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Showing papers in "Flow Turbulence and Combustion in 1968"


Journal ArticleDOI
TL;DR: In this paper, the authors considered the contact problem of a rigid cylinder pressed on an elastic layer connected rigidly to a rigid base and provided an asymptotic solution for all values c/b and for 0≦ν≦0.5.
Abstract: This paper deals with the contact problem of a rigid cylinder pressed on an elastic layer connected rigidly to a rigid base. It is assumed that there is no friction between cylinder and layer and that the cylinder is long enough to ensure a plane deformation. Asymptotic solutions are presented when the ratio of the half width c of the contact area to the thickness b of the layer is small and also when c/b is large. The breakdown of the asymptotic solution for large values of c/b when the material is incompressible, discussed by Koiter [6], is overcome by considering a more general solution of the Wiener-Hopf integral equation encountered. The results of both asymptotic solutions match so well that a satisfactory solution is obtained for all values c/b and for 0≦ν≦0.5.

171 citations


Journal ArticleDOI
Dennis C. Kuzma1
TL;DR: Fluid inertia effects in squeeze films are analyzed in this paper, where the agreement between theory and experiment is very good, and the experimental results are also shown to be very good as well.
Abstract: Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.

141 citations


Journal ArticleDOI
TL;DR: In this article, the laminar flow of a homogeneous viscous liquid in the inlet of a pipe is investigated numerically for a range of small and moderate Reynolds numbers where the boundary layer approximation is inapplicable.
Abstract: The laminar flow of a homogeneous viscous liquid in the inlet of a pipe is investigated numerically for a range of small and moderate Reynolds numbers where the boundary layer approximation is inapplicable. Velocity profiles and other characteristics of the flow are calculated and the results compared with approximate results obtained by other methods. The limiting case of vanishingly small Reynolds number is also treated analytically.

100 citations


Journal ArticleDOI
TL;DR: In this paper, a more general comparison equation theory for difference equations is developed, exploiting the fact that a difference equation can be considered as a differential equation of infinite order, and applying the theory to first order difference equations a useful generalization of the Euler-Maclaurin summation formula is found.
Abstract: In a previous paper [1] it was shown how to develop solutions to difference equations analogous to WKB solutions to differential equations. In the work now reported a much more general “comparison equation” theory [2] is developed for difference equations, exploiting the fact that a difference equation can be considered as a differential equation of infinite order. Second order difference equations are considered in the main; by applying the theory to first order difference equations a useful generalization of the Euler-Maclaurin summation formula is found.

50 citations


Journal ArticleDOI
TL;DR: In this article, a method for the solution of the elastokinetic boundary value problem for time dependent surface tractions and/or displacements, as well as body forces which are functions of time and space, was developed.
Abstract: This note develops a method for the solution of the elastokinetic boundary value problem for time dependent surface tractions and/or displacements, as well as body forces which are functions of time and space. The method of Williams is extended to resolve three-dimensional problems of elastodynamics by classical mathematical techniques.

39 citations


Journal ArticleDOI
TL;DR: In this paper, small amounts of long chain water soluble polymers have a marked effect on turbulent flow resulting in an appreciable reduction of turbulent friction and the maximum reduction in pipe flow resistance is obtained at such low concentrations that the density and viscosity are not altered appreciably.
Abstract: Small amounts of long chain water soluble polymers have a marked effect on turbulent flow resulting in an appreciable reduction of turbulent friction. The maximum reduction in pipe flow resistance is obtained at such low concentrations that the density and viscosity are not altered appreciably. The minimum friction curve varies as Re−2/3 and appears to be the same for all effective additives tested. The transition process is affected by these additives. Quantitative results are presented showing a reduction in the intensity of the turbulent flashes and the fraction of the time the flow is turbulent at a given Reynolds number.

31 citations


Journal ArticleDOI
TL;DR: In this article, the cross-polarization of electromagnetic waves by a statistically rough surface is calculated for a circularly polarized incident wave and a homogeneous dielectric surface with either a Gaussian or an exponential correlation function.
Abstract: Cross polarized power resulting from depolarization of electromagnetic waves by a statistically rough surface is calculated. This is done for a circularly polarized incident wave and a homogeneous dielectric surface with either a Gaussian or an exponential correlation function. The polarized return power is also obtained so that comparison between the two could be made.

