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.     

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.     

The physics and mechanics of fibre-reinforced brittle matrix composites

This review compiles knowledge about the mechanical and structural performance of brittle matrix composites. The overall philosophy recognizes the need for models that allow efficient interpolation between experimental results, as the constituents and the fibre architecture are varied. This approach is necessary because empirical methods are prohibitively expensive. Moreover, the field is not yet mature, though evolving rapidly. Consequently, an attempt is made to provide a framework into which models could be inserted, and then validated by means of an efficient experimental matrix. The most comprehensive available models and the status of experimental assessments are reviewed. The phenomena given emphasis include: the stress/strain behaviour in tension and shear, the ultimate tensile strength and notch sensitivity, fatigue, stress corrosion and creep.Nomenclature a _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - a _o Length of unbridged matrix crack - a _m Fracture mirror radius - a _N Notch size - a _t Transition flaw size - b Plate dimension - b _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - c _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - d Matrix crack spacing - d _s Saturation crack spacing - f Fibre volume fraction - f _l Fibre volume fraction in the loading direction - g Function related to cracking of 90 ° plies - h Fibre pull-out length - l Sliding length - l _i Debond length - l _s Shear band length - m Shape parameter for fibre strength distribution - m _m Shape parameter for matrix flaw-size distribution - n Creep exponent - n _m Creep exponent for matrix - n _f Creep exponent for fibre - q Residual stress in matrix in axial orientation - s _ij Deviatoric stress - t Time - t _p Ply thickness - t _b Beam thickness - u Crack opening displacement (COD) - u _a COD due to applied stress - u _b COD due to bridging - v Sliding displacement - w Beam width - B Creep rheology parameter _o/ _o ⁿ - C _v Specific heat at constant strain - E Young's modulus for composite - E _o Plane strain Young's modulus for composites - Unloading modulus - E _* Young's modulus of material with matrix cracks - E _f Young's modulus of fibre - E _m Young's modulus of matrix - E _L Ply modulus in longitudinal orientation - E _T Ply modulus in transverse orientation - E _t Tangent modulus - E _s Secant modulus - G Shear modulus - G Energy release rate (ERR) - G _tip Tip ERR - G _tip ^o Tip ERR at lower bound - K Stress intensity factor (SIF) - K _b SIF caused by bridging - K _m Critical SIF for matrix - K _R Crack growth resistance - K _tip SIF at crack tip - I _o Moment of inertia - L Crack spacing in 90 ° plies - L _f Fragment length - L _g Gauge length - L _o Reference length for fibres - N Number of fatigue cycles - N _s Number of cycles at which sliding stress reaches steady-state - R Fibre radius - R R-ratio for fatigue (_max/_min) - R _c Radius of curvature - S Tensile strength of fibre - S _b Dry bundle strength of fibres - S _c Characteristic fibre strength - S _g UTS subject to global load sharing - S _o Scale factor for fibre strength - S _p Pull-out strength - S _th Threshold stress for fatigue - S _u Ultimate tensile strength (UTS) - S _* UTS in the presence of a flaw - T Temperature - T Change in temperature - t Traction function for thermomechanical fatigue (TMF) - t _b Bridging function for TMF - Linear thermal coefficient of expansion (TCE) - _f TCE of fibre - _m TCE of matrix - Shear strain - _c Shear ductility - _c Characteristic length - Hysteresis loop width - Strain - _* Strain caused by relief of residual stress upon matrix cracking - _e Elastic strain - _o Permanent strain - _o Reference strain rate for creep - Transient creep strain - _s Sliding strain - Pull-out parameter - Friction coefficient - Fatigue exponent (of order 0.1) - Beam curvature - Poisson's ratio - Orientation of interlaminar cracks - Density - Stress - _b Bridging stress - ¯_b Peak, reference stress - _e Effective stress = [(3/2)s _ijs_ij]^1/2 - _f Stress in fibre - _i Debond stress - _m Stress in matrix - _mc Matrix cracking stress - ^o Stress on 0 ° plies - _o Creep reference stress - _rr Radial stress - ^R Residual stress - _s Saturation stress - _s ^* Peak stress for traction law - Lower bound stress for tunnel cracking - ^T Misfit stress - Interface sliding stress - _f Value of sliding stress after fatigue - _o Constant component of interface sliding stress - _s In-plane shear strength - ¯_c Critical stress for interlaminar crack growth - _ss Steady-state value of after fatigue - ^R Displacement caused by matrix removal - _p Unloading strain differential - _o Reloading strain differential - Fracture energy - _i Interface debond energy - _f Fibre fracture energy - _m Matrix fracture energy - _R Fracture resistance - _s Steady-state fracture resistance - _T Transverse fracture energy - Misfit strain - _o Misfit strain at ambient temperature     

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     

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.     

