Effect of angular inertia of lubricant in MHD hydrostatic thrust bearings

Summary Circumferential motion of a conducting lubricant in a hydrostatic thrust bearing is caused either by the angular motion of a rotating disk or by the interaction of a radial electric field and an axial magnetic field. Under the assumption that the fluid inertia due to radial motion is negligibly small in comparison with that due to angular motion, it is found analytically that the rotor causes an increase in flow rate and a decrease in load capacity, while both are increased by the application of an electric field in the presence of an axial magnetic field. The critical angular speed of the rotor at which the bearing can no longer support any load is obtained, and the possibility of flow separation in the lubricant is discussed.Nomenclature a recess radius - b outside disk radius - B ₀ magnetic induction of uniform axial magnetic field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M Hartmann number = (B ₀ ² h ²/)^1/2 - P pressure - P ₀ pressure at r=a - P _e pressure at r=b - Q volume flow rate of lubricant - Q ₀ flow rate of a nonrotating bearing without magnetic field - r radial coordinate - r _s position of flow separation on stationary disk - u, v fluid velocity components in radial and circumferential directions, respectively - W load carrying capacity of bearing - W ₀ load capacity of a nonrotating bearing without magnetic field - z axial coordinate - coefficient of viscosity - _e magnetic permeability - fluid density - electrical conductivity - electric potential - angular speed of rotating disk - _c critical rotor speed at which W=0     

Pulsatile blood flow through arterioles

An analytical study was made to examine the effect of vascular deformability on the pulsatile blood flow in arterioles through the use of a suitable mathematical model. The blood in arterioles is assumed to consist of two layers — both Newtonian but with differing coefficients of viscosity. The flow characteristics of blood as well as the resistance to flow have been determined using the numerical computations of the resulting expressions. The applicability of the model is illustrated using numerical results based on the existing experimental data. r, z coordinate system - u, axial/longitudinal velocity component of blood - p pressure exerted by blood - _b density of blood - µ viscosity of blood - t time - , displacement components of the vessel wall - T _t0,T ₀ known initial stresses - density of the wall material - h thickness of the vessel wall - T _t,T stress components of the vessel - K _l,K _r components of the spring coefficient - C _l,C _r components of the friction coefficient - M _a additional mass of the mechanical model - r ₁ outer radius of the vessel - thickness of the plasma layer - r ₁ inner radius of the vessel - circular frequency of the forced oscillation - k wave number - E ₀,E _t, , _t material parameters for the arterial segment - µ _p viscosity of the plasma layer - Q total flux - Q _p flux across the plasma zone - Q _h flux across the core region - Q mean flow rate - resistance to flow - P pressure difference - l length of the segment of the vessel     

Theory of single well tests in a leaky aquifer. Analytical solution for non steady flow

The evaluation of a pump test or a slug test in a single well that completely penetrates a leaky aquifer does not yield a unique relation between the hydraulic properties of the aquifer, independent of the testing conditions. If the flow is transient, the drawdown is characterized by a single similarity parameter that does not distinguish between the storativity and the leakage factor. If the flow is quasi stationary, the drawdown is characterized by a single similarity parameter that does not distinguish between the transmissivity and the leakage factor. The general non steady solution, which is derived in closed form, is characterized bythree similarity parameters.Nomenclature a e 0.8905 = auxiliary parameter - b thickness of the aquifer - b _c thickness of the semipervious stratum - B() auxiliary function - f(s),g(s) auxiliary functions in the complex plane - F(t),G(t) auxiliary functions of time - h undisturbed level of the phreatic surface - K conductivity of the aquifer - K _c conductivity of the semipervious stratum - m ₀ leakage factor - m dimensionless leakage factor - N(s) auxiliary function in the complex plane - Q _w (t) discharge flux - Q steady discharge flux - Q ₀ constant discharge flux during limited time - Q(t) dimensionless discharge flux - r ₀ radius of the well - r radial coordinate - r dimensionless radial coordinate - s complex variable - s ₀ pole - S storativity of the aquifer - S _n n'th part of an integration contour - t time - t dimensionless time - T transmissivity of the aquifer - ,,,,, dimensionless parameters - Euler's number - dummy variable - ₁(), ₂() auxiliary functions - (r, t) drawdown - ₀(t) drawdown in the well - (r, t) dimensionless drawdown - ₀(t) dimensionless drawdown in the well     

