N ({r _ik }) ≡ E _N ({I _j ({r _ik })} _N ), is obtained from symmetry considerations. The vectors r _ik are represented in the form of an expansion in the basis of the Bravais lattice. This makes it possible to represent the invariants {I _j ({r _ik })} _N in the form of polynomials of integers multiplied by τ ₂ ^m . Here, τ₂ is one-half of the edge of the unit cell in the A2 structure and m is a constant determined by the model of interaction energy in pairs, triples, and quadruples of atoms. The model interaction potential between atoms in the form of a sum of the Lennard-Jones interaction potential and similarly constructed interaction potentials of triples and quadruples of atoms is considered as an example. Within this model, analytical expressions for second-order and third-order elastic moduli of crystals with the A2 structure are obtained.     

Magnetized nanofluid flow of ferromagnetic nanoparticles from parallel stretchable rotating disk with variable viscosity and thermal conductivity

The current work aims at studying a constructed mathematical model with an examination of heat transfer in water-based nanofluids containing ferromagnetic nanoparticles flowing between parallel stretchable spinning discs with variable viscosity influence and variable conductivity. The nonlinear coupling of the ordinary differential equations of the momentum and energy equation with the partial differential equations based on the Navier-Stokes equation employing some influential similarity transformations. The transformed system of ordinary differential equations has been solved through the Chebyshev spectral collocation procedure (CSCP). The numerical results for the velocity and temperature distributions are shown in terms of graphical presentations. The existing available literature was utilized to test for validation of the numerical findings. The outcomes demonstrate that the stretching of the lower and upper disks and spinning parameters strengthens the impetus boundary layer and diminished the temperature boundary layer, whilst the variable thermal conductivity improved the convective and conductive strength of the ferromagnetic nanoparticles considered, and the Fe₃O₄ nanofluid displays a higher thermal conductivity strength than the Mn-ZnFe₂O₄ nanofluid.     

The influence of flow on the acoustic characteristics of a duct bend for higher order modes—A numerical study

A numerical technique was used to investigate the effects of flow on the acoustic transmission and reflection characteristics of a duct bend. The range of wave numbers examined extended to the cut-on value of the second cross-mode. Characteristics were studied in terms of the velocity potential, the acoustic pressure and the energy flux. The effects of locating a turning vane centrally in the bend were also examined in terms of the energy flux.     

A low order flow/acoustics interaction method for the prediction of sound propagation using 3D adaptive hybrid grids

A low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady subsonic compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics part described by the Nonlinear Perturbation Equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection, and diffraction. Sound propagation through an unsteady flow field is examined using static and dynamic flow/acoustics coupling demonstrating the importance of the latter.     

On the theory of thermal conductivity of dielectrics with inclusion of the interaction with a thermostat (theory and numerical experiment)

This paper reports on the results of investigations into the internal microscopic dissipative phenomena occurring in crystalline dielectrics in which the interaction of all subsystems with a thermostat plays a dominant role. It is shown that, in realistic physical situations where allowance is made not only for the coupling between interacting phonon subsystems of a dielectric but also for the interaction with a thermostat, the umklapp processes proceeding in samples with a size smaller than the critical value L₀ play an insignificant role. For these situations, it is proved that the phonon gas superflows through the volume without retardation and comes to rest only due to the interaction with immobile surface phonons of the thermostat. Numerical calculations demonstrate that the umklapp processes manifest themselves solely at high temperatures T (exceeding a temperature approximately equal to Θ_D/4, where Θ_D is the Debye temperature) and for samples with a size L>L₀, which, according to our estimates, should be of the order of 10 cm.     

A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.     

Application of the time dependent finite difference theory to the study of sound and vibration interactions in ducts

The time dependent finite difference theory is extended to the solution of the acoustic wave equation in rectangular ducts when acoustic/structural interactions are allowed at a duct wall. The treatment of the boundary condition which describes the coupling is examined, and the stability of the procedure is studied and found to depend on the nature of this coupling. The convergence of solutions is discussed as a function of the discretization of the solution domain, particularly at frequencies approaching resonance.     

A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity

The steady flow and heat transfer of an electrically conducting fluid with variable viscosity and electrical conductivity between two parallel plates in the presence of a transverse magnetic field is investigated. It is assumed that the flow is driven by combined action of axial pressure gradient and uniform motion of the upper plate. The governing nonlinear equations of momentum and energy transport are solved numerically using a shooting iteration technique together with a sixth-order Runge-Kutta integration algorithm. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that the combined effect of magnetic field, viscosity, exponents of variable properties, various fluid and heat transfer dimensionless quantities and the electrical conductivity variation, have significant impact on the hydromagnetic and electrical properties of the fluid.     

On classical and semiclassical properties of the Liouville theory with defects

Physics of Atomic Nuclei - The Lagrangian of the Liouville theory with topological defects is analyzed in detail and general solution of the corresponding defect equations of motion is found. We...     

A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer

The interfacial layer of nanoparticles has been recently shown to have an effect on the thermal conductivity of nanofluids. There is, however, still no thermal conductivity model that includes the effects of temperature and nanoparticle size variations on the thickness and consequently on the thermal conductivity of the interfacial layer. In the present work, the stationary model developed by Leong et al. (J Nanopart Res 8:245–254, 2006) is initially modified to include the thermal dispersion effect due to the Brownian motion of nanoparticles. This model is called the ‘Leong et al.’s dynamic model’. However, the Leong et al.’s dynamic model over-predicts the thermal conductivity of nanofluids in the case of the flowing fluid. This suggests that the enhancement in the thermal conductivity of the flowing nanofluids due to the increase in temperature does not come from the thermal dispersion effect. It is more likely that the enhancement in heat transfer of the flowing nanofluids comes from the temperature-dependent interfacial layer effect. Therefore, the Leong et al.’s stationary model is again modified to include the effect of temperature variation on the thermal conductivity of the interfacial layer for different sizes of nanoparticles. This present model is then evaluated and compared with the other thermal conductivity models for the turbulent convective heat transfer in nanofluids along a uniformly heated tube. The results show that the present model is more general than the other models in the sense that it can predict both the temperature and the volume fraction dependence of the thermal conductivity of nanofluids for both non-flowing and flowing fluids. Also, it is found to be more accurate than the other models due to the inclusion of the effect of the temperature-dependent interfacial layer. In conclusion, the present model can accurately predict the changes in thermal conductivity of nanofluids due to the changes in volume fraction and temperature for various nanoparticle sizes.