30 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that a knowledge of a given number of near field terms suffices to determine the same number of far field terms, thus disproving the previously held contention that p+1 near fields were needed to determine p far fields.
Abstract: An explicit formula is derived expressing the low frequency expansion of the far field coefficient for any radiating electromagnetic field in terms of the low frequency expansion of the near field. It is shown that a knowledge of a given number of near field terms suffices to determine the same number of far field terms, thus disproving the previously held contention that p+1 near field terms were needed to determine p far field terms.

28 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of anomalous thermal expansion on flow patterns and local heat transfer in water is investigated, and a more accurate picture of the flow phenomena can be obtained that agrees not only with experimental heat transfer data but also with theoretical results from existing literature.
Abstract: Thermal free convection in water is studied by melting ice spheres in water, the uniform temperature of which is varied between 0 and 10°C. Flow patterns as well as local heat transfer are examined. In particular, the effect of anomalous thermal expansion is investigated. From our observations a more accurate picture of the flow phenomena can be obtained that agrees not only with our experimental heat transfer data but also with theoretical results from existing literature.

24 citations


Journal ArticleDOI
TL;DR: In this article, an approximate method, an empirical one, a semi theoretical one, and the procedure due to Lindsay and Bromley are examined for prediction of thermal conductivity of polar-nonpolar gas mixtures.
Abstract: An approximate method, an empirical one, a semi theoretical one, and the procedure due to Lindsay and Bromley are examined for prediction of thermal conductivity of polar-nonpolar gas mixtures. With a modification of the approximate method we find, by analyzing experimental and calculated results of twelve different systems, that prediction of thermal conductivity is possible with an uncertainty of about 2%. This is important because experimental data on such gas systems are rare. The methods also permit computation of thermal conductivity at moderately high temperatures and for multicomponent mixtures.

23 citations


Journal ArticleDOI
TL;DR: In this article, the stability of boundary layer free convection from an inclined plane surface has been investigated, and the relative contributions of hydrodynamic and thermal effects are investigated, showing that thermal effects through surface inclinations are increasingly significant as the surface departs further from the vertical position and that positive and negative inclinations do not produce equal and opposite effects.
Abstract: The results of an experimental study of the stability of boundary layer free convection from an inclined plane surface are presented. In particular, the relative contributions of hydrodynamic and thermal effects are investigated. It is demonstrated that thermal effects, through surface inclinations, are increasingly significant as the surface departs further from the vertical position and that positive and negative inclinations do not produce equal and opposite effects.

Journal ArticleDOI
TL;DR: In this article, a numerical method is used to solve the heat transfer equations for laminar flow in ducts of rectangular cross section with simultaneously developing temperature and velocity profiles, both for constant wall temperature and for constant heat input per unit length of the duct.
Abstract: A numerical method is used to solve the heat transfer equations for laminar flow in ducts of rectangular cross section with simultaneously developing temperature and velocity profiles, both for constant wall temperature and for constant heat input per unit length of the duct. Like the solutions for a fully developed velocity profile, the Nusselt number for each aspect ratio is found to increase from a limiting value at large distances from the entry plane to a maximum at the entry plane. The results also show a strong effect of the Prandtl number on the heat transfer coefficients with uniform and fully developed velocity profiles representing the upper and lower limits respectively. Comparisons are made with analytical solutions for circular ducts and parallel plates and with experimental data.