The moving, plane heat source in an elastic medium

Summary This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.Nomenclature mass density - diffusivity - thermal conductivity - Q heat emitted by plane heat source per unit time per unit area - speed of propagation of plane heat source - shear modulus - Poisson's ratio - T temperature - _x, _y, _z normal stress components - u _x, u_y, u_z displacement components - c speed of irrotational waves - t time - x, y, z Cartesian coordinates - =x–vt moving coordinate     

New concepts in relative permeabilities at high capillary numbers for surfactant flooding

Flooding oil reservoirs with surfactant solutions can increase the amount of oil that can be recovered. Macroscopic modelling of the process requires relative permeabilities to be functions of saturation and capillary number. With only limited experimental data, relative permeabilities have usually been assumed to be linear functions of saturation at high capillary numbers. The experimental data is reviewed, some of which suggest that this assumption is not necessarily correct. The basis for the assumption is therefore reviewed and it is concluded that the linear model corresponds to microscopically segregated flow in the porous medium. Based on new but equally plausible complementary assumptions about the flow pattern, a mixed flow model is derived. These models are then shown to be limiting cases of a droplet model which represents the mixing scale within the porous medium and gives a physical basis for interpolating between the models. The models are based on physical concepts of flow in a porous medium and so the approach described here represents a significant improvement in the understanding of high capillary number flow. This is shown by the fact that fewer parameters are needed to describe experimental data.Notation A total cross-sectional area assigned to capillary bundle - A ⁽ⁱ⁾ physical cross-sectional area of tube i - c ⁽ⁱ⁾ ordered configurational label for droplets in tube i - c configuration label for tube i (order not considered) - D defined by Equation (26) - E(...) expectation value with respect to the trinomial distribution - S _r ⁽⁾ fractional flow of phase - k absolute permeability - k _r relative permeability of phase - k _r ⁰ endpoint relative permeability of phase - L capillary tube length in bundle model - m ⁽ⁱ⁾ number of droplets of phase a occupying tube i - n exponent for phase a in Equation (2) - N number of droplets in bundle model - N _c capillary number - p pressure - p(c') probability of configuration c - Q ⁽ⁱ⁾ total volume flow rate in tube i - S saturation of phase - S flowing saturation of phase - S _r residual saturation of phase - S _r ⁽⁾ saturations when fractional flow of phase is 1 in the case of varying residual saturations for three-phase flow ( ) - t _c residence time for droplet configuration c - v ⁽ⁱ⁾ total fluid velocity in bundle tube i - , phase label - p pressure differential across capillary bundle - ⁽ⁱ⁾ tube conductivity defined by Equation (7) - viscosity of phase - interfacial tension - gradient operator - ... average over tube droplet configurations     

Viscous properties of calcium carbonate filled polymer melts

Summary The viscous properties of calcium carbonate filled polyethylene and polystyrene melts were examined. The relative vircosity _r defined in the previous paper gave an asymtptotic value( _r)_l in the range of the shear stress below 10⁵ dyne/cm².( _r)_l of the calcium carbonate filled system was higher than that of the glass beads or glass balloons filled system at the same volume fraction of the filler. Maron-Pierce equation with ₀ = 0.44 was able to approximate the( _r)_l — relationship. However, it was deduced here that the high value of( _r)_l of calcium carbonyl filled system was due to the apparent increase of and this increase was attributed to the fixed polymer layer formed on the powder particle. By assuming the particle as a sphere with a diameter of 2 µm, the thickness of the fixed polymer layer was estimated as about 0.17 µm. The yield stress estimated from the Casson's plots increased exponentially with.

