Use of adjoint functions in investigations of heat conduction and transfer processes

An examination is made of the use of adjoint functions in heat conduction and convection theory. Formulas of perturbation theory are obtained for steady and unsteady cases, an interpretation of the physical meaning of adjoint temperature is given, and some applications of the theory are discussed.Notation (r,) thermal conductivity - t(r,) temperature - t *(r,) adjoint temperature - q_V(r,) density of heat release sources - p(r,) a parameter of adjoint equation - r generalized coordinate - time - (r_s, ) heat transfer coefficient - I linear functional of temperature - (r,;r₀,₀) and *(r,; r₀,₀) Green's function for t(r, ) and t *(r, ) - C(r,) volume specific heat - W(r, ) vector distribution of flow velocities - V, S volume and surface areas of body - R radius of HRE - r, radial and angular coordinates - F_in, F_out inlet and outlet flow areas of channel     

Hydrothermal Synthesis and Spectroscopic Properties of Crystalline ZnO Powders and Films

Polycrystalline zinc oxide is synthesized under mild hydrothermal conditions (150–250°C). The phase composition, morphology, and pulsed cathodoluminescence (PCL) spectra of ZnO powders, polycrystalline films, and single crystals are studied as a function of synthesis conditions (the nature of the precursor, the type and concentration of the solvent, solution temperature, and the redox potential of the system). The crystallite size in the resultant materials varies from 100 nm to 10 m, depending on the synthesis conditions. The PCL spectra measured under pulsed electron-beam ( 2 ns) or laser (Nd:YAG, fourth harmonic, = 266 nm, 10 ns) excitation show two bands in the UV and visible spectral regions. The intensity ratio between these bands depends on the ZnO preparation conditions. The influence of the precursor and solvent on the PCL spectrum of ZnO is studied. The redox potential of the system is shown to have a strong effect on the luminescent properties of the resultant material.     

Simultaneous determination of the thermal conductivity and diffusivity of metals using an electronic heater

A nonstationary method allowing simultaneous determination of the thermal conductivity and diffusivity of metals using an electronic heater is described.Notation q_e heat flux density - t temperature - x distance to thermocouple - heating time - t₀ temperature at time zero - thermal conductivity of material examined - a thermal diffusivity of material - c coefficient describing the energy losses - X₁, x₂, x₃ distance to first, second, and third thermocouples, respectively - ₁, ₂, ₃ times during which specimen is heated to temperature t at points X₁, x₂, X₃, respectively     

Theory of periodically driven,current-carrying,superconducting filaments. I. Spatially homogeneous states

Starting from the nonequilibrium theory of dirty superconductors in the Ginzburg-Landau regime, spatially homogeneous states with an applied currentI=I ₀+I ₁ cos (t) are considered. Expressions for the linear response (I₁ small) valid up to high frequencies (k _BT_c) are derived and evaluated analytically for the experimentally important case of smallI ₀ and ₀(T). Then the nonlinear response is treated for frequencies with _E1. Interesting new behavior is found for frequencies ₀ 1, where ₀ is essentially the GL relaxation time.     

Kinetic concept of the strength of solids

An examination of the time to failure for uniaxial tensile specimens of some 50 materials, measured in some cases over test decades of time, has suggested a universal rate relation between lifetime, stress, and temperature of the form = _o exp [(Uo - )/kT]. The constant _o is essentially the reciprocal of the natural oscillation frequency of atoms in the solid, U_o is the binding energy on the atomic scale, and is proportional to the disorientation of the molecular structure. Assuming the kinetic nature of bond destruction through the thermofluctuation mechanism, direct experimental verification of the phenomenon for polymers has been obtained using electron paramagnetic resonance.

