Absence Of Heat Conduction Research Articles

On the discrete equation model for compressible multiphase fluid flows

The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of heat conduction and mass transfer. We analyze the resulting probability coefficients and prove their local convexity, rigorously establishing that our version of DEM can model different flow regimes ranging from the disperse to stratified (or separated) flow. Moreover, we reformulate the underlying mesoscopic model in terms of an one-parameter family of PDEs that interpolates between different flow regimes. We also propose two sets of procedures to enforce relaxation to equilibrium. We perform several numerical tests to show the flexibility of the proposed formulation, as well as to interpret different model components. The one-parameter family of PDEs provides an unified framework for modeling mean quantities for a multiphase flow, while at the same time identifying two key parameters that model the inherent uncertainty in terms of the underlying microstructure.

Group-invariant solutions for one dimensional, inviscid hydrodynamics

In this paper, the results of the Lie group method carried out by Ovsiannikov are utilized to study the one-dimensional hydrodynamic equations governing compressible, inviscid fluid flow in the absence of heat conduction. One-parameter subgroups of the admissible R-parameter Lie group of point transformations of the system are applied to reduce the first-order, non-linear system of partial differential equations (PDE)s to a first-order system of ordinary differential equations (ODE)s. Closed-form solutions to the reduced ODE systems are subsequently determined using a linear velocity profile ansatz. These solutions are valid in one-dimensional (1D) planar, cylindrical and spherical geometries and are connected to solutions of the governing system of PDEs through an inverse map. The linear velocity type solutions were first considered by Sedov in 1953 and constitute a subclass of all possible similarity solutions of the compressible hydrodynamics equations. They further serve as illustrative examples of using solutions obtained for the reduced ODEs to find solutions of the associated system of PDEs. Consequently, the reduced systems of ODEs are provided in their entirety inviting additional solutions to be determined via alternative explicit or numerical solution techniques.

Gas-Flow Perturbation by a High-Power Heat Source

We consider a gas-dynamic model of a one-dimensional flow of non-viscous perfect gas in the absence of heat conduction when a high-power localized heat source is switched on. Within the framework of this model, it is possible to thoroughly analyze the problem of the gas-flow regimes, which occur as a result of switch-on of such a source, in a wide range of values of the energy-deposition power and initial gas-dynamic characteristics of the flow. Eventually, we obtain a sufficiently general insight into the character of the resulting flows and the conditions of their realizations.

Generating Theorems for Charged Anisotropy in General Relativity

For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.

Antennas for Short Distance Communications in Cryogenic Environment

Sets of bow-tie antennas, used in a single emitter-receiver near-field configuration and in array configuration, have been studied to be used as wireless means to transmit 8–12 GHz microwave signals from the cold stage of a cryogenic system to a room-temperature processing unit. Indeed, the absence of heat conduction allows increasing the performance of cryogenic systems and open the way to multichannel microwave systems that are necessary for imagers. Transmission loss has been found to be lower than 3 dB over a 1.5 GHz bandwidth while crosstalk in the array configuration is kept below −20 dB when antennas are located at around 90 mm transversally from each other.

Generalized hydrodynamics and microflows.

In this paper, a mathematical model within the framework of generalized hydrodynamics is developed for the description of flows in microsystems where the Knudsen number is large and the aspect ratio [(width)/(length)] is not so small. The model is based on a set of empirical generalized hydrodynamic equations, which are fashioned from the steady-state generalized hydrodynamic equations derived from the Boltzmann equation in a manner consistent with the laws of thermodynamics. The constitutive equations used for the model are highly nonlinear, unlike the Newtonian law of viscosity and the Fourier law of heat conduction, but they are thermodynamically consistent. In the absence of heat conduction, the model yields exact solutions for the velocity components and a nonlinear differential equation for the pressure distribution in the rectangular microchannel. The Langmuir adsorption model for surface-gas interaction is used for boundary conditions for the velocity. The calculated flow rate exhibits a Knudsen minimum with respect to the Knudsen number. The longitudinal velocity profile is also non-Poiseuille. The differential equation for pressure distribution is also solved approximately in order to obtain an analytic formula for the flow rate, which exhibits a Knudsen minimum. The formula, although approximate, provides considerable insights into the Knudsen flow phenomena in microchannels.

Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density

We present a sufficient condition on the blowup of smooth solutions to the compressible Navier-Stokes equations in arbitrary space dimensions with initial density of compact support. As an immediate application, it is shown that any smooth solutions to the compressible Navier-Stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support, and an upper bound, which depends only on the initial data, on the blowup time follows from our elementary analysis immediately. Another implication is that there is no global small (decay in time) or even bounded (in the case that all the viscosity coefficients are positive) smooth solutions to the compressible Navier-Stokes equations for polytropic fluids, no matter how small the initial data are, as long as the initial density is of compact support. This is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum. The blowup of smooth solutions to the compressible Euler system with initial density and velocity of compact support is a simple consequence of our argument. © 1998 John Wiley & Sons, Inc.

On the role of strain gradients in adiabatic shear banding

The effect of higher order strain gradients on adiabatic shear banding is investigated by considering the simple shearing of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. The competition between the gradient-dependent plastic flow and heat conduction and their influence on the shear band width and structure are examined. Two internal length scales, i.e., the deformation internal length and the thermal internal length, are incorporated into the linear stability analysis, which shows that the band width size scales either with the square root of the strain gradient coefficient (in the absence of heat conduction) or the thermal conductivity (in the absence of strain gradients), respectively. The numerical computation for the nonlinear problem reveals that the “diffusive” effect of the strain gradient is much stronger than that of the heat conduction and dictates the constitutive response of the material in the postlocalization regime, and shows that the deformation length scale is much larger than the termal length scale. The band width predicted by the gradient theory agrees reasonably well with the experimental observations found in the literature.

Temperature rises produced by a molecular beam striking a platinum surface

A platinum surface initially at room temperature is exposed to intense molecular beams of He, Ar, H{sub 2}, N{sub 2}, and SF{sub 6} emerging from a nozzle also at room temperature. The mass of the platinum is small, so after a few minutes it reaches a steady temperature uniform throughout the sample. Because the rate of heat loss to the surroundings is low, a thermocouple records temperature rises that for pure gases are as much as 30 K and that for mixtures of He with Ar can exceed 100 K. Interpretation of the results shows that these rises can be understood quantitatively and thus provide information about energy transfer occurring when gaseous molecules collide with surfaces. In particular the method gives (1) a way of measuring the temperature T{sub s} a surface attains at steady state due to interaction with gas molecules in the absence of heat conduction or radiation, (2) a simple determination of the average kinetic energy E{sub i} = 2k{sub B}T{sub s} of an incoming atomic beam without the need for measurement of the velocity distribution or the flux in the beam, and (3) a quantity {gamma} that, like an energy accommodation coefficient, is a measure ofmore » the effect of the temperature of the surface on the scattering.« less

Theoretical Analysis of Catalytic Combustion in a Monolith Reactor

A theoretical model of catalytic combustion is developed which allows calculation of temperature and reactant/product distribution in a tubular duct with catalytic walls. Under adiabatic conditions, as prevail in the central ducts of a catalytic monolith combustor, and in the absence of heat conduction along the reactor walls, the model provides an analytic solution. It exhibits the existence of multiple steady states and, for gas mixtures with low Lewis number, temperature excursions in excess of the adiabatic reaction temperature, Gas-phase reactions are shown to increase the fuel consumption in a given length of catalytic duct but leave unchanged the relations between the temperature and species distributions. The model is applied to a series of experimental results obtained with different fuels in tubular reactors. Satisfactory agreement is found between theoretical and experimental data when account is taken of the effects of heat loss from the reactor to the environment.