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Zusammenfassung Es wurden die viskosen Eigenschaften von Polyäthylen-und Polystyrol-Schmelzen untersucht, die mit Kalziumkarbonat-Teilchen gefüllt waren. Für die relative Viskosität _r, wie sie in einer vorangegangenen Veröffentlichung definiert worden war, ergab sich bei Schubspannungen unterhalb 10⁵ dyn/cm² ein asymptotischer Wert( _r)_l. Dieser war bei den mit Kalziumkarbonat gefüllten Schmelzen höher als bei Schmelzen, die bis zur gleichen Volumenkonzentration mit Glaskugeln oder Glasballons gefüllt waren. Die ( _r) _l —-Abhängigkeit ließ sich durch eine Gleichung nachMaron und Pierce mit ₀ = 0,44 beschreiben. Es wurde jedoch geschlossen, daß der hohe( _r)_l-Wert der mit Kalziumkarbonat gefüllten Schmelzen auf eine scheinbare Zunahme von zurückzuführen ist, verursacht durch eine feste Polymerschicht auf der Teilchenoberfläche. Unter Annahme kugelförmiger Teilchen mit einem Durchmesser von 2 µm ließ sich die zugeordnete Schichtdicke zu 0,17 µm abschätzen. Die mittels der Casson-Beziehung geschätzte Fließspannung ergab eine exponentielle-Abhängigkeit.

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With 7 figures and 1 table     

Axial annular flow of plastic fluids: dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ _c, λ will be such that flow commences when τ(κR) = τ(R) = τ _c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.

Mass transport in flow of sources

Steady and unsteady local concentration has been determined analytically for two- und three-dimensional sources and is presented for various boundary-concentrations, volumetric flows and diffusion coefficients. The steady cases have been evaluated numerically. In addition an unsteady two-dimensional mass transport has been evaluated.

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Stofftransport in Quellströmungen

Zusammenfassung Es wurden die stationäre und instationäre örtliche Konzentration von einer zwei- und drei-dimensionalen Quellströmung als Funktion verschiedener Randkonzentrationen, verschiedener Stromvolumen und Diffusionskoeffizienten analytisch bestimmt. Die stationären Fälle wurden numerisch ausgewertet. Außerdem wurde ein zwei-dimensionaler instationärer Stofftransport behandelt.

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Nomenclature a inner radius of circle (2-dimensional case), inner radius of sphere (three-dimensional case) - b } >a outer radius of circle (2-dimensional case), outer radius of sphere (three-dimensional case) - c concentration - c ₁,c ₂ given concentration at the boundariesr=a andb resp - c _i initial concentration at the timet=0 - D diffusion coefficient - I _n +1/2 modified spherical Bessel function - J _v ,Y _v Bessel function ofv-th order and first and second kind resp - k =b/a} > 1 diameter ratio - P _n ^o () Legendre polynomials - ¯ r, polar coordinates - r, , spherical coordinates - t time - u velocity in radial direction - V ₀ volumetric flow - ₀ V/4D flow parameter for two-dimensional flow - ₀ V ₀/8 D flow parameter for three-dimensional flow - _mn eigenvalues - _mn te] ² =n ² + ₀ ² ,=cos =r/a roots of determinant (28)     

A dynamic slip velocity model for molten polymers based on a network kinetic theory

In this paper the slip phenomenon is considered as a stochastic process where the polymer segments (taken as Hookean springs) break off the wall due to the excessive tension imposed by the bulk fluid motion. The convection equation arising in network theories is solved for the special case of a polymer/wall interface to determine the time evolution of the configuration distribution function (Q, t). The stress tensor and the slip velocity are calculated by averaging the proper relations over a large number of polymer segments. Due to the fact that the model is probabilistic and time dependent, dynamic slip velocity calculations become possible for the first time and therefore some new insight is gained on the slip phenomenon. Finally, the model predictions are found to match macroscopic experimental data satisfactorily.Nomenclature rate of creation of polymer segments - g(Q) constant of rate of creation of polymer segments - rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments due to destruction of its B-link - H Hookean spring constant - k Boltzmann's constant - n unit vector normal to the polymer/wall interface - n ₀ number density of polymer segments - n ₀ surface number density of polymer segments - Q vector defining the size and orientation of a polymer segment - Q ^* critical length of a segment beyond which the tension may overcome the W _adh - t time - t _h howering time of broken polymer segments - T absolute temperature - W _adh work of adhesion Greek Letters _n nominal strain - strain - _n nominal shear rate - shear rate - dimensionless constant in the expressions of h(Q), g(Q) - viscosity - ^T velocity gradient tensor - ₀ time constant - standard deviation of vectors Q at equilibrium - _w wall shear stress - stress tensor - ₀ equilibrium configuration distribution function of Q - configuration distribution function of Q     

Forming limit during superplastic deformation of sheet metals

ＦＯＲＭＩＮＧＬＩＭＩＴＤＵＲＩＮＧＳＵＰＥＲＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＳＨＥＥＴＭＥＴＡＬＳＤｕＺｈｉｘｉａｏ（杜志孝）;ＬｉＭｉａｏｑｕａｎ（李淼泉）;ＬｉｕＭａｂａｏ（刘马宝）;ＷｕＳｈｉｃｈｕｎ（吴诗惇）（Ｆａｃｕｌｔｙ４０２ｏ...     

