Heat flux measurement from the temperature field of a heated surface. 2. Inhomogeneous flux

Based on the previously obtained analytical solutions of the three-dimensional space-time problem of recalculating boundary conditions, algorithms are developed and a computational experiment is carried out to reconstruct the heat flux with arbitrary spatial distribution of the temperature field of the heated surface.Notation T(t, ) temperature over the plate surface - q(t ) heat flux to the plate surface - ={x,y} transverse coordinate - t time - k thermal conductivity - a ² thermal diffusivity - L plate thickness - Jacobi theta-function [4] - Fourier parameter - Jacobi theta-function [4] - transversal Laplacian Institute of Atmospheric Optics, Siberian Division, Russian Academy of Sciences, Tomsk, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 622–628, July–August, 1995.     

Heating of a bulky body by a circular heat source with heat elimination from the surface taken into account

Results of an analytical and numerical solution of the problem, in a form suitable for the determination of material properties, are given.Notation =(t–t_c)/(q₀R) and T= Bi= (t–t_c)/q₀ dimensionless temperature - q₀ heat flux, W/m² - Bi=R/ Blot criterion - R radius of the heating spot, the characteristic dimension, m - ¯r, ¯z radius and depth, m - r=¯r/R, z=¯z/R dimensionless radius and depth - time, sec - Fourier number - criterion - coefficient of heat elimination, W/m²·deg - heat conductivity, W/m·deg - c specific heat, J/kg·deg - density, kg/m³ - a thermal diffusivity, m²/sec - t _c temperature of the external medium Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 524–526, March, 1981.     

Nonstationary process of heat transfer in a tube with longitudinal fins

An analytical solution to the problem of nonstationary thermal interaction of a flow of a heat-transfer agent and a thin-walled tube with longitudinal fins is constructed for variable parameters of heat transfer.Notation u, temperatures of the fins - ,w temperatures of the tube walls - temperature of the flow of the heat-transfer agent - _i ,i= coefficients of heat transfer from the ambient medium to the fins and the tube walls, respectively - _i ,i= temperature distributions for the ambient medium - coefficients of heat transfer from the flow of the heat-transfer agent to the tube walls - q _i density of the heat flux to the corresponding portions of the tube - heat capacity, thermal conductivity, density, and thickness of the fin and tube material - c _p , ,G, F heat capacity, density, and flow rate of the heat-transfer agent, cross-sectional area of the tube - dimensions of the tube Bauman Moscow State Technical University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 673–680, June, 1994.     

Solution of the inverse boundary-value problem of heat conduction in an overdefined formulation

An interaction scheme is considered for the solution of a nonlinear inverse heat-conduction problem with the results of measuring the temperature at an arbitrary number of points within the body taken into account.Notation n number of temperature measurement points - , t time - _p, t_p length of the time interval - x a space coordinate - X_i(t) coordinates of the temperature measurement points - T(x, t) temperature - C(T) bulk specific heat of the material - (T) coefficient of material heat conduction - T(x, 0) initial temperature distribution - q heat flux density - f_i(t) , temperature measurement - ⁱ(z_i, t) , conjugate variable - ⁱ(z_i, t) , temperature variation - , , p parameters of the conjugate gradient method - s number of iteration - l number of points in a discrete representation of the time function - an error estimate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 776–781, November, 1983.     

On the motion of a curved and twisted rod

Summary In this paper, the equations of motion of a curved and twisted rod are derived from the basic principles of dynamics. The set of equations gives the extensional, flexural and torsional motions of the rod. The coupling among these types of motion due to the curvature and tortuosity of the rod is shown explicitly in the case of a helical spring. By successive simplification of the equations, the equations of motion of a circular ring and those of a straight rod are obtained. In this respect, the derived equations can be considered as a generalization of the elementary theories of rod in extensional, torsional and flexural motion.The dispersion relation of a helical spring is calculated for the two lower frequency modes. It is shown that the frequency-wave length relationship is not monotonically decreasing as in the cases of uncoupled flexural or torsional motion. Finally, frequencies are calculated based on the approximate frequency expression ofLove to show that Love's frequency expression for a helical rod is accurate.