A theory of composites modeled as interpenetrating solid continua

The differential equations and boundary conditions describing the behavior of a finitely deformable, heat-conducting composite material are derived by means of a systematic application of the laws of continuum mechanics to a well-defined macroscopic model consisting of interpenetrating solid continua. Each continuum represents one identifiable constituent of the N-constituent composite. The influence of viscous dissipation is included in the general treatment. Although the motion of the combined composite continuum may be arbitrarily large, the relative displacement of the individual constituents is required to be infinitesimal in order that the composite not rupture. The linear version of the equations in the absence of heat conduction and viscosity is exhibited in detail for the case of the two-constituent composite. The linear equations are written for both the isotropic and transversely isotropic material symmetries. Plane wave solutions in the isotropic case reveal the existence of high-frequency (optical type) branches as well as the ordinary low-frequency (acoustic type) branches, and all waves are dispersive. For the linear isotropic equations both static and dynamic potential representations are obtained, each of which is shown to be complete. The solutions for both the concentrated ordinary body force and relative body force are obtained from the static potential representation.

On the interaction of the electromagnetic field with heat conducting deformable semiconductors

The differential equations and boundary conditions describing the behavior of a finitely deformable, polarizable and magnetizable heat conducting and electrically semiconducting continuum in interaction with the electromagnetic field are derived by means of a systematic application of the laws of continuum physics to a well−defined macroscopic model. The model consists of five suitably defined interpenetrating continua. The relative displacement of the bound electronic continuum with respect to the lattice continuum produces electrical polarization, and electrical conduction results from the motion of the charged free electronic and hole fluids. Since partial pressures are taken to act in the conducting fluids, semiconduction boundary conditions arise, which have not appeared previously. The resulting rather cumbersome system of equations is reduced to that for the quasistatic electric field and static homogeneous magnetic field. In the absence of heat conduction, for the n−type semiconductor, nonlinear equations quadratic in the small field variables, for small fields superposed on a bias, are obtained from the latter, more tractable, system of equations. These small field equations reduce to four equations in four dependent variables. The linear portion of the small field equations is applied in the analysis of the propagation of both plane and surface waves in piezoelectric semiconductors subject to a static biasing electric field. On account of the aforementioned semiconduction boundary condition, the assumption of zero electric surface charge employed in previous treatments of the surface wave problem is not employed here.

Relativistic thermodynamics of irreversible processes. II: Heat conduction and diffusion; physical part

Synopsis The results of the relativistic thermodynamics of irreversible processes in an isotropic mixture of an arbitrary number of chemical components are reformulated, so far as heat conduction and diffusion are concerned, in three-dimensional tensor form with the help of quantities which are used in the non-relativistic theory. The transformation properties of the vectors J su(j) = ϱsu(j) ( v su(j) v ), where ϱsu(j) = density of rest mass of component j , v su(j) = velocity of component j , v = barycentric velocity, are examined. It is seen that J su(j) = J ′ su(j) + J ′ ∥ / su(j) (1 - v 2 / c 2 ) 1/2 , where J ′ su(j) is the vector J su(j) measured by an observer in the Lorentz frame where v = 0 and J ′ su(j) and J ′ ∥ / su(j) are the components of J ′ su(j) perpendicular and parallel to v respectively. As a consequence of the developed formalism it appears that the density of entropy, multiplied by a constant, is the fourth component of a four-vector. It is seen that in the absence of heat conduction and diffusion the entropy in a small element of volume is a Lorentz invariant quantity. Further, it appears that in all practical cases if there is heat conduction and diffusion the change of the entropy in an element of volume-is only very small under Lorentz transformations. The connection between different sets of heats of transfer occurring in the literature is derived. The heats of transfer are exactly or almost Lorentz invariant. Explicit formulae are given from which the difference between the results of the relativistic and the non-relativistic theory may easily be surveyed. The concentrations of the chemical components appear to be almost Lorentz invariant quantities.