Stoffaustausch zwischen zwei fluiden Phasen,von denen sich eine als Strahl in der anderen bewegt

Zusammenfassung Der Übergang eines Stoffes zwischen zwei fluiden Phasen wird betrachtet, von denen sich einer als Strahl in der anderen bewegt. Die Geschwindigkeit der laminar strömenden Phase wird durch eine Gleichung ausgedrückt, die Geschwindigkeitsprofile zwischen der Kolben- und der Rohrströmung kontinuierlich beschreibt. Der Transport des Stoffes im Strahl durch Diffusion in radialer und durch Konvektion in axialer Richtung wird für den isothermen, stationären Fall untersucht. Die das Problem beschreibende Differentialgleichung wird anscheinend erstmals geschlossen gelöst. Die Lösungen beinhalten konfluente hypergeometrische Funktionen. Berechnet werden Eigenwerte, Koeffizienten, örtliche und mittlere Konzentrationsfelder sowie Stoffübergangszahlen.

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Mass transfer between two fluids, one of the two fluids is moving as jet within the other

The mass transfer between two fluids is calculated, one of the two fluids is moving as a jet within the other. The velocity of the laminar flowing phase is expressed by an equation, which describes continously the velocity profiles from plug flow to tubular flow. For the isothermal, stationary state the transport of substance i by radial diffusion and by axial convection is investigated. It appears to be that the differential equations describing the problem are solved rigorously for the first time. The solutions contain confluent hypergeometrical functions. Results include eigenvalues, coefficients, local and mean concentration fields, mass transfer numbers.

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Verwendete Zeichen und ihre Bedeutung a - A, A_n Koeffizienten - B, B_n Koeffizienten - c Konzentration, Konstante im Anhang - C_r=0 Mittenkonzentration - c₀ Konzentration in Phase I bis z=0 - c_II Konzentration in Phase II - ¯c mittlere Konzentration, definiert in Gl. (35) - C Koeffizient, definiert in Gl. (A 21) - D Diffusionskoeffizient - Da Damköhlerzahl - E Funktion, gegeben durch Gl. (A 12) - f, f(R) Funktion f von R - f_n, f_n (R) Funktionswerte - g, g(Z) Funktion g von Z - g_n, g_n (Z) Funktionswerte - h(Z) Funktion h von z - H_q Koeffizienten, gegeben durch Gl. (A 10) - j Massenstromdichte - J _k , J_q Besselfunktion der Ordnungk, q - k definiert durch Gl. (A 9) - n laufende Zahl - m laufende Zahl - p laufende Zahl - Pe=Re·Sc Pecletzahl - q laufende Zahl - Q_n Koeffizienten, definiert in Gl. (31) - r radiale Koordinate - r₀ Radius - R r/r₀ - Re=u₀r₀/ Reynoldszahl - S=2r₀z Zylinderfläche - Sc=/D Schmidtzahl - Sh=2r₀ /D Sherwoodzahl - Sherwoodzahl, definiert in Gl. (52) - Sh_u Sherwoodzahl, definiert in Gl. (54) - Sh_z Sherwoodzahl, definiert in Gl. (40) - Sherwoodzahl, definiert in Gl. (45) - t R² - u Geschwindigkeit - u₀ maximale Geschwindigkeit - v - Volumenstrom - w Variable - x Variable - y abhängige Variable - z axiale Koordinate, Lauflänge - Z z/r₀ - Z_Pe dimensionslose Lauflänge, definiert durch Gl. (34) - a_n Koeffizienten, definiert durch Gl. (A 19) - Stoffübergangskoeffizient - Stoffübergangskoeffizient, definiert in Gl. (48) - _u Stoffübergangskoeffizient, definiert in Gl. (49) - _z Stoffübergangskoeffizient, definiert in Gl. (38) - Stoffübergangskoeffizient, definiert in Gl. (44) - definiert in Gl. (A 21) - Gammafunktion - c Konzentrationsdifferenz - m Stoffmenge - Zahl zwischen Null und Eins - laufende Zahl - kinematische Zähigkeit - (v) (t) - konfluente hypergeometrische Funktion - (t) - konfluente hypergeometrische Funktion - , _n Eigenwerte Hochzeichen - * kennzeichnet asymptotische Lösungen     