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Zur Bewegung eines gekrümmten und verdrillten Stabes

Zusammenfassung In dieser Arbeit werden die Bewegungsgleichungen eines gekrümmten, verdrillten Stabes von den Grundgleichungen der Dynamik hergeleitet. Dieses System von Gleichungen legt die Bewegung des Stabes durch Längsdehnung, Biegung und Torsion fest. Die Kopplung dieser Bewegunsarten, durch Krümmung und Verdrillung, wird für den Fall einer Spiralfeder explizit gezeigt. Durch Vereinfachung der Gleichungen werden die Bewegungsgleichungen des Kreisringes und die des geraden Stabes erhalten. In dieser Hinsicht können die hergeleiteten Gleichungen als Verallgemeinerung der elementaren Theorein der Bewegung eines Stabes betrachtet werden.Die Dispersionsgleichung der Spiralfeder wird für die beiden niedrigsten Frequenzen berechnet. Es wird gezeigt, daß das Verhältnis Frequenz-Wellenlänge nicht wie in den Fällen der ungekoppelten Biege-oder Torsionsbewegung monoton abnimmt. Abschließend werden die Frequenzen nach dem Loveschen Näherungsausdruck berechnet, um zu zeigen, daß die Genauigkeit dieses Ausdruckes für Spiralfedern gut ist.

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Nomenclature position vector of a point on axis of curved rod - position vector relating any pointB in a plane perpendicular to the axis of the rod to pointP where plane cuts axis of rod - R modulus of - linear momentum vector - density - axial force vector = - axial force vector at origin - transverse shear force vector - transverse shear force vector at origin - moment vector - moment vector at origin - s distance measured along axis of rod - t time - a radius of gyration of rod for circular sections - l total length of spring along axis - A cross-sectional area of rod - s/a — normalized coordinates measured along axis of rod - applied load vector - angular momentum vector - trihedral of space curve-unit vectors in tangential, normal and binormal directions - _t axial rotation - displacement vector - normalized displacement vector= - ₀,₀ curvature and tortuosity of rod - , normalized curvature and tortuosity of rod - , circular frequency and normalized frequency respectively - E, G Young's modulus and shear modulus - v Poisson's ratio - Wave number - pitch angle of helical spring - d wire diameter of helical spring - R coil radius of helical spring - N number of turns of helical spring With 5 Figures     

Calculation of the optical characteristics of radiation heat transfer in furnace chambers

A software system for calculating the problems of radiation heat transfer in two-phase media is considered. Results of the calculation of a radiation field in the combustion chamber of a specific steam generator are presented.Notation I(x, y, ) spectral intensity of radiation at the point (x, y) in the direction - B(T) spectral intensity of black body radiation at the temperature T=T(x, y) - , spectral coefficients of absorption and scattering of radiation - external normal to the boundary of the region - and T spectral emissivity factor and temperature of the heat-absorbing surface - Q density of the radiation flux incident on the chamber heat-absorbing surface Academic Scientific Complex A. V. Lyukov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 308–312, March, 1993.     

Stresses in a cylindrical shell supported by a core of a different material

Summary The stress problem of a thin cylindrical shell supported by an elastic core of a different material and subjected to arbitrary loading on its curved surface is considered. The problem is solved by applying the three-dimensional theory of elasticity to the core and using membrane or bending solutions for the shell. Equilibrium and compatibility equations are satisfied at the junction of the shell and the core. It is pointed out that the procedure can easily be extended to the case of a hollow core with or without another shell of another material in it. Numerical results are presented to illustrate the effectiveness of even a weak core in reducing the shell stresses.