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Zusammenfassung Eine Betrachtung der Bruchzeit von einachsigen Spannungsprüflingen aus ungefähr 50 verschiedenen Materialien gemessen in manchen Fällen über zehn Zeitdekaden, lässt einen allgemeinen Zusammenhang zwischen der Zeit bis zum Bruch (lifetime), der Zugspannung und der Temperatur, der Form = _o exp [(U_o - )/kT] vermuten.Die Konstante _o ist im wesentlichen die reziproke natürliche Schwingungsfrequenz der Atome im Festkörper, U_o ist die bindungsenergie zwischen den Atomen, und ist proportional des Disorientierung der molekularen Struktur. Unter der Annahme, dass die Bindungszerstörung kinetischer Natur ist und durch Thermofluktuation erfolgt, wurde eine direkte experimentelle Bestätigung der Zusammenhänge bei Polymeren durch Beobachtung der paramaguetischen Elcktronenresonanz erhalten.

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Résumé Un examen du temps de rupture pour des échantillons de traction uniaxes d'environ 50 matériaux, mesuré dans certains cas sur 10 décades de temps, a suggéré une relation universelle entre la durée de la résistance, la traction et la température, de la forme: = _o exp [(U_o - )/kT] La constante _o est essentiellement la réciproque de la fréquence naturelle d'oscillation des atomes dans le solide, U_o est l'énergie de liaison des atomes et est proportionnel à la désorientation de la structure moléculaire. En admettant la nature cinétique de la destruction de la liaison, par le mécanisme de fluctuation thermique, la vérification expérimentale directe du phénomène à été obtenue, pour des polymères, par la technique de la résonance paramagnétique des électrons.

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Invited lecture presented at the International Conference on Fracture, Sendai. Japan, Sept. 1965.     

Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

Molar momentum and heat transfer

Universal relations governing the molar transfer of momentum and heat are derived on the basis of a hypothesis about the dependence of the boundaries of the molar transfer region on the flow structure and with the use of a special mathematical transformation.Notation u average longitudinal velocity, m/sec - T average temperature, °K - T_w wall temperature, °K - kinematic viscosity coefficient, m²/sec - density, kg/m³ - c_p specific heat, J/kg·K - tangential stress, N/m² - t_w tangential stress at wall, N/m² - q_w specific heat flux at wall, W/m² - u_*=_w/ dynamic velocity, m/sec - *=q_w/c_pu_* characteristic temperature, °K - thickness of boundary layer, m - ₀ thickness of laminar sublayer, m - l = /u transverse space scale of average mole at wall, m - y⁺ = y/l _22C6; dimensionless coordinate - u⁺=u/u* dimensionless velocity - ⁺=(T_w – T)/* dimensionless temperature - ⁺=/_w dimensionless tangential stress - R=In (y⁺/ _o ⁺ )/In (⁺/ _o ⁺ ) generalized dimensionless co-ordinate - U = (u⁺ - u _o ⁺ )/(u _o ⁺ - u _o ⁺ ) generalized dimensionless velocity - Pr Prandtl number Indices * flow parameters evaluated at y⁺=1 - parameters at y⁺=⁺ - 0 parameters at y⁺= _o ⁺ - w parameters at wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 441–448, September, 1981.     

Loss of stress equivalence in solid-solution hardening

Available data on the temperature, T, and concentration, c, dependence of the critical resolved shear stress, , of numerous copper- and silver-based solid solutions have been examined with special reference to the stress equivalence of solid-solution hardening, i.e. a common single curve for all alloy concentrations and solute types in a correlation of =(78)–(298) with (78), as first demonstrated by Basinski et al. in 1972. For solid solutions based on a given solvent metal, the stress equivalence is lost if the value of exponent r in the relation (T) c^r varies with temperature. The critical concentration of the solute at which stress equivalence of solid-solution hardening is lost depends on the alloy system.     

