scholarly journals On the calculation of the velocity and temperature distributions for flow along a flate plate

1936 ◽  
Vol 154 (882) ◽  
pp. 364-377 ◽  
Keyword(s):  
Kinetic Theory ◽  
Turbulent Flow ◽  
Free Path ◽  
Mean Free Path ◽  
Mixing Length ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Temperature Distributions ◽  
The Mean

Kármán and Prandtl were the first investigators to publish theoretical ults for problems of turbulent flow involving plane boundaries. Before nsidering any particular problem the general considerations of these iters will be outlined. Prandtl's is, perhaps, the easier method to follow. He considered a bulent motion in which the mean velocity u remains parallel to a tain direction—O x , say,—and is a function of y only, O y being perpendicular to O x , and he arrived at the result τ = ρ l 2 | du / dy | du / dy (1) the shearing stress, where ρ is the density of the fluid and l is a length, led the mixing length; it is the analogue of the mean free path in the etic theory of gases. The conception of the mixing length of the sent problem is physically much less surely grounded than the mean e path of the kinetic theory.

The Present State of the Turbulence Problem

1933 ◽  
Vol 1 (1) ◽  
pp. 19-28
Author(s):  
Walter Tollmien
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Theory ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Fully Developed Turbulence ◽  
Developed Turbulence ◽  
The Mean ◽  
Real Goal

Abstract In this survey the author first describes certain types of turbulent flow, following which he deals successively with the production of turbulent motion; the instability of the laminar motion; fully developed turbulence; momentum interchange and mixing lengths; and relations between the shearing stress at the wall and the mean velocity distributions. Finally he takes up the calculation of skin friction for simple cases of fully developed turbulence, especially for that of the flat plate. Although the methods outlined have often led to practically useful results, it is the author’s belief that they should be considered only as advances toward the real goal of the turbulence theory. The derivation of turbulence phenomena from the hydrodynamical equations will, in his opinion, be possible only by the application of statistical methods.

scholarly journals Determination of the coefficient of inter-diffusion of gases and the velocity of ions under an electric force, in terms of mean free paths

1912 ◽  
Vol 86 (586) ◽  
pp. 197-206 ◽  
Keyword(s):  
Free Path ◽  
Equations Of Motion ◽  
Mean Free Path ◽  
Electric Force ◽  
Mean Velocity ◽  
The Mean ◽  
Definition Of ◽  
Good Agreement ◽  
Diffusion Of Gases

1. The properties of gases which depend on the velocity of agitation of molecules and the lengths of their free paths may easily be expressed in terms of the mean velocity of agitation and the mean free path when certain assumptions are made in order to simplify the investigations. The expressions thus found on the principles of the kinetic theory are in good agreement with the experimental results in most cases, but the formulæ that have been obtained for the coefficient of inter-diffusion of gases and the velocity of particles acted on by an external force are not so satisfactory. The equations of motion of two inter-diffusing gases have been given by Maxwell, and it may be shown from these that the exact value of the ratio of the coefficient of diffusion of ions to the velocity under unit electric force is N e /II, where N is the number of molecules per cubic centimetre of a gas at pressure II, and e the charge on an ion. The method adopted by Maxwell is perfectly general, there are no assumptions made as to the distribution of the velocities of agitation, and no particular definition of a collision of a free path is involved, so that there can be little doubt as to the accuracy of the result.

scholarly journals The motion of electrons in gases

1923 ◽  
Vol 103 (720) ◽  
pp. 53-57 ◽  
Keyword(s):  
Kinetic Theory ◽  
Electric Field ◽  
Free Path ◽  
Mean Free Path ◽  
Theoretical Formula ◽  
Kinetic Theory Of Gases ◽  
Thermal Agitation ◽  
Mean Velocity ◽  
Gas Molecules

The velocity ( v ) of an electron in a gas, due to an electric field of strength X, is given approximately by theoretical formula v = 0·815 X e λ/ m V. where e denotes the charge on the electron, λ its mean free path, m its mass, and V its mean velocity of thermal agitation. Townsend has made many determinations of this velocity v , and also of V, in several gases at different pressures ( p ) and finds that v is a function of X/ p , and that the values of λ given by the above equation are of the same order, in most cases, as those deduced from the viscosity by means of the kinetic theory of gases. The equation v = 0·815X e λ/ m V is obtained by assuming that there is no persistence of velocities when electrons collide with gas molecules.

