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

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

Widening the Scope of Working of Solid‐State Nd‐Glass Lasers

With the example of the serial model of a pulsed Ndglass laser, it is shown that the use of an unstable resonator with a semireflecting homogeneous exit mirror makes it possible to significantly decrease the laserbeam divergence and increase the uniformity of the radiationintensity distribution in the near zone. We were the first to obtain a laserbeam quality of (40–50) mm·mrad for technological glass lasers and to attain a depth of fusing of of 6.3 mm for steel (aspect ratio 10) for an energy of 23 J. The obtained uniformity of the radiationintensity distribution was estimated at the level of ±10%. The beamquality level attained for the Ndglass laser beam allows us to recommend it for both realization of deepfusion regimes and laser hardening without the use of external integrating optical elements.     

Variational method for measuring dielectric parameters of polar liquids at ultrahigh frequencies

Conclusions Owing to the use of nomograms the above method is universal and rapid. It is independent of the frequency at which the values of and are measured, and it is equally applicable for measuring dielectric parameters of polar liquids which are highly absorbent at ultrahigh frequencies and have one or two clearly expressed minima in the relationship of tol, and for liquids with low dielectric losses in the uhf range, whose measurement with adequate precision is difficult by other methods. Among the deficiencies of the suggested method one should note the two values obtained for _d and tan /2 from the nomogram readings. However, this deficiency can easlly eliminated either by comparing the two values for _d and tan /2 with those obtained for them from a similar nomogram and the second minimum in the relationship of tol, or by an approximate evaluation of _d and tan /2 by means of any other less precise measuring method.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 48–49, October, 1970.     

Mechanical properties and microstructure of β-SiAION-β-SiC composites by pressureless sintering

-SiAION--SiC composites containing up to 12 wt% -SiC were prepared by pressureless sintering. The strength of composites at room temperature remained relatively unchanged, whereas strength at 1200 °C increased for composites. The fracture toughness (K _IC) for composites was higher than that for -SiAION ceramics. The maximum value was 5.4 MPa m^1/2 for 6 wt% -SiC, and this was an improvement of 15% in comparison with -SiAION ceramics. From SEM observations, an improvement inK _IC values was attributed to crack deflections and branching-off of cracks. Intra-granular fractures were frequently observed in -SiAION. From TEM observations, -SiAION crystals were nanocomposites, within which existed the fine crystals in -SiAION crystal. For composite, -SiAION and -SiC crystals were directly in contact. The mismatching zone was observed in -SiC.     

Underpinning of a simple blunt flaw fracture initiation relation

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius . The relation gives the critical elastic flaw-tip peak stress _pcr, and has been derived using a two-extremes procedure, whereby the separate, and indeed exact, solutions for small and large s/ values are blended together to give an all-embracing relation that is valid for all s/ values. _pcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, _pcr essentially depends on only one geometrical parameter . This paper provides underpinning for the general thrust of the two-extremes procedure by appealing to exact results for the complete spectrum of s/ values from analyses of appropriate Mode III models. Results obtained by applying the two-extremes procedure are shown to be in very good agreement with the exact results.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

A high-temperature solid-state potentiometric sensor for nitrogen based on ceramic LaAl12O18N

The nitrogen-sensing properties of LaAl12O18N are described for the first time. Positive e.m.f. measurements at high temperature across the cells -Nb (N), -Nb2N, -Al2O3, LaAl12O18NLaAl11O18 (or LaAl12O18N)LaAl12O18N, -Al2O3, -Nb2N, -Nb4N3, were in agreement with PN2(-Nb2N, -Nb4N3)>PN2(-Nb(N), -Nb2N) for the idealized stoichiometric cell reaction -Nb4N3+2-Nb(N)3-Nb2N, thus demonstrating the nitrogen-sensing property of these cells. The e.m.f. for a variety of cells with electrodes containing -V2N, -Nb2N, -Ta2N and Ti2N, were consistent with the predicted equilibrium nitrogen partial pressures.     

Fabrication of β- and β′′-Al2O3 tubes by pressureless powder packing forming and salt infiltration

A new forming method, pressureless powder packing (PLPP), was studied to fabricate the - and -Al2O3 tubes. Alkali sources were infiltrated into the pores of -Al2O3 tube preforms that had been prepared by the PLPP forming method. The composition for the synthesis of -Al2O3 phase was Na2O · 0. 138Li2 · 4.4Al2O3. The -Al2O3 fraction of calcined and sintered bodies was increased with the increase of calcination temperature, and phase formation was largely affected by the type of starting -Al2O3. Large particle size and narrow size distribution of fused -Al2O3 resulted in uniform green microstructure that enhanced the homogeneity of alkali salts after infiltration, which was very important for the -Al2O3 formation. Sintered microstructure was uniform in all specimens but further development was required for density improvement.     

