Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

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.     

Hall-Effect in LuNi2B2C and YNi2B2C Borocarbides in Normal and Superconducting Mixed States

It was shown that the Hall resistivity _xy for LuNi ₂ B ₂ C and YNi ₂ B ₂ C is negative in the normal and mixed states and has no sign reversal below T _c . In the mixed state the scaling relation _{xy xx} (_xx is the longitudinal resistivity) was found for both compounds with 2.0. In the normal state a distinct nonlinearity in the _xy(H) dependence, accompanied by a large magnetoresistance, was found below 40 K only for LuNi ₂ B ₂ C. The difference in the behaviour of Lu- and Y-based borocarbides seems to be connected with the difference in the Fermi surfaces of these compounds.     

A method of joint determination of the effective coefficients of horizontal mixing of large particles and of external heat exchange in an organized fluidized bed

A method is proposed for the joint determination of the coefficients of horizontal particle diffusion and external heat exchange in a stagnant fluidized bed.Notation c_f, c_s, c_n specific heat capacities of gas, particles, and nozzle material, respectively, at constant pressure - D effective coefficient of particle diffusion horizontally (coefficient of horizontal thermal diffusivity of the bed) - d equivalent particle diameter - d_t tube diameter - H₀, H heights of bed at gas filtration velocities u₀ and u, respectively - H_a height of active section - l width of bed - L tube length - l _o width of heating chamber - N number of partition intervals - p=H/H₀ expansion of bed - s_n surface area of nozzle per unit volume of bed - S_h, S_v horizontal and vertical spacings between tubes - t_c, t₀, t_s, t_n, t_w initial temperature of heating chamber, entrance temperature of gas, particle temperature, nozzle temperature, and temperature of apparatus walls, respectively - u₀, u velocity of start of fluidization and gas filtration velocity - y horizontal coordinate - ^*, coefficient of external heat exchange between bed and walls of apparatus and nozzle - ₁, ₁, ₂, ... coefficients in (4) - thickness of tube wall - _b bubble concentration in bed - ₀ porosity of emulsion phase of bed - _n porosity of nozzle - =(t_s – t₀)/(t_c – t₀) dimensionless relative temperature of particles - _n coefficient of thermal conductivity of nozzle material - f, _s, _n densities of gas, particles, and nozzle material, respectively - _be=_s(1 – ₀) (1 – _b) average density of bed - time - _max time of onset of temperature maximum at a selected point of the bed - R =l _o/l Fourier number - Pe = ₁ l ²/D Péclet number - Bi = /_n Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 457–464, September, 1981.     

Influence of Saffman's lift force on the motion of a particle in a Couette layer

The article is concerned with the study of the effect of E. S. Asmolov's corrections to Saffman's lift force for the wall vicinity and a nonzero ratio of Reynolds numbers. It is shown in what way these corrections change the particle paths in a Couette layer and the conditions of deposition.Notation x=X/D, y=Y/D dimensionless longitudinal and transverse coordinates - u=U _p /U , =V _p /U dimensionless projections of particle velocity on the longitudinal and transverse axes - =tU /D dimensionless time - U ²/(18D) Stokes number - = _g / _p , coefficient of the gas kinematic viscosity - particle diameter - /D - _g , _p densities of the gas and particle material - du/d - dv/d - P _s Saffman's force - C coefficient in the formula for Saffman's force - yRe _d ^1/2 - A v _r Re _d ^1/2 - 3.08 - Re V _r / - Re _k ²/)U _g /Y - A Re/Re _k ^1/2 - Re _d U D/ - V _r ((U _g –U _p )²+V _p ² )^1/2 Indices g refers to gas parameters - p refers to the parameters of particles - 0 at the time momentt=0 - S Saffman's force - k Reynolds number based on the velocity gradient - based on velocity - r relative velocity - x projection on thex axis     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Transient thermal stress analysis of multilayered hollow cylinder

Summary This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.Nomenclature Lame's constant - density - C _v specific heat - k _r ,k radial and circumferential thermal conductivity - _r , linear radial and circumferential thermal expansion coefficient - E _r ,E radial and circumferential Young's modulus - v _r Poisson's ratio - ₀ reference temperature - ,T dimensional and nondimensional temperature - r ^*,r dimensional and nondimensional radial coordinate - ,t dimensional and nondimensional time - _r ^* , _r dimensional and nondimensional radial stress - ^* , dimensional and nondimensional circumferential stress - U, u dimensional and nondimensional radial component of displacement     