Journal ArticleDOI
TL;DR: In this paper, the solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient.
Abstract: The solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient The primary tangential velocity exhibits a single overshoot of its steady value while the growth of the secondary flows is monotonic The overshoot is seen to be a direct consequence of the lag in the development of the secondary flows An analytical solution is obtained for a related linearized problem: The angular velocity of an infinite disk, initially rotating with an infinite environment, is perturbed The oscillatory decays to the steady state, which occur in both unbounded and bounded linearized analyses, are discussed in relation to the overshoot in the impulsively started disk problem

Journal ArticleDOI
TL;DR: In this paper, the Von Karman similarity hypothesis is employed together with a description of the sublayer profile due to Deissler to predict the friction factor and the non-dimensional velocity profile in concentric annuli.
Abstract: Von Karman's similarity hypothesis is employed together with a description of the sublayer profile due to Deissler to predict the friction factor — Reynolds number relationship and the nondimensional velocity profile in concentric annuli. Theoretical results are presented for six radius ratios from 1.05 to 50 with 6 000

Journal ArticleDOI
TL;DR: In this article, a reciprocity relation between the transmitting and the receiving properties of an antenna is derived, where a single antenna is assumed to be capable of carrying external currents, both of the electric and the magnetic type.
Abstract: A reciprocity relation between the transmitting and the receiving properties of an antenna is derived. In the transmitting situation a certain part of the antenna, called “source domain”, is capable of carrying external currents, both of the electric and the magnetic type. In the receiving situation a plane electromagnetic wave is incident upon the antenna system. Whereas the customary way of deriving reciprocity relations in antenna theory starts with considering two separate antennas, the present method assumes a single antenna only.

Journal ArticleDOI
TL;DR: In this paper, the velocity potential and the surface elevation are calculated for the three-dimensional motion of surface waves excited by any local disturbance of the surface of a sea with constant depth.
Abstract: The velocity potential and the surface elevation are calculated for the three-dimensional motion of surface waves excited by any local disturbance of the surface of a sea with constant depth. Approximate values of the resulting wave integrals are given for large values of time and distance. The results are illustrated using physically plausible distributions of the initial disturbance. Some features of the waves are discussed.

Journal ArticleDOI
TL;DR: In this article, a theoretical investigation of the inertia effects in a squeeze film bearing with an electrically conducting lubricant in the presence of a uniform transverse magnetic field is presented.
Abstract: A theoretical investigation of inertia effects in a squeeze film bearing with an electrically conducting lubricant in the presence of a uniform transverse magnetic field is presented. The two cases of infinitely long rectangular plates and circular plates as bearing surfaces are considered. It is shown that the load supporting capacity of the bearing increases and the squeeze decreases if the lubricant inertia effects are taken into account. However, the inertia effect becomes smaller when the strength of the magnetic field increases.

Journal ArticleDOI
TL;DR: In this paper, a finite difference analysis for slip flow in the entrance region of the parallel plate channel and the plain tube is presented, and results are given for Knudsen numbers equal to 0, 0.01,0.03,0,05, and 0.1.
Abstract: A finite difference analysis is presented for slip flow in the entrance region of the parallel plate channel and the plain tube. Results are given for Knudsen numbers equal to 0, 0.01, 0.03, 0.05, and 0.1. The present results for the pressure distribution in the entrance region do not favour any particular one of the linear solutions to the problem which have been given previously. There is, however, very good agreement between the finite difference prediction of the developing velocity profiles and that of a certain linear solution.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the large path length limit for infrared gaseous radiation and showed that CO2 is a very poor transmitter of radiant energy relative to other absorbing-emitting gases, although just the opposite is true under optically thin conditions.
Abstract: The large path length limit is investigated for infrared gaseous radiation. This limit differs considerably, as the result of the wing regions of vibrationrotation bands, from the conventional Rosseland limit. For illustrative purposes, results are presented for a gas bounded by two parallel black plates and within which there is a uniform heat source. In order to demonstrate its range of applicability, the large path length limit is compared with numerical solutions for CO, CO2, H2O, and CH4. It is further shown that a gas such as CO2 is a very poor transmitter of radiant energy, relative to other absorbing-emitting gases, in the large path length limit, although just the opposite is true under optically thin conditions.

Journal ArticleDOI
TL;DR: In this article, the problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls and extended to the cases of large suction and large injection at the wall.
Abstract: The problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls. In [6] the heat transfer problem of a discontinuous change in wall temperature was solved. In the present paper the solution of Terrill for small suction at the walls is revised and the whole problem is extended to the cases of large suction and large injection at the walls. It is found that, for all values of the Reynolds number R, the limiting Nusselt number Nu ∞ increases with increasing R.