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Zusammenfassung Gegenstand der Untersuchung ist eine dünne Kreiszylinderschale, die durch einen elastischen Kern aus einem anderen Werkstoff gestützt ist und eine beliebige Belastung trägt. Die Lösung verbindet die strenge, dreidimensionale Theorie des zylindrischen Kerns mit der Membran- oder Biegetheorie der Schale. An der Grenze zwischen beiden Teilen müssen die Verschiebungen und gewisse Spannungskomponenten stetig übergehen. Es wird darauf hingewiesen, daß die Lösung leicht auf den Fall ausgedehnt werden kann, daß der Kern ein Hohlzylinder ist, der möglicherweise auf der Innenseite mit einer zweiten Zylinderschale verbunden ist. Zahlenergebnisse zeigen, daß selbst ein verhältnismäsig nachgiebiger Kern einen großen (und günstigen) Einfluß auf die Spannungen in der Schale ausübt.

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Principal Symbols a Radius of the middle surface of the shell - t Thickness of the shell - =1–t/2a - u _c,v _c,w _c Displacements respectively in the axial, circumferential and radial directions of a point in the core - X(x), (), (r/a) 3×3 square matrices - ,m Parameters - l Length of the cylinder - c A vector containing constantsc ₁,c ₂ andc ₃ - =r/a - =m+4(1–v _e) - E _c,v _e Elastic constants for the core material - Stresses at a point in the core - D _c - A vector containing _rx , _r and _r - (r/a) A 3×3 matrix - Displacements at the surfacer=a of the core - A vector containing - Amplitudes of displacements - A vector containing - =(x, ,a) - _ij Constants - A A square matrix containing constants _ij - Stress resultants in the shell as defined in reference [3] - p _x,p ,P _r Components of applied loading per unit area of shell's middle surface - () - ()· - u, v, w Displacements of a point on the middle surface of the shell - E _s,v _s Elastic constants for the shell material - D _s - K - k - p _xmn,p _mn,p _rmn Amplitudes of loadsp _x,p , p_r - u _mn, v_mn,w _mn Amplitudes of displacementsu, v, With 1 Figure     

Evidence of a new vicinal state on the4He crystal interface

Equilibrium shape of hcp⁴He crystals has been studied at low temperatures by means of a high resolution optical interferometer. The profile of the crystalline interface next to a horizontal c-facet was found to have a well defined border line separating two regions characterized by different angular behavior of the surface stiffness . For surfaces tilted by a small angle 10^–4 rad with respect to the facet, we find 1/, contrary to the dependence predicted by current theories. The tremendous increase of surface stiffness in the close vicinity to the facet orientation may be considered as strong evidence of a new surface state.     

Hydrodynamics of a vortex ring

We considered the kinematics and dynamics of a vortex ring in an incompressible fluid in toroidal coordinates. We obtained the change in the pressure difference along the boundary between two flow regions in the case of a moving torus.Notation , , toroidal coordinates - (V ;V ;V ) velocity of a fluid particle and its projections in toroidal coordinates - g ,g ,g metric tensor components - the Jacobian of transition to curvilinear coordinates - V ₀ velocity at the center of a vortex ring on its symmetry axis - x, y, z Cartesian coordinates - z, y, cylindrical coordinates - a distance from the axis of a torus (V=0) to its axis of symmetry (Oz) - angle between the Oy axis and the line that connects a fluid particle on the streamline =const, which represents a circle [16], with the center of this circle - U _z,U _y velocities in the cylindrical system of coordinates - ₀ stream function of a stationary vortex ring - velocity circulation - U V ₁, velocity of a rectilinear flow at infinity - ₁ stream function of a rectilinear flow - = ₀ + ₁ superposition of two flows - n=k ⁴=V ₁/V ₀ velocity ratio coefficient - R radius of a vortical region - U velocity of fluid particles at the boundary in polar coordinates (r, ) with the center at the coordinate origin (point 0) - fluid density - p ₀,p pressure at infinity and at a certain point of flow - pressure difference Polotsk State University, Polotsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 531–536, July–August, 1995.     