An instability mechanism for the sliding motion of finite depth of bulk granular materials

Summary Field observations and experimental records indicate that the primary mode of motion of many large landslides is that ofsliding rather thanflowing. Most of shear during sliding is concentrated at the base of slides, with little or no mixing taking place away from the base. This sliding motion may generate strong pressure waves at the interface between the quasi-static deforming granular mass and the grain-inertia dominated rapid granular flow, thus inducing a Kelvin-Helmholtz type instability mechanism for large landslides. The existence of a transitional zone in granular flow is essential for the generation of this type of instability waves. A model using a finite depth of elastic sliding bulk granular materials riding on a basal granular shear flow layer is estabilished to represent the sliding motion of these large volume of bulk granular materials. The balance and the stability of this sliding system are investigated under the perturbation of internal pressure waves. The generated instability waves will force favorable phase shifts between the overburden pressure and the sliding velocity, leading to a net reduction in the total power loss due to friction. The depth of sliding mass will affect the generation of this type of instability waves. Both analytical and numerical results show that smaller depth slides can induce stronger instability waves than larger depth slides do.Notation a perturbation wave amplitude - C nondimensional instability wave speed - C _i growth rate, the imaginary part ofC - C _r wave phase speed, the real part ofC - c _p compressional wave speed in elastic medium - c _s shear wave speed in elastic medium - D nondimensional depth of sliding mass - d depth of sliding mass - G shear modulus of elastic medium - H nondimensional basal depth - h depth of basal shear zone - i - K Coulomb friction coefficient - P _xx, P_yy lateral and normal pressures in granular material, respectively - P _xy shear stress in granular material - p ₀ amplitude of perturbation pressure - p _yy perturbation pressure - r nondimensional complex wave number of instability wave - S nondimensional wave number of shear wave - t time scale - U uniform sliding velocity of a landslide inx direction - u, v velocities inx direction andy direction, respectively - u ₀ granular flow velocity in the basal shear zone - V, V _c nondimensional sliding velocity and its critical velocity, respectively - W power loss to friction - internal friction angle - , Lame's potentials, and are time-independent amplitudes of and , respectively - perturbation wave surface profile - wave number of perturbation wave, _r and _i are the real and imaginary parts of - Poisson's ratio of elastic medium - wave frequency of perturbation wave - , _g density of granular material - stress component in elastic medium - Rankine's earth pressure coefficient - -K ² - Re{}, Im{} the real and imaginary parts of complex quantity inside {}, respectively - , the divergence and the curl of perturbation wave velocities, respectively - Laplacian operator - _ij Kronecker delta; _ij =1 fori=j, _ij =0 forij - ()i, ()j, ()ij tensor - ()1, ()e in sliding mass - ()2, ()b in ground     

Pair explosion in an exponential atmosphere

The problem of the interaction of two coaxial explosions in a barometric atmosphere is solved numerically based on the complete system of Navier-Stokes equations. Basic regularities that occur in the interference of two spherical shock waves of different intensities are studied. The last stage of the processes, when shock wave processes become unimportant and convection plays a dominant part, is investigated.Notation t time - r, z cylindrical coordinates - v=(u, ) velocity - density - p pressure - T temperature - ,k dynamic viscosity and thermal conductivity - V(t) calculation region - f(t), _± (t boundaries of the calculation region - z ₁ ,z ₂ altitudes of the centers of the lower and upper explosions - R ₁ ,R ₂ initial radii of the regions involved in the explosions - altitude of the homogeneous atmosphere - g acceleration due to gravity - adiabatic exponent - , , parameters - M Mach number - Re Reynolds number - Pr Prandtl number - c _p ,c _v specific heats Department of Theoretical Problems, Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 657–661, June, 1994.     

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.     

A gradient method of defining smooth solutions to inverse boundary-value problems in thermal conduction

An iterative algorithm is described for solving boundary-value inverse problems in thermal conduction by steepest descent, which utilizes information on the smoothness of the solution.Notation A, B linear operators - u element of solution space U - f exact reference data - f reference data uncertainty - value of reference data uncertainty - A^–1 inverse operator - u^(k)() k-th derivative of function u - _m length of observation interval - _i(t) polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - Jg discrepancy functional gradient - _n descent step along the discrepancy antigradient for the n-th iteration - K( –) kernel of integral equation - q() heat flux - T() measured temperature inside body Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 259–263, August, 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     

Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.     

The Infrared Hall Effect in YBCO: Temperature and Frequency Dependence of Hall Scattering

We measure the Hall angle, _H , in YBCO films in the far- and mid-infrared to determine the temperature and frequency dependence of the Hall scattering. Using novel modulation techniques we measure both the Faraday rotation and ellipticity induced by these films in high magnetic fields to deduce the complex conductivity tensor. We observe a strong temperature dependence of the mid-infrared Hall conductivity in sharp contrast to the weak dependence of the longitudinal conductivity. By fitting the frequency dependent normal state Hall angle to a Lorentzian _H () = _H /( _H – i) we find the Hall frequency, _H , is nearly independent of temperature. The Hall scattering rate, _H , is consistent with _H T ² up to 200 K and is remarkably independent of IR frequency suggesting non-Fermi liquid behavior.     

