A flat jet in a granular bed of finite height

The distribution of gas flows in the vicinity of the jet is discussed and the conditions of disruption of the static equilibrium of the bed, the formation and growth of a cavity, and the jet breakthrough of the bed are investigated qualitatively.Notation a, b functions calculated in [11] - C, C constants in (7) - F derivative of the complex potential - f function in (6) - G function defined in (19) - H dimensionless height of bed - h height of cavity - k coefficient introduced in (15) - p, po pressure inside bed and in cavity - p dimensionless pressure drop - Q, q dimensional and dimensionless jet flow rates - q₁, q₂ critical values - T dimensionless height of cavity - T₀, T₁ T₁, T₂ characteristic values of T - u,v filtration velocities - u, u_* initial filtration velocity in the bed and minimum fluidization velocity - u_o velocity scale introduced in (14) - u * velocity scale introduced in (14) - u* velocity of fictitious flow defined in (15) - U complex velocity - Z=X+iY, z=x+iy dimensionless coordinates - z=x+iy dimensional coordinates - coefficient of hydraulic resistance - parameter from (5) - specific weight of particles' material - porosity - =+i coordinates in the plane obtained from z=x+iy as a result a of conformai transformation - _m value of giving a minimum of the function G - f complex and real flow potentials - angle of internal friction - stream function - angle of inclination of boundaries of the region of plastic flow to the vertical Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 804–812, November, 1979.     

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.     

Diffusion separation of hydrogen from gas mixtures

Experiments are described and a model is evaluated for the process of production of superpure hydrogen from mixtures with ammonia and nitrogen by selective diffusion through thin metallic membranes.Notation j_H, j_C molar fluxes of hydrogen and ballast gas - k effective permeability coefficient (product of hydrogen solubility coefficient times diffusion coefficient, divided by membrane thickness) - l, L coordinate measured along supply channel and maximum value thereof (channel length) - M molecular weight of hydrogen - P working perimeter of diffusion cell - p, p pressure in supply and output channels - Q, Q_H mixture flow rate and hydrogen output for one cell or entire unit - S area of working section of supply channel - v velocity in output channel - x, x_o molar fraction of hydrogen in mixture and value thereof at inlet - z, Z dimensionless coordinate and length of apparatus - , dimensional and dimensionless hydraulic resistance coefficients - , _* dimensionless pressure in output channel and value thereof at outlet - dimensionless pressure (concentration) of hydrogen in supply channel - hydrogen density in output channel - relative output Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 100–108, July, 1984.     

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.     

Effect of the elastic factor on the hydrodynamic stability of a structurally viscous medium

The effect of relaxation phenomena on the hydrodynamic stability of the plane gradient flow of a structurally viscous medium is investigated using linear theory.Notation _ij stress tensor deviator - U_i components of the velocity vector - x_i coordinates - t time - P pressure - =₀L/^*V plasticity parameter - _o limiting shear stress - andc dimensionless wave number and the perturbation frequency - Re=VL/* Reynolds number - density - F_ij deformation rate tensor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 868–871, November, 1978.     

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.     

Enhancement of heat transfer of mixed convection for heated blocks using vortex shedding generated by an oblique plate in a horizontal channel

Summary The problem of heat transfer enhancement of mixed convective flow past heated blocks in a horizontal channel is investigated. The heat transfer enhancement in this paper has been accomplished by the installation of an oblique plate to generate vortex shedding, which is used in flow modulation. Results for the details of the streamlines in the channel and the Nusselt number along the blocks with and without an oblique plate have been presented.Notation C _p pressure coefficient (2f Pds/f ds) - d length of an oblique plate - ds surface area increment along an oblique plate - f_s frequency of the vortex shedding - Gr Grashof number - H channel wall-to-wall spacing - h height of the block - k thermal conductivity - L channel length - Nu Nusselt number - time-mean Nusselt number (f Nudt/f dt) - average time-mean Nusselt number - n normal vector - P dimensionless pressure (p ^*/(u ² ) - p ^* pressure - Pr Prandtl number (/) - q heat flux at the block boundary - Re Reynolds number (u w/v) - St Strouhal number (df_ssin /u ) - T^* temperature - T uniform inlet temperature - t dimensionless time (t ^* / (w/u )) - t dimensionless time increment - t ^* time - u uniform inlet velocity - u, v dimensionless velocity components (u=u ^*/u ,v=v ^*/v ) - u ^*,v ^* velocity components - w width of the block - x,y dimensionlessx ^*,y ^* coordinates (x=x ^*/w,y=y ^*/w) - x ^*,y ^* physical coordinates - thermal diffusivity - angle of inclination for a plate - dimensionless temperature ((T^*–T ^* )/(qw/k)) - v kinematic viscosity of fluid     