Signal rise time of the magnetic bolometer

We present measurements of the temperature dependent signal rise time _S and discuss a model for calculating _S(T). The bolometer consists of a paramagnetic sample and an absorber. The lattice is heated up by absorbing - particles, and the relaxation of the magnetization is measured with a SQUID. With decreasing temperatures _S first increases as ₁1/T, but then decreases strongly. At 30 mK it is reduced by orders of magnitude compared with ₁. This result is in agreement with a theoretical model which takes into account the heat capacities of the lattice, the resonant phonons, the spins, and thermal resistances between these capacities. Under the condition of the bottleneck effect _S is found to be proportional to T³. At low temperatures the lowest values of _S of 2 ms may already be limited by the Kapitza resistance. These are the first measurements of the spin-lattice relaxation times with the energy being transferred from the lattice to the spins.     

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.     

Pulse determination of thermal diffusivity and thermal conductivity for hemispherical specimens: nickel

A method is described for determining the thermal diffusivity, specific heat, and thermal conductivity in a hemispherical volume on the basis of duration of the reference signal.Notation r radius - R radius - r dimensionless coordinate - dimensionless temperature - time - _i duration of heat pulse - _1/2 time for temperature signal at r to attain half the maximum value - q_o amount of heat - a thermal diffusivity - thermal conductivity - density - c_p heat capacity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 864–869, May, 1981.     

Cellular microstructure and heterogeneous coarsening of δ′ in rapidly solidified Al-Li-Ti alloys

Four melt-spun Al-Li-Ti alloys with 2 wt% lithium and 0.10 to 0.35 wt% titanium have been obtained and heat-treated at 473 K for up to 1000 h. Rapid solidification gives rise to a matrix with titanium in solid solution which drastically alters the coarsening rate. While TEM studies of samples aged for short times show a homogeneous distribution of metastable phase, as ageing time is increased, and depending on the ribbon section, three different microstructures can be distinguished: (i) on the wheel side, the distribution is homogeneous; (ii) intermediate regions show particles delineating cells with narrow walls; (iii) on the gas side, particles delineate circular cells. A higher titanium content in the cell centres than on cell walls has been determined. The coarsening rate of in microstructure (i) above is slower than in binary Al-Li alloys. Cellular microstructures (ii) and (iii) show the preferential coarsening of particles on the walls, which is faster the higher the titanium concentration. Taking into account the fact that the partition coefficient of titanium in aluminium in the peritectic region is > 1, an explanation of phase evolution is given which leads to the conclusion that the effect of titanium in solid solution is to retain vacancies, restricting lithium diffusion.     

Effect of temperature on interfacial shear strengths of SiC-glass interfaces

The in situ temperature dependencies of both the debonding, _d, and frictional, _f, shear stresses of a C-coated 140 m SiC monofilament (Textron SCS-6 SiC fibre) were measured using the single fibre pullout-test. Two matrices, a borosilicate (7740 Corning Glass) and a soda-lime (Thomas Scientific) with different thermal expansion coefficients, were tested. At lower temperatures both _d and _f were found to decrease linearly with increasing temperature as a result of the relaxation of the residual stresses developed during processing, which were compressive in both cases. The stress free debonding shear stress for the borosilicate matrix was found to be 3.5 ± 1 M Pa and the friction coefficient between that matrix and the fibres was calculated to be 0.18. Fibre oxidation are believed to be responsible for enhanced bonding between the fibres and the borosilicate matrix at higher temperatures which results in an increase in both _d and _f. The large thermal expansion mismatch between the soda-lime matrix and the SiC fibres resulted in radial cracking of the former during processing. A technique is described where the whole temperature dependence of the interfacial shear stresses can be measured by a single specimen.     

Temperature-density parameters of Freon-13 on the saturation line

Experimental data of a high degree of accuracy are presented on the temperature-density parameters of Freon-13 on the saturation line in the density range of (0.08246–1.6061)·10 kg/m³.Notation T absolute temperature of phase transition from two-phase to one-phase state (or vice versa) - T_c critical temperature - , densities of liquid and vapor, respectively, on saturation line - _c density at critical points - average density - =(T_c–T)/2 reduced temperature - parameter of order, equal to ' – _c – b for the liquid phase and _c + b – "for the vapor phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 830–834, November, 1979.     

