Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.Notation u temperature - k coefficient of thermal conductivity - t time - x spatial variable - x₊ a point on the thermal wave front - a ² generalized coefficient of thermal diffusivity - , , , and s parameters of the process - (x^s) Dirac delta-function - B[, ] a beta function - v(, x), (t) auxiliary functions - A, C, T_o, T_m, T*, R, r, p, and _m constants and parameters Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.     

Hydraulic characteristics and vapor content in a channel with boiling of a liquid underheated up to the saturation temperature

A method is proposed for calculating the hydraulic characteristic and vapor content in a channel with underheated boiling.Notation H heated length of channel - d_t thermal diameter - d_h hydraulic diameter - _t thermal perimeter - _h hydraulic perimeter - s through cross section - N power of channel - q heat flux - G weight flow rate - W velocity - coefficient of heat transfer - t, T temperatures - t temperature difference - i enthalpy - P pressure - P pressure drop - x weight vapor content - volumetric vapor content - C_p heat capacity - r heat of vaporization - coefficient of thermal conductivity - coefficient of surface tension - liquid density - vapor density - g acceleration of gravity - _o coefficient of friction of liquid against the channel wall - shear stress - density of two-phase medium averaged over a channel cross section - dynamic viscosity Indices s on saturation line - en at channel entrance - l liquid - v vapor - w wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 784–792, November, 1979.     

Molar momentum and heat transfer

Universal relations governing the molar transfer of momentum and heat are derived on the basis of a hypothesis about the dependence of the boundaries of the molar transfer region on the flow structure and with the use of a special mathematical transformation.Notation u average longitudinal velocity, m/sec - T average temperature, °K - T_w wall temperature, °K - kinematic viscosity coefficient, m²/sec - density, kg/m³ - c_p specific heat, J/kg·K - tangential stress, N/m² - t_w tangential stress at wall, N/m² - q_w specific heat flux at wall, W/m² - u_*=_w/ dynamic velocity, m/sec - *=q_w/c_pu_* characteristic temperature, °K - thickness of boundary layer, m - ₀ thickness of laminar sublayer, m - l = /u transverse space scale of average mole at wall, m - y⁺ = y/l _22C6; dimensionless coordinate - u⁺=u/u* dimensionless velocity - ⁺=(T_w – T)/* dimensionless temperature - ⁺=/_w dimensionless tangential stress - R=In (y⁺/ _o ⁺ )/In (⁺/ _o ⁺ ) generalized dimensionless co-ordinate - U = (u⁺ - u _o ⁺ )/(u _o ⁺ - u _o ⁺ ) generalized dimensionless velocity - Pr Prandtl number Indices * flow parameters evaluated at y⁺=1 - parameters at y⁺=⁺ - 0 parameters at y⁺= _o ⁺ - w parameters at wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 441–448, September, 1981.     

Residual strain and texture in strontium-doped lanthanum manganite thin films

Thin films of La_0.67Sr_0.33MnO₃ (LSMO) have been deposited using liquid-delivery metal-organic chemical vapor deposition (MOCVD). X-ray diffraction (XRD) 2/ scans showed that all the films has a cubic structure. Studies of the in-plane crystallographic orientations (pole figure) revealed an (0 0 1) preferred growth structure on LAO, a weak (1 1 0) texture on Y-ZrO₂ (YSZ), a random texture on sapphire (SAP) and silicon (Si). Our attention is focused on residual strain and its deviations from linearity for vs. sin² plots. The strain evolution from 02<0.8 showed a curvature and a snake-like pattern. These anomalies are attributed to texture and strain gradients. In-plane strain decreased as the lattice mismatch increased and varied from 0.05 to 3.03% depending on the substrate. An attempt is made to establish a relationship between lattice mismatch, growth process, and residual strain.     