Optimization of multilayer thermal insulation

An iteration method is developed for determination of the thicknesses of layers of a multilayer thermal insulation with minimum mass, with consideration of temperature limitations. The penalty function method is employed.Notation M(h) target function - _i thickness of the i-th layer - p_i density of material in i-th layer - n number of layers of thermal insulation - y spatial coordinate - t time - Y_i, i = 0, 1, 2, ..., n coordinates of layer boundaries - Cⁱ(T) volume heat capacity of material in i-th layer - ⁱ(T) thermal conductivity coefficient of material in i-th layer - (y) initial temperature distribution - q thermal flux - t_c right-hand value of time interval - T _max ⁱ , i = 1, 2, ..., n maximum admissible temperatures on i-th boundary - penalty function - penalty parameters - g_i function considering temperature limitations - transformed function - k number of successive unconditional minimization problem - l number of iteration in search for local minimum - ,, s parameters of conjugate gradient method Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 286–291, August, 1980.     

Nonlinear liquid oscillations in spherical systems under zero-gravity

Summary Nonlinear free oscillations of the interface of a concentric frictionless immiscible liquid system in a spherical container are investigated in a zero-gravity environment. The natural frequencies are determined for the axisymmetric and asymmetric oscillations of the interfacial surface with the diameter ratio and density ratio as parameters. It was found that for small outer- to inner liquid density ratio the oscillations exhibit softening, while for large density ratios it renders hardening oscillation. The asymmetric oscillations exhibit in the softening range softer and in the hardening range harder liquid oscillations. For a liquid layer around a rigid center sphere the oscillations of the free liquid surface yields softening behavior, where for thinner layers the softening effect is more pronounced.Nomenclature a radius of spherical container, or radius of rigid center sphere - b radius of undisturbed interfacial surface, or radius of undisturbed free liquid surface - k=a/b diameter ratio - pressure - pressure (dimensionless) - , , spherical coordinates - dimensionless radius - R _i main radii of curvaturei=1, 2 time - dimensionless time - v _i liquid velocity (j=1 spherical layer region,j=2 inner liquid sphere region) - V volume of the liquid - Y _nm tesseral surface harmonics - _i density of liquids - velocity potential - dimensionless velocity potential - interfacial surface- or free surface elevation - dimensionless interfacial surface- or free surface elevation - ₀ maximum elevation - circular frequency - circular frequency - _n0 axisymmetric natural frequency - _n1 asymmetric natural frequencym=1 - _nm ⁽⁰⁾ natural frequency of linearized liquid system - mean curvature - _nm Kronecker symbol With 10 Figures     

Higher approximations for supersonic flow past slowly oscillating bodies of revolution

Summary Supersonic flow past slowly oscillating pointed bodies of revolution is studied. Starting from the complete nonlinear potential equation an elementary linearized solution is discussed and it is shown how this solution together with the method of matched asymptotic expansions can be used to derive an elementary second-order slender body theory. This approach is further demonstrated for the oscillating cone and its range of validity is evaluated by comparison with other theoretical methods.

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Zusammenfassung Es wird die Überschallströmung um langsam schwingende spitze Rotationskörper untersucht. Ausgehend von der vollständigen nichtlinearen Potentialgleichung wird zuerst eine elementare linearisierte Lösung besprochen und gezeigt, wie diese Lösung im Verein mit der Method of matched asymptotic expansions zur Herleitung einer elementaren Schlankkörpertheorie zweiter Ordnung verwendet werden kann. Die Theorie wird am Beispiel des schwingenden Kegels näher erläutert und mit anderen Methoden verglichen.

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Symbols a Velocity of sound - c _N Normal force coefficient - Damping coefficient - F _(x) Dipole distribution - k Reduced frequency - M Mach number - R (x) Meridian profile - t Time - x, r, Cylindrical coordinates - - Ratio of specific heats - Amplitude of oscillation - Thickness ratio - Perturbation potential - Zero angle of attack potential - æ - Velocity potential - Out-of-phase potential - - In-phase potential - - Source coordinate With 4 Figures     

Eine Erweiterung der Analogie zwischen der Gasdynamik und Flachwasserströmungen auf rotierende Systeme mit konservativen Massenkräften

Zusammenfassung Die bekannte Analogie zwischen den Theorien reibungsfreier flacher Wasserströmung und der isentropen idealen Gasdynamik wird im zweidimensionalen instationären Fall durch Zulassung rotierender Bezugssysteme und konservativer Massenkraftfelder erweitert. Damit kann man in einem rotierenden Wasserbehälter mit geeignet gestaltetem Boden u. a. atmosphärische Probleme näherungsweise studieren.

