Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Heat transfer in a “pseudoturbulent” bed of dispersed material

A two-phase model is proposed for the steady heat exchange between a surface and a pseudoturbulent bed of dispersed material. Expressions are obtained for the temperature fields of the gaseous and solid phases.Notation _g effective thermal conductivity of gaseous phase - _s effective thermal conductivity of the mixed solid phase - porosity - _m molecular thermal conductivity - d particle diameter - temperature of dispersed bed at a large distance from heat source - , g gas temperature - _p particle temperature - _w wall temperature - x current coordinate in the direction perpendicular to the wall - l bed thickness - q heat flux - coefficient of heat exchange between wall and pseudoturbulent bed of dispersed material - ^* coefficient of interphase heat exchange - _g=_g/_w dimensionless gas temperature - _p = _p/_w dimensionless particle temperature - Y = x/d dimensionless coordinate - L =l/d dimensionless bed thickness - A_h dimensionless coefficient of interphase heat exchange - Nu_g = d/_s Nusselt number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 465–469, September, 1981.     

Thermal and electrical characteristics of a high-frequency electrothermal fluidization bed

Based on an analysis of the thermal and the electrophysical characteristics of a fluidization bed with dielectric clay particles, a method has been developed of distending such particles by means of a high-frequency electric field for the production of ceramic sand.Notation R, r radius of a grain and the radius to any inside point - T(r) temperature inside a grain - T_c temperature at the grain center - T_s temperature at the grain surface - T₀ ambient temperature - time coordinate - ₀ time of temperature leveling inside a grain - _a time of temperature leveling between grain and ambient medium - thermal conductivity of grain material - c specific heat in terms of volume of grain material - _G thermal conductivity of gas - heat transfer coefficient - q volume rate of heat generation - dielectric permittivity of grain material - f frequency of high-frequency electric field - E_m amplitude of high-frequency electric field - tan loss tangent of grain material - C capacitance of effective capacitor with fluidized bed - C_m mean effective capacitance - C₀ capacitance of effective capacitor with stationary bed - D, H diameter and height of reactor - h height of fluidized bed - m=h₀/H relative initial fill of a reactor - w linear velocity of gas stream Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 969–975, June, 1972.     

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.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

Universal simulation of degenerating homogeneous turbulence

The problem of universal simulation of the dynamics of a turbulent velocity field (universal in the sense of arbitrary values of the Reynolds turbulence number) is treated on the basis of the moment model in the second approximation.Notation ¯q² _i ² double the kinetic turbulence energy - _u ² =5v¯q²/_u Taylor turbulence scale squared - _u=v1/x_k)²> kinetic-energy dissipation function - N_Re,=¯q²_u / Reynolds turbulence number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 46–52, January, 1982.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Residual thermal stresses in the pull-out specimen: A finite element calculation

The residual thermal stress field in the pull-out specimen is calculated in the case of a high properties thermoset system (carbon-bismaleimide). The calculation is performed within the framework of the linear theory of elasticity by means of a finite element method. The specimen is modelled as a three-phase composite (holder-fibre-matrix). The meniscus which forms at the fibre entry is taken into account in order to provide a realistic stress concentration. The latter is far higher than the matrix strength. Evidence that fibre debonding propagates from the fibre end during cooling is then produced.Nomenclature T thermal load - L _e embedded length - r _f fibre radius - _c curvature radius of the meniscus (fibre entry) - r _c radial dimension of the finite element mesh - E _m,E _h matrix and holder moduli - E _A,E _T fibre axial and transverse moduli - _m, _h matrix and holder thermal expansion coefficients - _A, _T fibre axial and transverse thermal expansion coefficients - _rr, , _zz, _rz non-zero components of the residual stress field - _rr ⁱ , ^im , _zz ^im , _rz ⁱ stresses at the interface in the matrix (r=r _f + ) - _rr ⁱ , ^if , _zz ^if , _rz ⁱ stresses at the interface in the fibre (r=r _f–) - _p1 maximum principal stress - _zz ^f mean axial stress over the fibre section - _rupt ^m matrix strength - u _r ,u _z non-zero components of the displacement field     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