Coefficients of mass transfer between a fluidized bed and the surface of a capillary-porous body

Results are presented from a theoretical determination of coefficients of mass transfer between a fluidized bed of porous particles and a capillary-porous body.Notation a particle radius - F area of contact of particles with the surface of the body - f percentage of area of surface of product in contact with the bubble phase - g acceleration due to gravity - i flow of liquid mass from a unit area of the surface - N number of fluidizations - n number of particles coming into contact with a surface of unit area per unit of time - p_p, p_b capillary potentials of particles and product - R₂, R₁ radii of narrow and broad pores inside the product - r radius of capillaries in the particles - S area of the surface being treated - T temperature of the bed - t time of treatment - u percentage content of liquid in the specimen - V volume of the product being treated - v mean square component of the fluctuation velocity of the particles in the direction normal to the surface - , * standard and corrected mass-transfer coefficients determined from (5) and (9) - _b, _b, _p porosities of product determined for all and for only the small pores and the porosity of the material of the particles - _d, _m porosity of the dense phase and the porosity of the bed in the state of minimum fluidization - _b, _p angles of wetting of the materials of the product and particles, respectively, by the liquid binder - , viscosity and density of the liquid - ₀ density of the dry product - surface tension coefficient of the liquid - characteristic time of contact of particles with the surface - Re_m Reynolds number corresponding to particle radius and minimum-bed-fluidization velocity [6] Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 460–465, March, 1981.     

Turbulent mixing of fluids with different densities flowing through a pipe

A one-dimensional model of a disperse mixture in a turbulent stream is constructed, with the mutual effect of mixture concentration and turbulence intensity taken into account.Notation ₀ mean-over-the-section density - p pressure - _t turbulent viscosity - U average longitudinal velocity - g acceleration of gravity - angle of pipe inclination from the horizontal - x, r cylindrical coordinates - t time - V average radial velocity - C average concentration - D_t turbulent diffusivity - c₀ mean-over-the-section concentration - K effective turbulent diffusivity - U₀ mean flow velocity - X distance, in the moving system of coordinates - a pipe radius - ₀ frictional stress at the inside surface of the pipe - u_* transient turbulent velocity - b turbulence intensity - l linear scale factor - chemical potential of mixture - density of mixture - d₁, d₂ densities of homogeneous fluids - y₊ thickness of laminar layer - y distance from the inside pipe surface - ₊ derivative of velocity at the layer boundary on the turbulent side - hydraulic drag - Gr Grashof number - Re Reynolds number - ₁, ₂, coefficients in the equation for K_* - K_* dimensionless effective diffusivity - =U₀t/2a dimensionless time - =X/2a dimensionless distance Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 992–998, June, 1972.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Voltage-current characteristics of a type-II superconductor placed in a transverse magnetic field

We have measured the voltageV appearing along a type-II superconducting sample carrying a longitudinal currentI in the presence of a transverse magnetic fieldH. The analysis of the nonlinear part ofV(I) curves does not verify the recent model of Sherrill and Payne. The linear part ofV(I) curves shows that the flux-flow resistivity _f is exponential inH nearH _c2, as Axt and Joiner found. We estimated the parameter =(H _c2/_n)(d_f/dH)_{H=H c2} as a function of the reduced temperature and have compared it to some of the existing theories.     

Numerical simulation of hydrodynamics of a weakly compressible gas-liquid medium

A method for numerical simulation of the hydrodynamic parameters of a gas-liquid medium with allowance for its weak compressibility is proposed. Application of the method is illustrated by the example of the calculation of the hydrodynamics of a melt in a ladle during its filling and the blow.Notation V, V velocity of the medium and its value - W diffusion velocity of the gas phase - g free fall acceleration - , ₀, ₁ densities of the medium, the liquid, and the gas phases - p pressure - ; ₀, , , , coefficients of the gas content in the flow, gas content in the medium, dynamic and kinematic viscosity, surface tension - _ef effective dynamic viscosity coefficient - Re _d ,b its parameters: the grid Reynolds number and the ratio of the mixing length to the grid subinterval - polytrope exponent - R, H radius and height of the tank - R _fl radius of the flow - time step - d grid subinterval Institute of Technical Thermophysics of the Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, September–October, 1995, pp. 774–780.     

Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures

Using superleak condenser transducers, the velocity of second soundU ₂ has been measured near the superfluid transition temperature T in³He-⁴He mixtures with molar concentrationsX of³He of 0.0, 0.038, 0.122, 0.297, and 0.440. We have obtained the superfluid density _s/ fromU ₂ on the basis of linearized two-fluid hydrodynamics. The results for _s/ are consistent with those obtained from the oscillating disk method, as expected from two-fluid hydrodynamics. The value of _s/ at eachX could be expressed by a single power law, _s/=k, where =1-T/R, with the experimental uncertainty. It is found that the exponent is independent of concentration forX0.44 within the experimental uncertainty. This concentration independence of is in agreement with the universality concept. From the conclusion that the values of are universal forX0.44, the concentration dependence of the superfluid component _s is expressed by an empirical equation _s(X, )=²_s(0, ). It is found that corresponds to the volume fraction of⁴He in the superfluid³He-⁴He mixture. The value of is in agreement with that obtained from the measurement of the molar volume by others.This paper is based on a thesis submitted to Tokyo University of Education in partial fulfillment of the requirements for the Ph.D. degree.     

Distribution of finely dispersed particles with respect to residence time in a vortex chamber

The motion of finely dispersed particles is described statistically with the use of the Fokker-Planck equation. An expression is obtained for the particle distribution function with respect to residence time. Results of the calculation illustrate the dependence of the average particle residence time in the apparatus on the process parameters.Notation A constant - C' parameter characterizing the intensity of random forces - d _p particle diameter, m - K drying rate coefficient - r radial coordinate of the particle, m - R ₀ radius of the outlet orifice, m - R radius of the chamber, m - u,u _in,u _eq instantaneous, initial, and equilibrium moisture contents of the particle, kg/kg - V _r radial gas velocity, m/sec - W tangential velocity of the particle, m/sec - x=r/R dimensionless variable - dynamic viscosity, Pa·sec - _p, _g density of the particles and gas, kg/m³ - time, sec - angular velocity of gas suspension, sec^–1 Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 552–558, July–August, 1995.     

Numerical study of turbulent heat transfer and flow characteristics of hot flow over a sudden-expansion with base mass injection

Summary This study presents the numerical calculations of the fluid flow and turbulent heat transfer characteristics of hot flow over a sudden-expansion with cold air base mass injection. The turbulent governing equations are solved by a control-volume-based finite-difference method with power-law scheme, the well knownk- model, and its associate wall function to describe the turbulent behavior. The velocity and pressure terms of momentum equations are solved by the SIMPLE (Semi-Implicid Method for Pressure-Linked Equation) method. In this study non uniform staggered grids are used. The parameters interested include the inlet Reynolds number (Re), inlet temperature (T₀), and the injection flow rate (Q). The numerical results show that the reattachment lengths are reasonably predicted with a maximum discrepancy within 9.1%. It also shows that the base mass injection suppresses the horizontal velocity and turbulence intensity. In these high temperature heat transfer characteristics, the heat transfer coefficient increased with increasing inlet temperature and inlet Reynolds number, but decreased with increasing injection flow rate of the cooling air.Nomenclature C ₁,C ₂,C turbulent constant - E constant - G generation rate of turbulent kinetic energy - H channel height at inlet - i turbulence intensity - k turbulent kinetic energy - Nu local Nusselt number - q _w heat flux - Re Reynolds number - S source term - T temperature - T ₀ inlet temperature - TI turbulent intensity - U ₀ inlet velocity - U friction velocity - U,V x, y component velocity - Reynolds shear stress - X reattachment length - y ⁺ dimensionless distance from the wall - dependent variables - diffusion coefficient of equation - thermal diffusivity of fluid - density - von Kármán constant - turbulent Prandtl number - dynamic viscosity - kinematic viscosity - _w wall shear stress - turbulent energy dissaption rate - length scale constant     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Anisotropic Electrical Transport in MgB2 Single Crystals

We report on study of transport properties of MgB₂ single crystals. The normal state resistivity has been found to be anisotropic with resistivity ratio _c / _ab =3.5. In agreement with the results of band structure calculations the normal state Hall effect measurements with H//ab-planes and H//c-axis show two type carrier behavior. Below T _c, the in-plane as well as the out-of-plane Hall resistivity, _xy and _zx , display no sign change anomaly. Furthermore, both _xy and _zx have been found to scale with corresponding longitudinal resistivity with the same exponent =1.5.     

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     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains