One-Dimensional Fluids

In this section we proceed from the lattice-type 1-D models to continuous 1-D systems. The latter has the characteristic fluidity of the liquid state. 

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In order to be able to explain the observed results plasma modeling was applied. A one-dimensional fluid model was used, which solves the particle balances for both the charged and neutral species, using the drift-diffusion approximation for the particle fluxes, the Poisson equation for the electric field, and the energy balance for the electrons [191] (see also Section 1.4.1). 

The radial distance distribution in simple atomic and molecular fluids is determined essentially by the exclusion volume of the particles. Zemike and Prins [12] have used this fact to construct a one-dimensional fluid model and calculated its radial distance correlation function and its scattering function. The only interaction between the particles is given by their exclusion volume (which is, of course, an exclusion length in the one-dimensional case) making the particles impenetrable. The statistical properties of these one-dimensional fluids are completely determined by their free volume fraction which facilitates the configurational fluctuations. 

We note that later too—even in recent years—Ya.B. has turned his attention to this sphere of problems we have here a paper by Ya.B. devoted to diffusion in a one-dimensional fluid flow (6), papers on hydrodynamics and thermal processes in shock waves which are reviewed in the next section, and on the hydrodynamics of the Universe in the next volume in the section devoted to astrophysics and cosmology. Here we consider only Ya.B. s papers on magnetohydrodynamics or, more precisely, on the problem of magnetic... 

Equation (3.47) is known as the advection equation. For one-dimensional fluid flow the advection equation reduces to... 

On the basis of the previous theoretical treatment of one-dimensional fluids, in both the bulk and the confined state, w e now discuss some key features of these systems. Specifically, we shall consider the confined fluid to be thermally and materially coupled to the (infinitely large) bulk so that in ther-modymamic equilibrium both systems are maintained at the same chemical potential p, and temperature T. However, in the absence of any attractive interactions between either fluid molecules or betv een a fluid molecule and the hard substrate, the latter becomes a more or less trivial parameter that does not affect thermal properties of the hard-rod fluid. Because of Eqs. (1.50) and (2.79), we have... 

The first three virial coefficients are easily computed, the fomrth with considerably more effort. - The fifth virial coefficients (except for the one-dimensional fluid) are Monte Carlo estimates. Nijboer and van Hove have also expanded g(r) in powers of p, up to and including the second power. 

Consider three viscometers described briefly below where slow rotation of a solid surface produces one-dimensional fluid flow in which the nonzero velocity component depends on two spatial coordinates. 

Answer. The following functional form of the low-Reynolds-number one-dimensional fluid velocity profile is based on solid-body rotation at r = R and conforms to the no-shp boundary condition at the fluid-solid interface ... 

It is only necessary to consider diffusional fiux across the lateral surface because axial diffusion is insignificant at high mass transfer Peclet numbers. The generalized quasi-macroscopic mass balance for one-dimensional fluid flow through a straight channel with arbitrary cross section and nonzero mass flux at the lateral boundaries is... 

This equation considers gas flow in roadways as one dimensional fluid flow, properties of gas flow are uniform in the same section of roadways. Considering flow of micro-unit along roadway branch i as object of study, the one dimensional unsteady-state flow mometum equation is as follows ... 

S. Pal, G. Srinivas, S. Bhattacharyya, and B. Bagchi, Intermitteney, current flows, and short time diffusion in interacting finite sized one-dimensional fluids. J. Chem. Phys. 116 (2002), 5941. 

The veins are thin-walled tubular structures that may collapse (i.e., the cross-sectional area does not maintain its circular shape and becomes less than in the unstressed geometry) when subjected to negative transmural pressures P (internal minus external pressures). Experimental studies (Moreno et al., 1970) demonstrated that the structural performance of veins is similar to that of thin-walled elastic tubes (Fig. 3.10). Three regions may be identified in a vein subjected to a transmural pressure When P > 0, the tube is inflated, its cross section increases and maintains a circular shape when P < 0, the tube cross section collapses first to an ellipse shape and at a certain negative transmural pressure, a contact is obtained between opposite walls, thereby generating two lumens. Structural analysis of the stability of thin elastic rings and their postbuckling shape (Flaherty et al., 1972), as well as experimental studies (Thiriet et al., 2001) revealed the different complex modes of collapsed cross sections. In order to facilitate at least a one-dimensional fluid flow analysis, it is useful to represent the mechanical characteristics of the vein wall by a tube law relationship that locally correlates between the transmural pressure and the vein cross-sectional area. 

The z -dependence in this asymptotic formula is the same as that of the pair-correlation function h( z ) at large z in a one-dimensional fluid in which the correlation length is [cf. (9.36)]. The decay (9.81) is characteristically one-dimensional because the density gradient in the interface is one-dimensional. In mean-field theory, with 7 = 1 and with v(x) given by (9.71), we find 4 = In 4 from (9.79), which we may verify from (9.10) and (9.81), with 0 =, to be the right result. 

KAERI has been developing the CORONA code (Tak et al., 2014) for a core thermo-fluid analysis of a prismatic VHTR. The CORONA code is targeted for a whole core thermo-fluid analysis of a prismatic VHTR with fast computation and reasonable accuracy. The computational efficiency was achieved by combining the 3-D sohd heat conduction with a one-dimensional fluid flow network and adopting a block-wise parallel computation. 

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