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Summary The well known analogy of the theories of nonviscous shallow water flows and isentropic ideal gasdynamics is generalized in the two-dimensional nonstationary case to apply to rotating systems with conservative body forces. This enables one, in particular, to simulate atmospheric problems by use of a rotating water tank with suitable bottom shape.

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Liste der verwendeten Symbole spezifische Wärme des Gases bei konstantem Druck - Fr in (2) definierteFroude-Zahl - Gravitationsbeschleunigung - H ortsabhängige Ruhetiefe bei Drehung des Wassers als starrer Körper - Druck - atmosphärischer Druck auf der freien Wasseroberfläche - Bezugslänge - Zeit - absolute Temperatur - Geschwindigkeitskomponenten parallel zu den Achsen - kartesische Koordinaten - durch Abweichung von der Drehung des Wassers als starrer Körper verursachte orts-und zeitabhängige Änderung der Wassertiefe - Verhältnis der spezifischen Wärmen des Gases - zu gehörende Wellenlänge - Dichte - Winkelgeschwindigkeit Mit 1 Textabbildung1 Boden des Wasserbehälters 2 freie Wasseroberfläche II freie Wasseroberfläche bei einer Drehung des Wassers als starrer KörperEin oberer Querstrich gibt an, daß die betreffende Größe eine physikalische Dimension hat; Größen ohne einen solchen Querstrich sind dimensionsfrei.     

Slip flow past an approximate spheroid

Summary Creeping axisymmetric slip flow past a spheroid whose shape deviates slightly from that of a sphere is investigated. An exact solution is obtained to the first order in the small parameter characterizing the deformation. As an application, the case of flow past an oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are deduced and some observations made.Notation A _n, B_n, C_n, D_n, E_n, F_n, b₂, d₂ Constants - a, b radii of spheres - coefficient of sliding fraction - D drag - , _m parameters characterizing the deformation of the sphere - c a(1+) - viscosity coefficient - - dimensionless coordinate - I _n Gegenbauer function - P _n Legendre function - Stream function - U stream velocity at infinity     

Effect of nonlinearity of gas mixtures on the process of their partition by thermal diffusion

Under consideration is the effect of nonideality of the components in a gas mixture on the process of their separation by thermal diffusion. It is demonstrated that in the expressions for the heat flux and the mass flux, the thermodiffusion ratio and the characteristic of diffusional thermal conductivity the effect of nonideality appears in the heat of mixing.Notation p pressure - density - length of the mean free path for molecules during transport of particles - length of the mean free path for particles during a transfer of the mean velocity - n molecule concentration - M molecular weight - I particle flux - J mass flux - m mass of a molecule - t time - D_ij coefficient of interdiffusion for a binary mixture - D _i ^T coefficient of thermal diffusion - K_T thermodiffusion ratio - _T thermodiffusion constant - x_i molar fraction of the i-th component in the mixture (r), intermolecular interaction potential - r intermolecular distance - collision integrals - T temperature - T^* referred temperature - R universal gas constant - k Boltzmann constant - Ñ Avogadro's number - v mean velocity of molecules - ¯V diffusion rate - _{i, trans} thermal conductivity associated with translatory degrees of freedom - f_i(r, v, t) velocity distribution function of molecules - viscosity - _i chemical potential of the i-th component - c_i mass fraction - _o thermal conductivity at the initial instant of time - thermal conductivity in the steady state - _DT diffusional component of thermal conductivity - g and h molar thermodynamic functions - ¯g and ¯h specific thermodynamic functions - c_p specific heat - J_q heat flux - J_q reduced heat flux - B second virial coefficient - U^* transport energy - coefficient of thermal expansion - coefficient of isothermal compression - f_i activity coefficient for the i-th mixture component Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 829–839, May, 1981.     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