Heat transfer of cylindrical bodies when a system of round jets flows over them

An experimental installation for the study of the heat transfer of cylindrical bodies in interaction with multijet streams is described. The test data are generalized in criterial dependences with allowance for the range of variation of the heights of rise of the cylinders above the jet grids.Notation D, d diameters of cylinders and of openings of jet grid, m - R radius of jet grid, m - h, h=h/d absolute and relative heights of rise of cylinder above jet grid - S₁, S₂ longitudinal and transverse distances between rows of openings in jet grid, m - w average discharge velocity of jets, m/sec - , average and local coefficients of heat transfer, W/m²·deg - , coefficients of thermal conductivity and kinematic viscosity, W/m·deg, m²/sec - Nu_d=d/ Nusselt number - Re_d=wd/ Reynolds number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 773–776, November, 1979.     

Use of adjoint functions in investigations of heat conduction and transfer processes

An examination is made of the use of adjoint functions in heat conduction and convection theory. Formulas of perturbation theory are obtained for steady and unsteady cases, an interpretation of the physical meaning of adjoint temperature is given, and some applications of the theory are discussed.Notation (r,) thermal conductivity - t(r,) temperature - t *(r,) adjoint temperature - q_V(r,) density of heat release sources - p(r,) a parameter of adjoint equation - r generalized coordinate - time - (r_s, ) heat transfer coefficient - I linear functional of temperature - (r,;r₀,₀) and *(r,; r₀,₀) Green's function for t(r, ) and t *(r, ) - C(r,) volume specific heat - W(r, ) vector distribution of flow velocities - V, S volume and surface areas of body - R radius of HRE - r, radial and angular coordinates - F_in, F_out inlet and outlet flow areas of channel     

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.     

Unsteady motion of a fluid near a disk rotating in a magnetic field

The effect of a magnetic field on the velocity distribution in a fluid close to an unsteadily rotating disk is investigated.Notation r, , and z coordinates in the radial, circular, and axial directions - t time - u, v, and w radial, circular, and axial velocity components - u₀ radial velocity of external potential flux - v₀ circular velocity of the disk - (t) angular velocity of the disk - p pressure - density - v kinematic viscosity - B₀ characteristic of the applied magnetic field - electrical conductivity of fluid - R and Z dimensionless coordinates in the radial and axial directions - =Z/2 dimensionless coordinate - T dimensionless time - U, V, and W radial, circular, and axial components of dimensionless velocity - P dimensionless pressure - a, , and ₀ constants with dimensionality t^–1 - m, n, and positive numbers - k =a constant - = = B ₀ ² / parameter characterizing the magnetic field     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Heat exchange in two-phase flow about a surface located in a rectangular channel

Similitude equations are obtained on the basis of the principle of superposition of separate effects to calculate heat exchange between surfaces with complexshaped cross sections located in a rectangular channel during their cooling by a two-phase flow.Notation T, q temperature and heat flux - T_w mean surface temperature - I, R current and electrical resistance - V volume of the material - , , anda heat-transfer coefficients, thermal conductivity, and linear expansion of the material - relative functions - =_m; ^* = _m ^{* *} _s ^* ; temperature factor - X relative weight content of liquid phase Indices w surface - f incoming flow - v volume - m two-phase flow - angle of attack - s shape of surface - * pertains to surface with swirl vanes Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 780–786, May, 1980.     

The mechanism of adhesion of moist powders to solid surfaces in the presence of a temperature field

An examination is made of the basic factors which influence the creation of forces causing powders to adhere to solid surfaces in the presence of a temperature field. An experimental investigation has been conducted on an apatite concentrate.Notation p_c capillary pressure - density of fluid - g acceleration due to gravity - h_cap, h limiting and actual height of capillary rise - surface tension - r radius of equivalent capillary - q specific suction force - k_w water saturation coefficient - V_w volume of water in pores - V_pore volume of pores - Wg humidity by weight - R particle radius - polar angle - _c area of contact - N total adhesive force - _m, _w specific weight of powder and water     