Journal ArticleDOI
TL;DR: In this paper, a linearised solution of the unsteady one-dimensional conservation equations is obtained which describes the variations in the average flow properties external to the boundary layer, and a simple method of estimating shock tube test times is outlined, based on self similar solutions of the constant shock speed analysis.
Abstract: A theoretical and experimental investigation of the limitation on shock tube test times which is caused by the development of laminar and turbulent boundary layers behind the incident shock is presented. Two theoretical methods of predicting the test time have been developed. In the first a linearised solution of the unsteady one-dimensional conservation equations is obtained which describes the variations in the average flow properties external to the boundary layer. The boundary layer growth behind the shock is related to the actual extent of the hot flow and not, as in previous unsteady analyses, to its ideal extent. This new unsteady analysis is consequently not restricted to regions close to the diaphragm. Shock tube test times are determined from calculations of the perturbed shock and interface trajectories. In the second method a constant velocity shock is assumed and test times are determined by approximately satisfying only the condition of mass continuity between the shock and the interface. A critical comparison is made between this and previous theories which assume a constant velocity shock. Test times predicted by the constant shock speed theory are generally in agreement with those predicted by the unsteady theory, although the latter predicts a transient maximum test time in excess of the final asymptotic value. Shock tube test times have also been measured over a wide range of operating conditions and these measurements, supplemented by those reported elsewhere, are compared with the predictions of the theories; good agreement is generally obtained. Finally, a simple method of estimating shock tube test times is outlined, based on self similar solutions of the constant shock speed analysis.

Journal ArticleDOI
TL;DR: In this article, the authors consider plane deformations of an incompressible elastic material and show that by a suitable choice of strain energy function, they can find the class of deformations with constant local rotation angle.
Abstract: In this paper we consider plane deformations of an incompressible elastic material and we show that by a suitable choice of strain energy function we can find the class of deformations with constant local rotation angle. Although the form for the strain energy function is chosen in the first place for mathematical convenience it does correspond to physically reasonable behaviour and such a theory may be regarded as a first order theory. The class of solutions obtained are expressed in a parametric form involving an arbitrary function, simple choices of which correspond to the well known exact solutions of finite elasticity.

Journal ArticleDOI
TL;DR: In this article, a two bulb glass apparatus was used to measure the concentration diffusion coefficient of the binary gas systems He-Ar and Ne-Kr. The coefficients were determined for equimolar mixtures at temperatures between 0°C and 70°C.
Abstract: A two bulb glass apparatus was used to measure the concentration diffusion coefficient of the binary gas systems He-Ar and Ne-Kr. The coefficients were determined for equimolar mixtures at temperatures between 0°C and 70°C. The diffusion was followed as a function of time by withdrawing samples and analyzing them in a specially designed thermal conductivity analyzer with high accuracy. The diffusion coefficients agree with earlier reported experimental values and with those obtained on the basis of the Chapman-Enskog theory in conjunction with the modified Buckingham exp-six and Lennard-Jones (12-6) intermolecular potentials. The smoothed values were used to predict viscosity and thermal conductivity of these mixtures as a function of composition and temperature.

Journal ArticleDOI
TL;DR: In this article, a matched asymptotic expansion for the eigenvalues arising in perturbations about the Blasius solution was proposed, and good agreement was obtained with the numerical results of Libby.
Abstract: A further term is found in the asymptotic expansion suggested by Stewartson for the eigenvalues arising in perturbations about the Blasius solution. The method employed is that of matched asymptotic expansions, and good agreement is obtained with the numerical results of Libby.

