Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

Thermal Conductivity of the Four-Leg Spin-Ladder System La2Cu2O5 Single Crystal

We have investigated the magnetic susceptibility, , and the thermal conductivity, , in magnetic fields for the four-leg spin-ladder system La₂Cu₂O₅ single crystal. The in a magnetic field parallel to the ladder exhibits a kink at 130 K in correspondence to the magnetic ordering. The along the ladder exhibits a peak at 25 K and a shoulder at 14 K, which are probably related to the thermal conductivity due to magnons, _magnon, and that due to phonons, _phonon, respectively. The perpendicular to the ladder, on the other hand, exhibits only one broad peak related to _phonon. The observed large anisotropy of has been explained based upon the anisotropy of _magnon.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

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.     

Varistor characteristics in PTCR-type (Ba,Sr)TiO3 ceramics prepared by single-step firing in air

This paper deals with donor, acceptor-codoped (Ba_0.4Sr_.6)TiO₃ ceramics with distinct varistor characteristics at room temperature, which were prepared by single-step firing in air. The materials, with the Curie point at around –90 °C, exhibited a large PTCR (positive temperature coefficient of resistivity) effect of more than seven orders of magnitude in the temperature range –90 °C (the resistivity 10³ · cm) to room temperature ( > 10¹⁰ · cm). An apparent dielectric constant of >20000 and tan < 0.05 (at 100 kHz) were observed for the present materials at room temperature, and moreover, the materials exhibited nonlinear current-voltage characteristics with the nonlinear coefficient, , in the range 7–12 and the varistor field, E_v, in the range 0.3–1.0 kV/cm. The value of in the present materials increased systematically with increasing in their PTCR temperature range. It has been found that there exists a close correlation between and the grain-boundary potential barrier height, e, obtained from the -T characteristic of the materials. An almost linear relationship was also found to exist between and log E_v for the present materials.     

Behaviour of amorphous poly(ethylene terephthalate) annealed at T<T g by thermally stimulated currents

Thermally stimulated current (TSC) discharges in open circuit of amorphous poly(ethylene terephthalate) (PET) corona-charged electrets show a heteropolar relaxation at 87 °C, ₁ between and peaks. This relaxation tends to become homopolar when the sample is annealed at temperatures below the glass transition temperature. This is due to the formation of a trapped charge density on the surface of the material that originates, during the TSC discharge, a current that counteracts the one that results in ₁ This trapping effect, which initially is null, increases with annealing due to the rise in resistivity. On the other hand, TSC discharges in short-circuited annealed samples result in a heteropolar peak, ^*, that corresponds to ₁ The area of ^* increases with the annealing time in a bounded way. This peak is related to the formation of thermal nuclei (embryos) in the bulk of the material that act as heterogeneities. This suggests that ₁ is associated with a barrier-type polarization. If the annealed sample is heated to temperatures above the glass transition temperature, the tendency to the inversion of ₁ vanishes and ^* disappears, whereas and are modified. This suggests that relaxation is related to a Maxwell-Wagner-Sillars effect.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites

When a matrix crack encounters a fibre that is inclined relative to the direction of crack opening, geometry requires that the fibre flex is bridging between the crack faces. Conversely, the degree of flexing is a function of the crack face separation, as well as of (1) the compliance of the supporting matrix, (2) the crossing angle, (3) the bundle size, and (4) the shear coupling of the fibre to the matrix. At some crack face separation the stress level in the fibre bundle will cause it to fail. Other bundles, differing in size and orientation, will fail at other values of the crack separation. Such bridging contributes significantly to the resistance of the composite to crack propagation and to ultimate failure. The stress on the composite needed to produce a given crack face separation is inferred by analysing the forces and displacements involved. The resulting model computes stress versus crack-opening behaviour, ultimate strengths, and works of failure. Although the crack is assumed to be planar and to extend indefinitely, the model should also be applicable to finite cracks.Glossary of Symbols a radius of fibre bundle - C 2 _f /aE _f - ^* critical failure strain of fibre bundle - _b bending strain in outer fibre of a bundle - _c background strain in composite - _f axial strain in fibre - _s strain in fibre bundle due to fibre stretching = _f - () strain in composite far from crack - E Young's modulus of fibre bundle - E _c Young's modulus of composite - E _f Young's modulus of fibre - E _m Young's modulus of matrix - f() number density per unit area of fibres crossing crack plane in interval to + d - F total force exerted by fibre bundle normal to crack plane - F _s component of fibre stretching force normal to crack plane - F _b component of bending force normal to crack plane - G _m shear modulus of matrix - h crack face opening relative to crack mid-point - h _m matrix contraction contribution to h - h _f fibre deformation contribution to h - h _max crack opening at which bridging stress is a maximum - I moment of inertia of fibre bundle - k fibre stress decay constant in non-slip region - k ₀ force constant characterizing an elastic foundation (see Equation 7) - L exposed length of bridging fibre bundle (see Equation 1a) - L _f half-length of a discontinuous fibre - m, n parameters characterizing degree of misalignment - N number of bundles intersecting a unit area of crack plane - P _b bending force normal to bundle axis at crack midpoint - P _s stretching force parallel to bundle axis in crack opening - Q() distribution function describing the degree of misalignment - s _f fibre axial tensile stress - s _f ^* fibre tensile failure stress - S stress supported by totality of bridging fibre bundles - S _max maximum value of bridging stress - v fibre displacement relative to matrix - v elongation of fibre in crack bridging region - u _coh non-slip contribution to fibre elongation - U fibre elongation due to crack bridging - v overall volume fraction of fibres - v _f volume fraction of bundles - v _m volume fraction matrix between bundles - w transverse deflection of bundle at the crack mid-point - x distance along fibre axis, origin defined by context - X distance between the end of discontinuous fibre and the crack face - X ^* threshold (minimum) value of X that results in fibre failure instead of complete fibre pullout - y displacement of fibre normal to its undeflected axis - Z() area fraction angular weighting function - tensile strain in fibre relative to applied background strain - ^* critical value of to cause fibre/matrix debonding - angle at which a fibre bundle crosses the crack plane - (k ₀/4EI)^1/4, a parameter in cantilever beam analysis - v_m Poisson's ratio of matrix - L (see Equation 9) - shear stress - _* interlaminar shear strength of bundle - _d fibre/matrix interfacial shear strength - _f frictional shear slippage stress at bundle/matrix interface - angular deviation of fibre bundle from mean orientation of all bundles - angle between symmetry axis and crack plane     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