External heat transfer in polydispersed fluidized beds at elevated temperatures

The authors present results of a theoretical and experimental study of heat transfer in polydispersed fluidized beds of coarse particles at temperatures up to 1273 K.Notation a tube radius - C_f specific heat of the gas - d_i mean diameter of the i-th fraction - g acceleration due to gravity - H height of the fluidized bed - J=fu mass flow rate of gas - ₀ thickness of the gas film on the heat transfer surface - m₀ porosity at the onset of fluidization - m porosity - r radius - R radius of the equipment - tf, °C, T_f, °K gas temperature - T₀ initial gas temperature - T_t8, T_w temperature of the fluidized bed and of the heat transfer surface, u, u₀, speed of filtration and speed at the start of fluidization - a heat-transfer coefficient - _w, _b emissivities of the heat transfer surface, and the fluidized bed - _S emissivity of the particles - _e effective (apparent) emissivity of the fluidized bed - _f viscosity of the gas - _f thermal conductivity of the gas - _f ⁰=_f0 ^c+nc_fJd₂/m thermal conductivity of the gas at t_f=0°C - _f ^c molecular thermal conductivity of the gas - _f ^c at temperature (T_w+T_t8)/2 - _f0 ^c molecular thermal conductivity of the gas at t_f=0°C, =gl_f/gl_f0 ^c - _S, _f density of particles in the gas - Stefan-Boltzmann constant - Ar=gd_1fS-_f)/_f ² Archimedes Number - Pe=c_fJ₀ ²/Hm_f0 ^c Peclet number - Re=ud_1f/_f Reynolds Number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 767–773, May, 1989.     

Inertia of measurements with “auxiliary-wall” type heat meters

The article examines the problem of thermal inertia on the basis of an auxiliary-wall type heat meter, it demonstrates the boundaries of applicability of the approximate relationship for calculating non-steady-state heat fluxes.Notation q() non-steady-state heat flux through the heat meter - _i,a _i thermal conductivity, thermal diffusivity, and thickness of the heat meter, respectively - ₂,a ₂ thermal conductivity and thermal diffusivity, respectively, of the base of the heat meter - t() temperature gradient over the thickness of the heat meter - index of thermal inertia - time - s parameter of Laplace transform - t₁ (x, ) temperature of the heat meter at point x - t₂(x, ) temperature of the base - t_c ambient temperature - Y_q(s) transfer function from the heat flux q() to the temperature gradient t() Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 298–305, August, 1980.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Direct and inverse heat-conduction problems for a semiinfinite rod for a partial outflow of heat through the surface

Analytical solutions of the direct and inverse problems of nonstationary heat conduction in a thin semiinfinite rod are given for the case of radiative heat fluxes at the lateral surfaces and a partial outflow of heat by convection and radiation through the end of the rod.Notation thermal diffusivity - x₁ coordinate along the length of the rod - t₁ time - t=t₁/d² dimensionless time (Fourier number) - x=X₁/d relative coordinate - T_o initial temperature - Boltzmann constant - Sk=aT_c ³d/ Stark number - Bi=d/ reduced Biot number - emissivity Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 148–153, July, 1984.     

Complex microstructural changes in as-cast eutectoid Zn-Al alloy

Phase transformations and microstructural changes of an as-cast eutectoid Zn-Al alloy (ZnAl₂₂Cu₂) were investigated during isothermal holding. The typical dendritic structures consisted of _s phase as a core with the edge of decomposed _s phase and decomposed _s in the interdendritic regions. A series of complex phase transformations was observed. Both decompositions of _s and _s were determined at an early stage of ageing and a four-phase transformation, _f+T+, was observed at the boundaries of _f phase and the phase, instead of clearly observed at the boundaries of phase, in a solution-treated Zn-Al alloy during prolonged ageing.     

Experimental investigation of fluctuations in the velocity of the solid phase in a fluidized bed

The results are given on a spectral-correlation analysis of fluctuations in the velocity of the solid phase in installations having diameters of 0.3 and 0.7 m in a free fluidized bed, and one retarded by low-volume checkers, of sand (d=0.23 mm) and silica gel (d=0.19 mm).Notation D_i, d diameter of installation and average particle diameter - u, u₀ velocity of gas filtration in an empty cross section of the installation and velocity of start of fluidization - f frequency - H, h initial height of charge of material and height above gas-distribution grid - I, A temporal and spatial integral scales of fluctuations in velocity of solid phase - density of material - , ² root-mean-square deviation from average velocity of motion of solid phase (pulsation velocity) and its dispersion - time of shift - R() estimate of normalized autocorrelation function - G(f) smoothed normalized estimate of spectral density Indices v vertical - h horizontal Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 19–25, July, 1980.