Journal ArticleDOI
TL;DR: In this paper, an analysis for the transient cooling or heating of a stagnant layer of hot radiating gas surrounded by a cold gas capable of absorbing and emitting radiation is presented, and a scheme is developed for the numerical solution of the nonlinear integrodifferential equations of energy conservation.
Abstract: An analysis is presented for the transient cooling or heating of a stagnant layer of hot radiating gas surrounded by a cold gas capable of absorbing and emitting radiation. Scattering of radiation is neglected, and energy transfer by conduction and convection is considered to be negligible compared with radiation. The gas is assumed to be perfect and in local thermodynamic equilibrium. The heating of a cold gas by a diffuse and a collimated radiation flux incident on the boundary of the gas from some external source is considered, and the dependence of physical and radiative properties on temperature is taken into account. The problem is formulated exactly using radiative transfer theory. A scheme is developed for the numerical solution of the nonlinear integrodifferential equations of energy conservation. Starting with arbitrary, but given, initial temperature profiles, temperature distributions and local radiative fluxes are predicted as a function of time for a wide range of physically interesting conditions.

Journal ArticleDOI
J. S. Yu1
TL;DR: In this paper, the isothermal p-V relation for Al2O3 at 295 °K was established by using a polynomial quadratic in p to represent the bulk modulus, BT, as a function of pressure.
Abstract: The isothermal p-V relation for Al2O3 at 295 °K is established by using a polynomial quadratic in p to represent the isothermal bulk modulus, BT, as a function of pressure. The second order derivative of BT with respect to pressure at p=0 is evaluated from available ultrasonic data. Comparison between experimental compression measurements and the present calculated results shows excellent agreement up to at least 1 megabar. It also shows that there seems to exist a phase transition in the neighborhood of 1.3 megabars.

Journal ArticleDOI
TL;DR: In this paper, the orthogonal trajectories of van der Pol's equation were solved in terms of modified Bessel functions, and a graph was given which would permit plotting the solutions of the solutions with an accuracy higher than that attainable with the usual methods.
Abstract: The family of trajectories (in the phase plane) of van der Pol's equation is a one parameter family of curves; no explicit analytical expression for it is known. The same is true for the orthogonal trajectories of this family. The differential equation of the orthogonal curves is solved here exactly in terms of modified Bessel functions. Two curves of the orthogonal family are found to be especially simple, and a graph is given which would permit plotting the solutions of van der Pol's equation with an accuracy higher than that attainable with the usual methods.

Journal ArticleDOI
TL;DR: In this paper, the inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law were considered. And they found that the inertia forces decrease the load capacity of the externally pressurised bearing with a given flow rate and the inertia effect increases with the flow behaviour index.
Abstract: The inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law are considered. It is found that the inertia forces decrease the load capacity of the externally pressurized bearing with a given flow rate and the inertia effect increases with the flow behaviour index. At a given feeding pressure, on the other hand, the inertia increases or decreases the load capacity when the flow behaviour index is smaller than or greater than 3, respectively. For squeeze films between circular plates and rectangular plates, the rate of squeeze is slowed down by the inertia and the inertia effect is larger in dilatant lubricants than in pseudoplastic lubricants.

Journal ArticleDOI
TL;DR: In this article, it was shown that for a given wall angle, wall temperature, and internal heat source (sink) strength, solutions of this type are possible only for certain combinations of centerline Mach number, Reynolds number, ratio of specific heats, and Prandtl number.
Abstract: A study is made of source type diabatic (nonadiabatic) flow of a viscous, heat conducting perfect gas in a conical nozzle. For such a flow a class of exact solutions to the Navier-Stokes equations is possible provided the transport properties vary as the n-th power of the absolute temperature. It is found that for a given wall angle, wall temperature, and internal heat source (sink) strength, solutions of this type are possible only for certain combinations of centerline Mach number, Reynolds number, ratio of specific heats, and Prandtl number. Some examples of calculated velocity and temperature profiles are presented for the special case where the viscosity and thermal conductivity vary as the square root of the absolute temperature.

Journal ArticleDOI
TL;DR: In this article, the heat transfer problems of uniform wall temperature and uniform heat flux at wall are solved for small suction Reynolds numbers, and the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).
Abstract: The steady laminar flow of an incompressible, viscous, and electrically conducting fluid between two parallel porous plates with equal permeability has been discussed by Terrill and Shrestha [6]. In this paper, using the solution of [6] for the velocity field, the heat transfer problems of (i) uniform wall temperature and (ii) uniform heat flux at wall are solved. For small suction Reynolds numbers we find that the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).