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

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls

Summary A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a two-dimensional rectangular enclosure in which two side walls are maintained at uniform heat flux condition. The horizontal top and bottom walls are thermally insulated. A finite difference scheme comprising of modified ADI (Alternating Direction Implicit) method and SOR (Successive-Over-Relaxation) method is used to solve the governing equations. Computations are carried out over a wide range of Grashof number, Gr and Hartmann number, Ha for an enclosure of aspect ratio 1 and 2. The influences of these parameters on the flow pattern and the associated heat transfer characteristics are discussed. Numerical results show that with the application of an external magnetic field, the temperature and velocity fields are significantly modified. When the Grashof number is low and Hartmann number is high, the central streamlines are elongated and the isotherms are almost parallel representing a conduction state. For sufficiently large magnetic field strength the convection is suppressed for all values of Gr. The average Nusselt number decreases with an increase of Hartmann number and hence a magnetic field can be used as an effective mechanism to control the convection in an enclosure.List of symbols Ar aspect ratio,H/L - B ₀ induction magnetic field - H ₀ magnetic field,H ₀=B ₀/ _m - g gravitational acceleration - Gr Grashof number,gq(L/k)L ³/v ² - H height of the enclosure - Ha Hartmann number, - k thermal conductivity - Nu local Nusselt number - average Nusselt number - p pressure - Pr Prandtl number, / - q heat flux - t time - T dimensionless temperature, (–₀)/q(L/k) - u vertical velocity - U dimensionless vertical velocity,uL/ - v horizontal velocity - V dimensionless horizontal velocity,vL/ - x vertical coordinate - X dimensionless vertical coordinate,x/L - y horizontal coordinate - Y dimensionless horizontal coordinate,y/L - thermal diffusivity - thermal expansion coefficient - temperature - ₀ reference temperature - density - kinematic viscosity - viscosity - _m magnetic permeability - electrical conductivity - stream function - dimensionless stream function, / - dimensionless time,t/L ² - vorticity - dimensionless vorticity, L ²/ - X grid spacing inX-direction - Y grid spacing inY-direction - time increment - ² Laplacian operator     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

Oxidation of an Al2O3-γAlON ceramic composite

The oxidation of dispersed aluminium oxynitride particles in an alumina matrix has been studied. The kinetics law of this reaction is linear and the activation energy is 420±40 kJ mol^–1 (100±10 kcal mo^–1). A-alumina layer is formed and leads to-alumina above 1200° C. The-alumina formation produces surface compressive stresses, and thus the mechanical properties ( _f, HV) are improved. We have proved that the formation of-alumina in the Al₂O₃-AION composite can lead to the best properties for this ceramic. A-alumina layer has a very interesting effect on the wear resistance of this material.     

The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.     

A Monte Carlo Study of Disorder in the High Pressure Mixed Crystal N2-Ar

In order to obtain a better notion of the experimental results in our laboratory, Monte Carlo calculations have been performed of the N ₂-Ar crystal on the N ₂-rich side, in the p-T region where the and phases exist in pure N ₂. Considering the enthalpy, the system prefers the Ar atoms to be located on the sphere positions. The * phase is present for mixtures down to but is most likely metastable. The *-* transition shifts to lower temperatures with decreasing . The 2 ^nd order transition within the phase continues to exist to even smaller . In contrast to the * -* transition, the transition temperature for the 2 ^nd order transition does not shift to lower temperatures. For a mixture of it is within 5 K from the pure 2 ^nd order transition at a pressure of 7.0 GPa.