Heat flow model of rapid solidification with nonhomogeneous thermal contact

A heat flow model is presented of the solidification process of a thin melt layer on a heat conducting substrate. The model is based on the two-dimensional heat conduction equation, which was solved numerically. The effect of coexisting regions of good and bad thermal contact between foil and substrate is considered. The numerical results for thermal parameters of the Al-Cu eutectic alloy show considerable deviations from one-dimensional solidification models. Except for drastic differences in the magnitude of the solidification rate near the foil-substrate interface, the solidification direction deviates from being perpendicular to the substrate and large lateral temperature gradients occur. Interruption of the thermal contact may lead to back-melting effects. A new quantity, the effective diffusion length, is introduced which allows some conclusions to be drawn concerning the behaviour of the frozen microstructure during subsequent cooling.Nomenclature _i ,a _i Thermal diffusivity _i = _i /c _{i i} ,a _i = _i / ₁ - c _i Specific heat capacity - d Foil thickness - D Solid state diffusion coefficient - e_x, e_z Unit vectors - H Latent heat of fusion - h ,h Foil-substrate heat transfer coefficients - i Index: 1, melt; 2, solidified foil; 3, substrate - _i ,k _i Thermal conductivityk _i = _i / ₁ - n Normal unit vector - Nu ,Nu Nusselt numbers for regions of badNu(x,) and good thermal contact, respectivelyNu =h Nu _d / ₁,,Nu(x, )=h(x,)d/ ₁ - R Universal gas constant - , s Position of the liquid-solid interface ¯s/d=s=s _xe_x+s _ze_z - Local solidification rate /d = s =s _xe_x +s _ze_z - t Real time - T _i Temperature field - T ₀ Ambient temperature - T _f Melting temperature - u _i Dimensionless temperature fieldu _i (x, z,)=T _i (x,z,)/T _f - u ₀ Dimensionless ambient temperatureu ₀=T ₀/T _f - _i Local cooling rate within the foil _i = du _i /d - W Stefan numberW=H/c ₁ T _f - ,x Cartesian coordinate parallel to the foil-substrate interfacex= /d - ₀,x ₀ Lateral extension of foil sectionx ₀= ₀/d - ₁,x ₁ Lateral contact lengthx ₁= ₁/d - ,z Cartesian coordinate perpendicular to the foil-substrate interfacez= /d - ₀,z ₀ Substrate thicknessz ₀= ₀/d - E Activation energy of diffusion - T Initial superheat of the melt - u Dimensionless initial superheat u=T/T _f - (x) Step function - _eff Dimensionless effective diffusion length - _i Mass density - Dimensionless time=t ₁/d ² - _f, _f(x, z) Total and local dimensionless freezing time, respectively     

Temperature-density parameters of Freon-13 on the saturation line

Experimental data of a high degree of accuracy are presented on the temperature-density parameters of Freon-13 on the saturation line in the density range of (0.08246–1.6061)·10 kg/m³.Notation T absolute temperature of phase transition from two-phase to one-phase state (or vice versa) - T_c critical temperature - , densities of liquid and vapor, respectively, on saturation line - _c density at critical points - average density - =(T_c–T)/2 reduced temperature - parameter of order, equal to ' – _c – b for the liquid phase and _c + b – "for the vapor phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 830–834, November, 1979.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Construction of explicit functions for determining the coefficients of internal heat and mass transfer from the data of measurements in nonstationary regimes

For a number of laws governing the variation of the characteristics of internal heat and mass transfer with respect to a spatial variable, we derive explicit functions relating them to the results of measurements of nonstationary temperatures or other potentials.Notation time - r coordinate - T temperature - thermal conductivity - c volumetric heat capacity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 794–797, November, 1983.