Clausius: the kinetic theory of gases

2020 ◽  
pp. 543-551
Author(s):  
Robert T. Hanlon
Keyword(s):  
Heat Capacity ◽  
Kinetic Theory ◽  
Free Path ◽  
Mean Free Path ◽  
Kinetic Theory Of Gases ◽  
Path Distance ◽  
The Mean ◽  
Monatomic Gas

Rudolf Clausius developed the first modern version of the kinetic theory of gases. His derivation provided the means to predict the heat capacity of a monatomic gas and to quantify the mean free path distance traveled by atoms between collisions.

Size Effects of Heat Conduction for Silicon Nanograins

2014 ◽  
Vol 633-634 ◽  
pp. 34-37
Author(s):  
Ya Fen Han ◽  
Hai Dong Liu
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Kinetic Theory ◽  
Free Path ◽  
Size Effects ◽  
Mean Free Path ◽  
Structure Model ◽  
The Mean

The structure model of silicon nanograins was built. And then based the modification of the mean free path of phonons according to the size of nanograins, the expression of thermal conductivity in nanograins was obtained according to the phonon kinetic theory. The dependence of the thermal conductivity of silicon nanograins on size was investigated. The results showed that thermal conductivity of nanograins decrease with the reduction of characteristic sizes when the characteristic sizes of nanograins are comparable to or smaller than the phonon mean free path.

ON FULLY DEVELOPED TURBULENT FLOW IN CURVED CHANNELS

1956 ◽  
Vol 34 (11) ◽  
pp. 1134-1146 ◽  
Author(s):  
A. W. Marris
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Radius Of Curvature ◽  
Mixing Length ◽  
Mean Velocity ◽  
Curved Channels ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
Theoretical Results

Formulae for the radial distribution of velocity and vorticity for the case of fully developed turbulent flow in the channel between concentric and infinitely long cylinders are developed on a similarity vorticity transfer theory, by postulating an Eulerian mixing length function dependent on both position and radius of curvature. The theoretical results obtained for the mean velocity distribution across the channel compare satisfactorily with existing experimental data when the curvature dependent parameters are given appropriate numerical values.

New First and Second Order Slip Models for the Compressible Reynolds Equation

2003 ◽  
Vol 125 (3) ◽  
pp. 558-561 ◽  
Author(s):  
Lin Wu ◽  
D. B. Bogy
Keyword(s):  
Free Path ◽  
Reynolds Equation ◽  
Mean Free Path ◽  
Second Order ◽  
Surface Element ◽  
Length Scale ◽  
Mean Velocity ◽  
First Order ◽  
Lubrication Equation ◽  
The Mean

In the original derivations of the first order and the second order slip models of the generalized Reynolds equation in the literature [3,4], a length scale equal to the mean free path of the gas molecules was used in a Taylor series expansion of the mean velocity field. The coefficients of the correction terms in the derived lubrication equation depend on that length scale. This choice of the length scale is arbitrary to some extent. In this paper, new first order and the second order slip models are derived using a somewhat more physical approach, in which the requirement that the expansion length scale be the mean free path is relaxed. In this approach the momentum transfer rate across each surface element is obtained by summing up the contributions from each group of molecules impinging on the surface at an angle θ to the surface normal within a solid angle dω. The new second order slip lubrication equation appears to be preferable to the original one when the inverse Knudsen number is small, and it is free of any contact pressure singularity, whereas the new first order slip model continues to contain the unacceptable pressure singularity in the limit as the spacing approaches zero, as does the original first order model.

scholarly journals I. On the applications of the kinetic theory to dense gases

1896 ◽  
Vol 187 ◽  
pp. 1-14
Keyword(s):  
Kinetic Theory ◽  
Free Path ◽  
Relative Motion ◽  
Mean Free Path ◽  
Dense Gases ◽  
Centre Of Gravity ◽  
Mean Pressure ◽  
The Mean

The motion of a great number of elastic spheres, when their aggregate volume does not bear an evanescent ratio to the containing space, has received little attention from writers on the kinetic theory. In what respect, beyond the shortening of the mean free path, will it differ from that of the rare medium usually discussed ? I think that the answer to this question is that there exists in all systems, dense or rare, a tendency for the spheres to move together in masses or streams, and so to diminish the mean pressure per unit of area, and the number of collisions per unit of volume and time. And this tendency has an appreciable influence on the form of the motion as soon as the ratio of the aggregate volume of the spheres to the containing space becomes appreciable. If a part of the system, say n spheres, be at any instant contained in a volume V, they have energy, T r of the motion of their common centre of gravity. And they have energy, T r , of relative motion. As the spheres increase in diameter, the ratio T r /T s , will be found to diminish on average. But the number of collisions per unit of volume and time, given T, or T r , + T s , depends on T r , and therefore diminishes by the diminution of T r .

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

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