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.     

New high permittivity and low loss ceramics in the BaO–TiO2–Nb2O5 composition

New dielectric ceramics with formula BaTi3Nb4O17 and Ba6Ti14Nb2O39 have been prepared and characterized. BaTi3Nb4O17 was densified to 92% of TD after firing at 1310 °C for 4 h. However, Ba6Ti14Nb2O39 fired under optimized conditions (1260 °C for 4 h) showed only 85% TD together with secondary phase. The crystal system of both of the compositions is orthorhombic. The BaTi3Nb4O17 has r56, Qu2100 (at 4.402 GHz), f+86 p.p.m. K-1 and Ba6Ti14Nb2O39 as r50, Qu650 (4.359 GHz) and f+165 p.p.m. K-1. © 1998 Kluwer Academic Publishers     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

Dielectric properties of chemically treated wood

Dielectric properties along the grain for absolutely dried untreated and seven kinds of chemically treated Sitka spruce (Picea sitchensis Carr.) woods were measured. Cole-Cole's circular arc law was applied to the results of the relaxation due to the motions of methylol groups. The following changes were caused by chemical treatments. In polyethylene glycol (PEG) impregnation, the distribution of relaxation times became very narrow, the generalized relaxation time (_m) was considerably decreased, and the relaxation magnitude (₀ – ) was slightly increased. In acetylation, the distribution of relaxation times became very broad, _m was considerably increased, and (₀ – ) was remarkably decreased. In propylene oxide treatment, the distribution of relaxation times became slightly narrow and _m was decreased. _m was slightly decreased in formalization, phenol-formaldehyde (PF) resin treatment and wood methyl methacrylate (MMA) composite. (₀ – ) was decreased in formalization and PF-resin treatment and was hardly changed in wood-MMA composite and heat treatment. The distribution of relaxation times was almost unchanged in formalization, PF-resin treatment, wood-MMA composite and heat treatment.     

Influence of various divalent impurities on dislocation density in KCl:Mg2+, Ca2+, Sr2+ or Ba2+ single crystals

Single crystals of nominally pure KCl and KCl doped with Mg²⁺, Ca²⁺, Sr²⁺ or Ba²⁺ were deformed by compression at 77–254 K; during the tests strain-rate cycling was conducted in association with ultrasonic oscillation. The data were analyzed in terms of strain-rate sensitivity ((/ln)) versus stress decrement (). The curve for KCl doped with the divalent impurities has two bending points and two plateau regions. It is proposed that the variation of strain-rate sensitivity at the second plateau place on the curve with shear strain ((/ln)/) is due to a change in forest dislocation density with shear strain. The forest dislocation density for the specimens seemed to increase by the divalent additions in the compression test on account of the jogs on the screw dislocations. It depended on the concentration of impurities and also on the size of impurity in the specimens at a given temperature. Unfortunately, it was not possible to determine whether a change in the size of impurity influences mobile dislocation density, , from the values of / for KCl doped with Ca²⁺, Sr²⁺ or Ba²⁺.     

Microscopic elastic limit of disperse-hardened condensed Cu-Mo materials

The concentration dependence of the microscopic elastic limit _s of vacuum Cu-Mo condensates before and after thermomechanical treatment is investigated. The value of _s was determined by the method of freely damping torsional oscillations. It is demonstrated that the relationship between the _s of the condensates and the molybdenum concentration is expressed by a curve with a maximum in the 2.7–3% Mo interval. It is established as a result of structural investigations that a reduction in _s in Cu-Mo condensates with high molybdenum concentrations is governed by the development of relaxation processes (transition from slip to microtwinning).Translated from Problemy Prochnosti, No. 6, pp. 18–23, June, 1993.