Mass transfer of a single bubble in a minimally fluidized granular bed

The transfer of a gas admixture through the boundary of a cloud of closed circulation of gas is examined with a view to both molecular and convective dispersion.Notation a particle radius - c concentration of the admixture - D, D _c tensors of effective diffusion coefficients and of coefficients of convective dispersion, respectively - D parameter in (14) - D₀, D_m coefficients of molecular diffusion, respectively not taking and taking compressibility into account - F, f functions in (17) and (18), respectively - f fraction of the volume of the sphere with radius R_B occupied by the wake of the bubble - g acceleration of gravity - K mass-transfer coefficient determined in (22) - k coefficient in (7) - L coefficient in (22) - p, s functions determined in (13) - Q, q flow of admixture for the entire bubble and local flow, respectively - r_B, R_c radii of bubble and of cloud of closed circulation, respectively - r radial coordinate - U lift velocity of the bubble - u=v-w; u₀=u_*/u_* minimum velocity of fluidization - V volume of bubble - v, w mean gas velocities in the gaps between particles and of the particles, respectively - parameter determined in (8) - , parameters from (14) - porosity of the dense phase and of the cloud - polar angle - independent variable introduced in (12) - p = 1 - flow function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 323–333, August, 1980.     

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.     

Distribution of the phase front in the freezing of finely-dispersed soils

The process of the freezing of soils is examined with allowance for the migration of moisture in the freezing and thaw zones.Notation , x time and space coordinates - t, W, L dimensionless values of temperature, moisture content, and ice content - c,a, D volumetric heat capacity, diffusivity, and diffusion of moisture - density of the skeleton - W_e equilibrium value of moisture content - enthalpy of phase transformations - _* characteristic time - , gw, , dimensionless values of temperature, moisture content, ice content, and diffusion coefficient of the moisture - Fo Fourier criterion - Ste Stefan number - n empirical constant Indices 0, 1, and 2 pertain to the initial and boundary states Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 805–810, May, 1989.     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Structure of flows in vortices

The structure of a gradient vortical flow was studied experimentally.Notation v_x, v_y, v_z flow velocity components in a rectangular coordinate system - v, v_r, v_z flow velocity components in a cylindrical coordinate system - v₁ tangential velocity at the boundary of solid revolution at r = r₁ - l length of the vortex - kinematic viscosity - R radius of the forming cylinder - circulation in the region of potential flow - second air flow rate through the eddy of ascending flows - Re=v₁r₁/ tangential Reynolds number - N=Q/r_o radial Reynolds number - a=l/r₀ configuration ratio for the vortex model - s=r_o/2Q effective exchange coefficient - a ^*=l/r configuration ratio for the vortex generator - s^*=R/Q constructive exchange coefficient - p=p–p pressure drop in the vortex relative to atmospheric pressure p - r^*= r/r₁ dimensionless radius of the vortex - v^*=v/v₁ dimensionless tangential velocity - a ^*/a gradient ratio Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 611–618, October, 1980.     

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.     

Heat transfer and the combustion temperature of coke particles in a fluidized bed

The temperature of carbon particles undergoing combustion in a fluidized bed is measured. Heat-transfer laws are ascertained.Notation a diffusivity of air - c heat capacity of air - D diffusion coefficient of oxygen in air - d₀, d initial and running diameters of carbon sphere - d_i diameter of inert particles - k rate constant for carbon monoxide combustion - q calorific value of carbon oxidation to CO₂ - T temperature difference between burning particle and fluidized bed - X, X_n oxygen concentration in the fluidized bed and on the surface of the burning particle - Z, Z_n running concentration of carbon monoxide and concentration on the surface of the burning particle - heat-transfer coefficient between fluidized bed and burning particle - _m maximum heat-transfer coefficient between fluidized bed and a stationary body submerged in the bed - masstransfer coefficient between fluidized bed and burning particle - thermal conductivity of air - kinematic viscosity of air - ₀, gr, ₄ density of oxygen, air, and inert material - relative thickness of burning gas layer - relative thickness of diffusion boundary layer Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 21–27, January, 1982.     

Heat and mass transfer effects on flow past an impulsively started vertical plate

Summary An exact solution to the problem of lfow past an impulsively started infinite vertical plate in the presence of uniform heat and mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown graphically. The rate of heat transfer, the skin-friction, and the Sherwood number are also shown on graphs. The effect of different parameters like Grashof number, mass Grashof number, Prandtl number, and Schmidt number are discussed.List of symbols C species concentration near the plate - C species concentration in the fluid far away from the plate - C dimensionless concentration - C _p specific heat at constant pressure - D mass diffusion coefficient - g acceleration due to gravity - Gr thermal Grashof number - Gc mass Grashof number - j mass flux per unit area at the plate - K thermal conductivity of the fluid - Nu Nusselt number - Pr Prandtl number - q heat flux per unit area at the plate - Sc Schmidt number - t time - t dimensionless time - T temperature of the fluid near the plate - T temperature of the fluid far away from the plate - T _w temperature of the plate - u velocity of the fluid in thex-direction - u ₀ velocity of the plate - u dimensionless velocity - x coordinate axis along the plate - y coordinate axis normal to the plate - y dimensionless coordinate axis normal to the plate - volumetric coefficient of thermal expansion - ^* volumetric coefficient of expansion with concentration - coefficient of viscosity - kinematic viscosity - density - skin-friction - dimensionless skin-friction - dimensionless temperature - er fc complementary error function - similarity parameter     