The bipore model in solid-liquid extraction: the batch process

This paper presents the exact analytical solution for the general case of transient mass transfer between a solid with a biporous structure (with a micro and a macroporosity) and the entouring finite fluid. The transport inside the solid is by molecular diffusion and outside of it the convective film resistance is included. A general expression is given which is valid for the infinite plate, for the infinite cylinder and for the sphere. The standard monopore case is obtained as a particular solution.

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Das Bipor-Modell in der fest-flüssig Extraktion: Das diskontinuierliche Verfahren

Zusammenfassung Es wird die exakte analytische Lösung für den allgemeinen Fall der instationären Stoffübertragung zwischen einem Festkörper mit biporöser Struktur (bestehend aus einer Mikro- und einer Makroporosität) und dem äußeren Fluid vorgestellt. Der Transport in dem Feststoff erfolgt mittels molekularer Diffusion. Außerhalb der Feststoffpartikel wird der konvektive Filmwiderstand berücksichtigt. Eine allgemeine Formel wird angegeben, die für die unendliche Platte, für den unendlichen Zylinder und für die Kugel anwendbar ist. Die Lösung für das übliche monopore Modell ergibt sich als Sonderfall.

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Nomenclature c _a concentration of liquid in micropores - c _b concentration of liquid in macropores - ¯c average concentration in the particle - c₁ initial value of ¯c - c _e concentration in liquid outside the particle - c _e1 initial value ofc _e - D _a ,D _b effective diffusivity in the micro resp. in the macro structure limit ofE for infinite time - f _n form-function defined in Eqs. (20), (21) and (22) - F _n function defined in Eq. (33) - f, g,h Laplace transforms ofc _a ^* ,c _b/* and ¯c^* resp. - I ₀ ,I ₁ modified Bessel functions of the first kind, order zero and first order resp. - J ₀ ,J ₁ Bessel functions of the first kind, order zero and first order resp. - k _c mass transfer coefficient - M _p mass of the solid particles - n numerical form constant, 1 for the plate, 2 for the cylinder and 3 for the sphere - N function defined in Eq. (19) - R _a radius of the microporus spheres - R _b size of the particle (for the plate2R _b is its thickness, for cylinder and sphere: the radius) - r radial coordinate inside the microporous sphere - r ^* =r/R _a adimensional forrt time - t ^* -t/ _b adimensional for time (Fourier Number) - V volume of fluid phase (exterior to solid) - x position coordinate inside the solid particle - x ^* =x/R _b adimensional forx - =(M_pp)/(V_p) volume of fluid inside the particles divided by volume of fluid outside - y=(R _b k _c )/D _b adimensional for the mass transfer coefficient - _a mircoporosity - _b microporosity - _p = _b + (1 _b ) _a total porosity of the particle - =_p/_b – 1=(1 -_b @#@) ( _a / _b ) adimensional parameter, characteristic for the biporous structure - _p density of particle - _a =R _a/2 / (D _a / _a) characteristic (micro) time - _b =R _b/2 / (D _b / _b) characteristic (macro) time - = _a / _b adimensional parameter, characteristic for the biporous particle     