Microstructure refinement with forced convection in aluminium and superalloys

The cooling and average local solidification times were determined for slow solidifiation of Al-4.4 wt% Cu alloy under natural convection and under electromagnetically forced axisymmetric rotation during liquid cooling and solidification in graphite moulds. Cooling rates were measured within situ thermocouples. The conditions needed to stabilize the radial temperature gradient with rotation were established. The microstructure size decreased with increasing rotation, as did the local solidification times. The average grain and dendrite size without imposed rotation is coarser near the mould wall compared with the centre of the casting. This trend is reversed with imposed rotation. Rotation also led to a smaller spread of grain and dendrite size at any chosen height of the casting. These results are discussed in relation to existing theories, and several reasons for an improved heat transfer coefficient with rotation are presented. Forced convective solidification was then carried out for various shapes of integral investment cast Nimonic-90 alloy solidifying under modified conditions that prevented columnar grain formation. Similar results to those recorded for the aluminium case were obtained and are presented here. The major conclusion is that observations indicating a reduction of microstructure spacing during forced convection should also consider improved heat extraction at the mould-metal interface.List of symbols Gr Grashof number =gTZ ^{3 3}/ ³ - g _r acceleration in radial direction - g acceleration in direction - g _z acceleration inZ direction (gravity) - h heat transfer coefficient - k _l thermal conductivity of liquid - Nu _z Nusselt number =hZ/k _l - Pr Prandtl number =/ - Ra Rayleigh numberGr Pr - R radius of mould - Re _r Reynolds number =V ₀ R/ - T temperature - T temperature difference in radial direction - Ta Taylor number = ²4H ⁴ W ²/ ² - V velocity - W r.p.m. - thermal diffusivity - coefficient of volume expansion - viscosity - density Mr G. S. Reddy is also a post graduate student registered at the Banaras Hindu University, Varanasi, India.     

The reversion of martensite to austenite in certain stainless steels

An investigation has been made of the reversion of martensite () to austenite () in two stainless steels (i) Fe-16 wt% Cr-12 wt% Ni (of low interstitial content) (ii) Fe-15 wt% Cr-8 1/2 wt% Ni-2 wt% Mo-0.09 wt% C. The alloys were refrigerated to produce 12 to 15% martensite () and then heated for short times at various temperatures ranging from below A _s to above A _f. With rapid heating the reversion of to occurs largely by a shear mechanism. In the Fe-16Cr-12Ni alloy individual grains of transform to grains of reversed of similar size and shape. In the carbon-containing alloy there is evidence of break-up of the grains on reversion. An increase in the strength results from reversion and this is attributable mainly to the high dislocation density of the reversed .     

Adhesion to skin

The failure energy of an adhesive bond can be factorized into two terms, one of which is a dimensionless loss function and the other, the true interfacial bonding energy, ₀. Experimental techniques have been developed to effect a separation of these two terms and thus measure ₀, but they are unsuitable for the pressure-sensitive adhesives used in surgical tapes and dressings. This is because these adhesives flow readily under load. This paper describes an extrapolation technique by which this problem can be resolved. Adhesive peel data are extrapolated both to zero peel velocity and zero load, to give a true threshold value for peeling energy which is independent of temperature. Values of ₀ are given for a natural-rubber based adhesive and substrates of glass and human skinin vivo. For glass ₀ = 28J m^–2 and for normal skin ₀ 14J m-2.     

Transient heat conduction in hollow spheres with a moving inner boundary

The finite integral transform method is used to obtain the solution of unsteady heat conduction problems for a hollow sphere with a moving internal boundary and various boundary conditions at the outer surface. For the solution of the problems of interest integral transform formulas are presented with kernels (16), (20), and (24) and the corresponding inversion formulas (18), (22), (26), (29) and characteristic equations (17), (21), (25), (28), (31), (33).Nomenclature a, thermal diffusivity and conductivity - t temperature of phase transformation - density - heat transfer coefficient - Q total quantity of heat passing through inner boundary - F latent heat of phase transformation - Fo(1,)=a/R ₁ ² , Fo(i,)=/r _i ² , Fo(i, _i)=a _i/r _i ² Fourier numbers - Bi₂=R₂/ Biot number     

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

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

Experimental study of the boundary between single-phase convection and boiling in underheated cryogenic liquids

The effect of pressure and underheating on the position of the boundary between heat-transfer regimes in liquid helium and hydrogen is investigated.Notation q heat flux - p pressure - =T_s–T underheating - T_s saturation temperature - T temperature of liquid - T=T_wa – T T_s=T_wa – T_s - T_wa temperature of heat-emitting surface - A,a, B, b, C constants - m, n indices - Nu Nusselt number - Ra Rayleigh number - thermal conductivity - coefficient of cubical expansion - kinematic viscosity - g acceleration - standard deviation Indices 01 conditions of convection-boiling transition - 02 conditions of boiling-convection transition Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 5–11, January, 1982.     

Thermal Expansion and Isothermal Compressibility of TlIn1 – xNdxSe2 (0 ≤ x≤ 0.08) Crystals

The thermal expansion coefficient () and isothermal compressibility ( _T ) of TlIn_{1 – x} Nd _x Se₂(0 x 0.08) crystals were measured between 77 and 400 K. In the range 77–160 K, both and _T increase with temperature, the increase in being much steeper. At higher temperatures, and _T change very little. The observed composition dependences of and _T are interpreted in terms of energy-band structure.     

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.