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     

Developing combined convection of non-Newtonian fluids in an eccentric annulus

Summary Laminar combined convection of non-Newtonian fluids in vertical eccentric annuli, in which the inner and outer walls are held at different constant temperatures is considered and a new economical method of solution for the three-dimensional flow in the annulus is developed. Assuming that the ratio of the radial to the vertical scale, , is small, as occurs frequently in many industrial applications, then the governing equations can be simplified by expanding all the variables in terms of . This simplification gives rise to the presence of a dominant cross-stream plane in which all the physical quantities change more rapidly than in the vertical direction. The solution trechnique consists of marching in the vertical streamwise direction using a finite-difference scheme and solving the resulting equations at each streamwise step by a novel technique incorporating the Finite Element Method. The process is continued until the velocity, pressure and temperature fields are fully developed, and results are presented for a range of the governing non-dimensional parameters, namely the Grashof, Prandtl, Reynolds and Bingham numbers.List of symbols Bn Bingham number, - d ^* difference between the radii of the outer and inner cylinders,r _o ^*–r_i ^* - e ^* distance between the axes of the inner and outer cylinders - e eccentricity,e ^*/d^* - F ^* external force acting on the fluid - g ^* acceleration due to gravity - g ^* gravitational vector, (0,0,g ^*) - Gr Grashof number, _m *² g**(T ₀*–T _e*)d*³/ _m *² - K ^* consistency of the fluid - L ^* height of the cylinders of the annulus - n flow behaviour index - p ^* dimensional pressure - P dimensionless pressure gradient - Pr Prandtl number, _m */ _m ** - r _i ^* radius of the inner cylinder of the annulus - r _o ^* radius of the outer cylinder of the annulus - r _T wall temperature difference ratio,(T _i ^*–T_e ^*)/(T_o ^*–T_e ^*) - Re Reynolds number, _m d*w _m */ _m * - T dimensionless temperature of the fluid,(T ^*–T_e ^*)/(T_o ^*–T_e ^*) - T _dif ^* temperature difference between the walls of the annulus - T _e ^* temperature at the fluid at the entrance of the annulus - T _i ^* temperature at the inner cylinder of the annulus - T _o ^* temperature at the outer cylinder of the annulus - u dimensionless transverse velocity in thex direction,u ^*/(w_m ^*) - U dimensionless transverse velocity in the annulus,Reu - u ^* fluid velocity vector, (u ^*, v^*, w^*) - v dimensionless transverse velocity in they direction,v ^*/(w_m ^*) - V dimensionless transverse velocity in the annulus,Rev - w dimensionless vertical velocity,w ^*/w_m ^* - w _m scaling used to non-dimensionalise the vertical velocity - x dimensionless transverse coordinate,x ^*/d^* - y dimensionless transverse coordinate,y ^*/d^* - z dimensionless vertical coordinate,z ^*/L^* - Z dimensionless vertical coordinate,z/Re - Z _r dimensionless distance in the vertical direction where the final wall temperatures are attained,Z _r ^*/L^* - * dimensional molecular thermal diffusivity - * coefficient of thermal expansion, - dimensional rate of strain tensor - dimensionless ratio of the length scales in the annulus,d ^*/L^* - * dimensional apparent non-Newtonian viscosity - _m * mean viscosity, - * dimensional fluid density - _m * dimensional reference fluid density - * dimensional stress tensor - yield stress     

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.     

Change of pressure in wells opening up highly inhomogeneous porous collectors

We consider a generalized averaged model of the filtration of a weakly compressible liquid in a highly inhomogeneous medium. We construct an approximate analytical solution of the problem that describes the change in the pressure field around a well in a circular bed. We investigate the effect of the parameters of a highly inhomogeneous bed on the form of the well pressure stabilization curve.Notation c Euler constant - D diameter of a weakly permeable block - Ei symbol of the integral exponential function - h bed thickness - K(t), K _* (t) kernels of integral operators - K ₀ symbol of the Macdonald function - k permeability - P pressure - Q constant discharge of the well - r radius - s complex variable - t time - t _* time of the relaxation of a weakly permeable block - U(r, t) reduced pressure - U(t) function taking into account the internal flow of the fluid from one medium to the other - fraction of the volume of the bed per block - ^* reduced coefficient of compressibility - characteristic scale of inhomogeneity - ratio of piezoconductivities of a block and a crack - Laplace operator - piezoconductivity - ratio of elastic amounts of weakly permeable blocks and systems of cracks - viscosity of the fluid - dimensionless time - integration variable. Indices: 1, weakly permeable blocks - 2 system of cracks - 0 initial value - w value in the well - e effective value - overbar Laplace transform Institute for the Problems of Oil and Gas of the Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 444–450, May–June, 1995.     

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.