Measurements of thermally stratified pipe flow using image-processing techniques

The cross-correlation technique and Laser Induced Fluorescence (LIF) have been adopted to measure the time-dependent and two-dimensional velocity and temperature fields of a stably thermal-stratified pipe flow. One thousand instantaneous and simultaneous velocity and temperature maps were obtained at overall Richardson numberRi = 0 and 2.5, from which two-dimensional vorticity, Reynolds stress and turbulent heat flux vector were evaluated. The quasi-periodic inclined vortices (which connected to the crest) were revealed from successive instantaneous maps and temporal variation of vorticity and temperature. It has been recognized that these vortices are associated with the crest and valley in the roll-up motion.List of symbols A Fraction of the available light collected - C Concentration of fluorescence - D Pipe diameter - I Fluorescence intensity - L Sampling length along the incident beam - I ₀ Intensity of an excitation beam - I _c (T) Calibration curve between temperature and fluorescence intensity - I _ref Reference intensity of fluorescence radiation - Re _b Reynolds number based on bulk velocity,U _b D/v - Ri Overall Richardson number based on velocity difference,gDT/U ² - t Time - t Time interval between the reference and corresponding matrix - T Temperature - T ₁,T ₂ Temperature of lower and upper layer - T ^* Normalized temperature, (T–T ₁)/T - T _c (I) Inverse function of temperature as a function ofI _c - T _ref Reference temperature - T Temperature difference between upper and lower flow,T ₂ –T ₁ - U ₁ Velocity of lower stream - U ₂ Velocity of upper stream - U _b Bulk velocity - U _c Streamwise mean velocity atY/D=0 - U Streamwise velocity difference between upper and lower flow,U ₁–U ₂ - u, v, T Fluctuating component ofU, V, T - U, V Velocity component of X, Y direction - X Streamwise distance from the splitter plate - Y Transverse distance from the centerline of the pipe - Z Spanwise distance from the centerline of the pipe - Quantum yield - Absorptivity - vorticity calculated from a circulation - Kinematic viscosity - circulation     

Messung des binären Diffusionskoeffizienten in einem Entmischungssystem mit Hilfe der Photonen-Korrelationsspektroskopie

Zusammenfassung Die dynamische Lichtstreuung in Form der Photonen-Korrelationsspektroskopie wird in einem Entmischungssystem beispielhaft zur Messung des binären Diffusionskoeffizienten eingesetzt. Mit einem Versuchsaufbau wird nahe dem kritischen Entmischungspunkt mit der Homodyn-Methode und weit davon entfernt mit der Heterodyn-Methode gearbeitet. Ein Verfahren ermöglicht die Korrektur der Störeinflüsse des Heterodyn-Anteils bei der Homodyn-Messung. Fürn-Hexan/Nitrobenzol wird der Diffusionskoeffizient für vier unterschiedliche Konzentrationswerte als Funktion der Temperatur ausgemessen. Bei der kritischen Konzentration zeigt er bei gleicher Temperatur den kleinsten Wert und läßt sich nahe dem kritischen Entmischungspunkt durch einen einfachen Potenzansatz mit der reduzierten Temperaturdifferenz =T (– T_c)/T_c ausdrücken. Die statistische Genauigkeit ist besser als 1 %. Die Übereinstimmung mit Literaturwerten ist gut.

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Measuring of the binary diffusion coefficient in a separation system with photon-correlation-spectroscopy

The dynamic light scattering in form of photon-correlation spectroscopy is examplary used in a separation system for measuring the binary diffusion coefficient. In a test setup the homodyntechnique is used near the critical separation point and in distance the heterodyn-technique is used. A special method allows the correction of the disturbing influences of the heterodyn-part using the homodyn-measuring. Forn-hexane/nitrobenzene the diffusion coefficient is measured for four different concentration values as a function of temperature. At the critical concentration with constant temperature the coefficient shows the minimum value and it is expressed near the critical separation point with an elementary exponential equation with the reduced temperature difference =T (– T_c)/T_c. The statistical precision is better than 1%. The conformity with the literature is well.

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Abbreviations

Formelzeichen A Konstante - B Konstante - b Konstante - b ₁ Konstante - b₂ Konstante - C Konstante - c Konzentration - c _c kritische Konzentration - D Konstante - D ₁₂ binärer Diffusionskoeffizient - E ₀ elektrisches Feld des Laserlichts - E _s elektrisches Feld des Streulichts - G () Korrelationsfunktion - I ₀ Intensität des Referenzlichts - _s mittlere Intensität des Streulichts - k ₀ Wellenvektor des Laserlichts - k _s Wellenvektor des Streulichts - n Brechungsindex der zu untersuchenden Flüssigkeit - p Druck - q Streuvektor - R Ortsvektor - r Ortsvektor - T Temperatur, Zeit - t Zeit - x Molenbruch Griechische Buchstaben reduzierte Temperaturdifferenz; Dielektrizität - Frequenz des Laserlichts - statistische Schwankungen der Dielektrizitätskonstante - ₀ Wellenlänge des Laserlichts - Streuwinkel - Zeit - _c Zeitkonstante - kritischer Exponent     