Joule-Thompson effect in a disperse medium

An expression for the Joule-Thompson coefficient of a polydisperse medium subject to throttling is derived in the relaxation approximation of thermodynamics of irreversible processes, with both temperature and velocity relaxation in the phases taken into account.Notation A_qk, A_fk thermal and momentum interphase exchange affinities - _qk, _fk relaxation parameters - T, w temperature and velocity of a phase relaxation in the mixture - density of the mixture - T_o, T_k temperature of the carrier phase and of the k-th group of solid particles - p pressure of the carrier phase - h enthalpy of the mixture - W _o ² /2 specific kinetic energy of the carrier phase - _o, _k volume concentration of the carrier phase and of the k-th group of solid particles - _o, _k true density of the carrier phase and of the k-th group of solid particles - c_v and c_p constant-volume and constant-pressure specific heats of the mixture - c_k specific heat of the k-th group of solid particles - c_v, c_p constant-volume and constant-pressure specific heats, respectively, of the mixture referred to volume - _qk, _fk temperature and velocity relaxation times, respectively, of the k-th group of solid particles - t times - frequency in the Fourier series expansion - differential Joule-Thompson coefficient (adiabatic throttle effect) - N number of groups of particles in the mixture Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 825–829, November, 1979.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

o′-β′ sialon ceramics

Powders of Si₃N₄, Al₂O₃ and SiO₂ were mixed with Y₂O₃ as sintering aid and hot-pressed to form o- sialon. During sintering, the o phase preferentially precipitated in the temperature region of 1550 to 1600 °C, and the phase precipitated at temperatures of 1700 °C and above. The resultant microstructure consisted of dual phases of o and . The mechanical properties of o- sialon were improved with increasing amount of the phase. When SiO₂ required for the formation of the o phase was all included in the grain boundary phase, o- sialon exhibited a three-point bending strength as much as 1400 MPa. The oxidation resistance of o- sialon is expected to improve due to the presence of the o phase, but actually was not so good due to the presence of the grain-boundary glassy phase and impurities.     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Structure and Diamagnetic Properties of (Pb0.6SnyCu0.4 ? y)Sr2(Y1 ? xCax)Cu2Oz

The effect of Sn doping in (Pb_0.6Sn _y Cu_{0.4 – y} )Sr₂(Y_{1 – x} Ca _x )Cu₂O _z with 0 y 0.3 and 0 x 0.7 was investigated. It was established that a nearly pure 1212 phase can be obtained at 0 y 0.1 and 0 x 0.3. The obtained XRD patterns as well as the results of the EDX and ICP-AES analyses showed that Sn substitution is possible in the (Pb,Cu)-1212 phase. Superconductivity was observed at 0.4 x 0.7. The onset of the diamagnetic transitions varied from 10 to 30 K. The influence of the strong Pb deficiency on the superconducting properties of the samples was discussed.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

Stress intensity factors in a fully interacting,multicracked, isotropic plate

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF's). Analytical derivations of these SIF's for a multicraked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology for the rigorous solution of the system of singular integral equations for SIF's is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, has been developed and validated.Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcracks' location, orientation, size, and interaction are accounted for.List of symbols offset angle between inner tips of two parallel cracks - _lr, _mz direction cosines between two local coordinate systems - _jl strain tensor - offset of notch-microcracks system with respect to Y axis - _k four roots of the characteristic equation - v Poisson's ratio - _jl ^o , _jl ^T far-field and total stress field, respectively - _XX ^o , _YY ^o , _XY ^o components of stress in global coordinate system - _j angle defining local frame orientation - , normalized real variable - (s, y) Fourier transform of Airy stress function with respect to x variable - a _j half crack length - a ₁₁, a₁₂, a₂₂ coefficients of strain-stress relationship - d normalized radial (tip) distance - f _nj auxiliary functions - k ₁, k₂ mode-I and mode-II stress intensity factors - ker _inf ^sup Fredholm kernels - p _j normal traction at crack surface - q _j shear traction at crack surface - s Fourier variable - r _j, r_kX, r_kY position vector and its components, for an origin of local frame - u, v x, y component of displacement, respectively - w weight function - x _j y_jand X, Y local and global coordinates - [A] matrix of coefficients - C' _j, C_j functions of s in Fourier space (i.e., constrants in x, y-real space) - E Young modulus - F _j(x_j, y_j) Airy stress function - G_nj(_p) discrete auxiliary function - {} loading function vector