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.     

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.     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Thermal conductivity and heat capacity of solid silver bromide (AgBr) under pressure

The thermal conductivity, , and the heat capacity per unit volume, c _p , have been measured for solid silver bromide (AgBr) using the transient hot-wire method. Measurements were made at temperatures in the range 100–400 K and at pressures up to 2 GPa. c _p was found to be independent of temperature and pressure over these ranges. of AgBr was found to be similar to that of AgCl, which was measured previously. For AgBr, only acoustic phonons needed to be taken into account up to 340 K, but optic phonons probably carried some heat at higher temperatures. The Leibfried-Schlömann (LS) formula could describe the ratio (AgCl)/(AgBr), but not the ratio (1 GPa)/(0) for either substance. An empirical modification of the LS formula could describe the latter ratios but not the former. Further theoretical developments are required for understanding of (P) for even such relatively simple substances as AgCl and AgBr.     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Branching of the Falkner-Skan solutions for λ<0

Summary The Falkner-Skan equation f+ff+(1-f²)=0,f(0)=f(0), is discussed for <0. Two types of problems, one with f()=1 and another with f()=-1, are considered. For =0^- a close relation between these two types is found. For <-1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f-1. The numerical results indicate that the solution branches with f()=1 and those with f()=-1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for <-1, is presented.     

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.     

Method and apparatus to determine the monochromatic normally hemispherical reflectivity of heat-shield materials

A method and apparatus are described for the determination of the monochromatic normally hemispheric reflectivity _n; results of measuring _n for number of composite materials are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 3, pp. 442–448, March, 1982.     

Remarks on wave solutions of the nonlinear heat-conduction equation

Wave solutions of the nonlinear heat-conduction equation are analyzed and their relation to self-similar solutions is established. Solutions of the hyperbolic and the nonlinear heat-conduction equations are compared.Notation k(T) thermal diffusivity coefficient - relaxation parameter - g²=₀/c_v@ square of the heat wave velocity - ₀ and k₀ heat-conduction and thermal diffusivity constant - density - c_v specific heat at constant volume - T temperature - t time - x, y, z space coordinates Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 907–913, May, 1981.     

Effect of the weight of the admixture on the turbulence structure of a two-phase jet

The effect of gravity on the turbulence structure of an inclined two-phase jet is evaluated according to the Prandtl theory of mixing length.Notation C_x drag coefficient for a particle - D_p particle diameter - g_i components of the acceleration g due to gravity acting on a particle in the direction of jet flow (g_i=g sin ) and in the direction normal to it (g_i=g cos ) - V_poi ^±, V_goi ^± fluctuation components of the velocities of the particles and gas, respectively, at the end of a mole formation - V_fi free-fall velocity of a particle - l _u mixing length - m_p particle mass - t _p length of time of particle-mole interaction - V_pi ^±, V_gi ^± positive and negative fluctuation velocities of particles and of the gas respectively, with the components u_p ^±, u_g ^±, v_p ^±, v_g ^±, k=V_goi/V_fi - V_i ^± relative velocity of the gas - jet inclination angle relative to the earth's surface - empirical constant - _u, jet boundaries in terms of velocity and concentration - _u=y/ _u dimensionless velocity ordinate - =y/ dimensionless concentration ordinate - admixture concentration - u_m, _m velocity and the concentration of the admixture at the jet axis - _g dynamic viscosity of the gas - _s, _g densities of the particle material and of the gas - _g, _p shearing stresses in the gas and in the gas of particles - _m, ₀ shearing stresses in the mixture and in pure gas, respectively Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 422–426, March, 1981.     

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.     

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.     

Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity _h of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density and specific heat c as the anisotropic materials, the thermal conductivity _h is shown to be equal to , which is a geometrical mean of the thermal conductivities in the direction of the plane _x and the thickness _y of the anisotropic materials. For an alumina silica blanket (=125 kg·m^–3), the thermal conductivities _h , _x , and _y were measured in the temperature range between –140 and 300°C using the transient hot-wire method for _h and the cyclic heat method for _x and _y . In the same way, the thermal conductivities _h , _x , and _y of a rock wool (=121 kg·m^–3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of _x , it is confirmed that the proposed method can estimate the measured values reasonably well.     

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.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Dynamics of vapor bubbles in nitrogen tetroxide under conditions of pipe depressurization

A study was made of the effect of nonequilibrium phase transformations on the dynamics of vapor bubbles with the sudden occurrence of a pressure drop.Notation C_pv, C specific heat capacities (at constant pressure) of the vapor and liquid - _v, densities - T_v, T temperatures - V_v, V velocities - P_v, P pressures - W_v, W mass velocities on the bubble surface - _v, thermal conductivities of the vapor and liquid - adiabatic exponent of the vapor - surface tension - kinematic viscosity - j rate of phase transformations - m mass - heat of phase transformation Indices v vapor phase - liquid phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 764–769, May, 1988.     

Thermophysical properties data on molten semiconductors

Thermophysical properties of molten semiconductors are reviewed. Published data for viscosity, thermal conductivity, surface tension, and other properties are presented. Several measurement methods often used for molten semiconductors are described. Recommended values of thermophysical properties are tabulated for Si, Ge, GaAs, InP, InSb, GaSb, and other compounds. This review shows that further measurements of thermophysical properties of GaAs and InP in the molten state are required. It is also indicated that a very limited amount of data on emissivity is available. Space experiments relating to thermophysical property measurements are described briefly.Nomenclature Density - C _p Specific heat - Kinematic viscosity - Dynamic viscosity= - Thermal diffusivity - Thermal conductivity=C_p - Volumetric thermal expansion coefficient - Surface tension - d/dT Temperature coefficient of surface tension - g Gravitational acceleration - T Temperature - T Temperature difference - L Characteristic dimension     

Determination of the effective thermal conductivity of a plate in nonsteady experiment

The article describes a method of finding the effective thermal conductivity of multilayered structures at the nonsteady stage of the experiment and an experimental installation with automatic systems for setting the experimental regime and processing the experimental data.Notation thickness of the layer of heat insulation - x coordinate - t(x, ) temperature at the point of the material with the coordinate x at the instant - thermal conductivity - _ef effective thermal conductivity - c heat capacity - density of the material - C_d heat capacity of the disk per unit area of the base - m cooling rate of the disk - P_c thermal contact resistance - P_r thermal resistance of the investigated layer Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 616–620, October, 1988.