Natural convection in partitioned enclosed spaces of solar collector

The two-dimensional, steady, laminar natural convection phenomena in partitioned enclosure of solar collector has been studied numerically. Heat conduction along the partition is considered. An iterative finite-difference scheme is employed to solve the governing equations in the flow field. The effects of Rayleigh number, thermal conductivity ratio, partition angle, tilt angle, and aspect ratio on both the local and average heat transfer coefficients of the solar collector have been discussed. The range of Rayleigh number tested was up to 5 × 10⁴, the thermal conductivity ratio of 4.5 and 30, partition angle from 10 deg to 170 deg, tilt angle from 10 deg to 90 deg, and aspect ratio varied between 0.2 and 10. The results indicate that the convective heat transfer is strongly affected with the aspect ratio of the enclosures.

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Freie Konvektion in unterteilten Kammern von Solarkollektoren

Zusammenfassung Die zweidimensionale, stetige, laminare freie Konvektion in unterteilten Kammern von Solarkollektoren wurde numerisch untersucht. Die Wärmeübertragung entlang dieser Kammern wurde betrachtet. Ein iteratives Finite-Differenzen-Schema wurde angewandt um die Gleichungen, welche das Strömungsfeld beschreiben, zu lösen. Der Einfluß der Rayleigh-Zahl, der thermische Leitfähigkeit, des Kammerwinkels, des Neigungswinkels und der Längenverhältnisse auf die örtlichen und durchschnittlichen Wärmeübertragungskoeffizienten des Solarkollektors wurde diskutiert. Der Bereich der Rayleigh-Zahl erstreckte sich bis zu 5 × 10⁴, das Verhältnis der thermischen Leitfähigkeit betrug 4.5 und 30, der Kammerwinkel lag zwischen 10° und 170°, der Neigungswinkel zwischen 10° und 90° und das Längenverhältnis variierte zwischen 0.2 und 10. Die Ergebnisse beinhalten, daß die konvektive Wärmeübertragung sehr stark durch das Längenverhältnis der Kammern beeinflußt wird.

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Nomenclature a slope of the partition with respect to the horizontal - A H/L=cell aspect ratio - A _w t/L=wall aspect ratio - g acceleration due to gravity - h local heat transfer coefficient - average heat transfer coefficient - H cell length - k thermal conductivity of fluid within the cell - k _w thermal conductivity of the cell wall - L plate spacing - Nu _f h L/k=local cell Nusselt number - L/k=average cell Nusselt number - overall average Nusselt number - qL/k _w t(T _h–T _c)=average wall Nusselt number - Pr /=Prandtl number - q heat transfer in the cell wall from the hot to cold plate per unit depth - Ra g L ³ T/=Rayleigh number - R _k k _w/k=ratio of wall thermal conductivity to that of the fluid - t thickness of cell wall - T _c cold plate temperature - T _f temperature in cell - T _h hot plate temperature - T _w temperature in cell wall - u, U dimension and dimensionless velocities inx-direction - v, V dimension and dimensionless velocities iny-direction - x distance measured from the bottom of the cell (Fig. 1) - X x/L=normalized distance ofx - y distance measured from hot plate (Fig. 1) - Y y/L=normalized distance ofy - x ₁ distance measured in wall (Fig. 1) - X ₁ x/L=normalized distance ofx ₁ Greek symbols thermal diffusivity of fluid - coefficient of volumetric expansion of fluid - partition angle with respect to the hot plate - _f T _f–T _c/T _h–T _c=dimensionless temperature in cell - _w T _w–T _c/T _h–T _c=dimensionless temperature in cell wall - kinematic viscosity of fluid - enclosure tilt angle from horizontal - dimensional vorticity - L ²/=dimensionless vorticity - dimensionless streamline     

Thermal wave propagation within a medium with the inert heat source

A heat conduction equation of a new type is derived which takes into account the finite velocity of heat flux propagation and the relaxation of heat source capacity. The equation is solved for a semi-infinite body and a step change in temperature at the surface. The analysis shows that as the time increases the obtained solution moves from the solution of the classical hyperbolic equation without energy generation towards the solution of the classical hyperbolic equation with energy generation.

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Ausbreitung thermischer Wellen in einem Medium mit träger Wärmequelle

Zusammenfassung Es wird eine neuartige Wärmeleitungsgleichung abgeleitet, welche die endliche Geschwindigkeit der Ausbreitung des Wärmestromes und die Relaxation der Kapazität der Wärmequelle berücksichtigt. Die Gleichung wird für einen halbunendlichen Körper und eine schrittweise Temperaturänderung an der Oberfläche gelöst. Die Analyse zeigt, daß mit zunehmender Zeit sich die Lösung der klassischen hyperbolischen Gleichung ohne Wärmeerzeugung in eine solche mit ebenfalls klassischer hyperbolischer Gleichung mit Wärmeerzeugung wandelt.

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Nomenclature a thermal diffusivity,k/( c _p - c _p specific heat at constant pressure - C speed of heat propagation - C ₁,C ₂ constants - k thermal conductivity - q _v steady capacity of internal heat source - q _vd transient capacity of internal heat source - r ₁,r ₂ roots of characterisitc equation - t time - t _k relaxation time of heat flux - t _q relaxation time of internal heat source capacity - T temperature - T ₀ surface temperature - u() unit step function - x, y, z Cartesian coordinates - X dimensionless coordinate - , constant coefficients - dimensionless temperature - density - dimensionless time - _r-t_qt_k ratio of relaxation times - dimensionless steady capacity of internal heat source - _d dimensionless transient capacity of internal heat source     

The Reissner–Sagoci Problem for a Non-homogeneous Half-space with a Surface Constraint

This paper deals with the problem of twisting a non-homogeneous, isotropic, half-space by rotating a circular part of its boundary surface (0 r < a, z = 0) through a given angle. A ring (a < r < b, z = 0) outside the circle is stress-free and the remaining part (r > b, z = 0) is rigidly clamped. The shear modulus is assumed to vary with the cylindrical coordinates, r, z by the relation (z) = ₁(c + z), c 0 where ₁, c and are real constants. Expressions for some quantities of physical importance, such as torque applied at the surface of the disk and stress intensity factors, are obtained. The effects of non-homogeneity on torque and stress intensity factor are illustrated graphically.     

Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

For many solid materials the stress relaxation process obeys the universal relationF = – (d/d lnt)_max = (0.1 ± 0.01) ( ₀ — _i ), regardless of the structure of the material. Here denotes the stress,t the time, ₀ the initial stress of the experiment and _i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storageE () and lossE () moduli. Useful numerical approximations ofE () andE () are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence ofE (). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.     

Reynolds number dependence of the drag coefficient for laminar flow through electrically-heated photoetched screens

Experiments are performed to measure the drag coefficient of electrically-heated screens. Square-pattern 80 mesh and 100 mesh screens of 50.8 m-wide wires photoetched from 50.8 m thick Inconel sheets are examined. Ambient air is passed through these screens at upstream velocities yielding wire-width Reynolds numbers from 2 to 35, and electrical current is passed through the screens to generate heat fluxes from o to 0.17 MW/m², based on the total screen area. The dependence of the drag coefficient on Reynolds number and heat flux is determined for these two screens by measuring pressure drops across the screens for a variety of conditions in these ranges. In all cases, heating is found to increase the drag coefficient above the unheated value. A correlation relating the heated drag coefficient to the unheated drag coefficient is developed based on the idea that the main effect of heating at these levels is to modify the Reynolds number through modifying the viscosity. This correlation is seen to reproduce the experimental results closely.List of Symbols A total screen cross sectional area - C fitting coefficient, near unity - c _D heated drag coefficient - c _{D, 0} unheated drag coefficient - C _p air specific heat at constant pressure - D photoetched wire width, sheet thickness - h _s stagnation point heat-transfer coefficient - k air thermal conductivity - M distance between adjacent wires - O open area fraction - p air pressure - p air pressure drop across screen - Pr Prandtl number for air, c _p/k - Q total electrical power to screen - R radius of curvature at stagnation point - Re _D wire width Reynolds number, UD/ - T air temperature - U air speed upstream of screen - air specific heat ratio - air density - air viscosity - exponent in temperature power law for viscosity - () quantity () evaluated at heated screen temperature The authors thank John Lewin and Bob Meyer for their assistance in the design and fabrication of the heated screen test facility and Tom Grasser for his help in performing the experiments. This work was performed at Sandia National laboratories, supported by the U.S. Department of Energy under contract number DE-AC04-94AL85000.