Influence of rhenium on the microstructures and mechanical properties of a mechanically alloyed oxide dispersion-strengthened nickel-base superalloy

The influence of a 3 wt% Re addition on the creep strength and microstructure of a mechanically alloyed and oxide dispersion-strengthened nickel-base superalloy was investigated. Two alloys, Ni–8Cr–6.5Al–6W–3Ta–1.5Mo–6Co–1Ti–3Re–0.15Zr–0.05C–0.01B–0.9Y₂O₃ (3Re alloy) and a non-rhenium containing (0Re) alloy were prepared for this study.The 3Re alloy showed two-fold improvement in creep life compared with that of 0Re alloy, presumably due to a change in the mode of the precipitate-dislocation interaction. For the 3Re alloy, finer, more cuboidal and aligned precipitates are formed, which force the mobile dislocations at the – interfaces to cut precipitates in order to proceed. Shearing of precipitates is evinced by the existence of stacking faults and results in an increase of creep strength. In constrast, lower creep strength was observed for 0Re alloy because a dislocation looping mode is dominant with coarser and more irregularly shaped precipitates present in this alloy. Another possible explanation for an improved creep strength of 3Re alloy is related to the tangled dislocation structure formed by the interaction between glide dislocation and interfacial dislocation, which also acts as an effective barrier for further glide dislocation motion. A 3 wt% Re addition significantly retards coarsening kinetics. Rhenium acts as a rate-controlling species upon the volume diffusion-controlled coarsening process because it is a heavy elemenet and also it almost solely partitions to the matrix. X-ray diffraction experiments showed that the magnitude of the lattice mismatch between and increased with the 3 wt% Re addition from 0% to –0.26% at room temperature. Increased lattice mismatch for 3Re alloy causes the formation of more aligned and cuboidal precipitates rather than random and odd-shaped precipitates for 0Re alloy, and it also accelerates the coalescence between cuboidal precipitates.     

Numerical study of flow in a constricted curved annulus: An application to flow in a catheterised artery

The flow of an incompressible Newtonian fluid in a curved annulus with a local constriction at the outer wall is investigated numerically. The three-dimensional nonlinear elliptic partial differential equations governing the flow are simplified by use of small curvature and mild constriction approximations. The simplified equations of motion, which are locally two-dimensional elliptic in nature at each cross-section, are solved numerically by means of the finite-difference method described by Collins and Dennis [Quart. Jour. Mech. Appl. Math. 28 (1975) 133–156]. Although the results are restricted to small curvature and mild constriction, these are valid for all Dean numbers D in the entire laminar flow regime. The numerical results show that, for higher values of radii ratio k, the pressure gradient, pressure drop, and frictional resistance increase considerably and they vary markedly across the constricted length. These results are used to estimate the increase in frictional resistance in an artery when a catheter is inserted into it. In the absence of constriction (₁=0) and depending on the value of k ranging from 01 to 07, the frictional resistance increases by a factor ranging from 132 to 2391 for D=500 and 120 to 1656 for D=2000. But, in the presence of constriction (₁ = 01) with the same range for k, the increase in frictional resistance is by a factor ranging from 134 to 4232 for D=500 and 118 to 295 for D=2000. In a straight annulus, the increased factor ranges from 174 to 3261 for ₁=0 and 178 to 5827 for ₁ = 01 (for all Dean numbers D).     

Plane thermal stresses around holes under steady distribution of temperature

Summary A method for determining the plane thermal stress distribution in a multiply connected region under steady distribution of temperature is presented. The analysis is based on the complex variable approach and permits, if the thermal field is known, the simple determination of theKolosoff functions. The method is illustrated using two examples.

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Zusammenfassung Es wird eine Methode zur Bestimmung des ebenen Wärmespannungszustandes in einem mehrfach zusammenhängenden Bereich unter stationärer Temperaturverteilung angegeben. Die Analyse benützt die komplexe Darstellung und erlaubt die einfache Bestimmung derKolosoff-Funktionen, wenn das Temperaturfeld bekannt ist. Die Methode wird anhand von zwei Beispielen illustriert.

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Notation c constant which take valuesc=E/(1–) for plane strain and - c E for plane stress - Re{} real part of - u, v components of displacement vector - T temperature - z complex variable (x+i y) - coefficient of thermal expansion - complex variable in a mapped plane - boundary value ofz or - Kolosoffs constant which takes values =3–4 for plane strain and =(3–)/(1+) for plane stress - shear modulus of elasticity - Poissons ratio - _xx,_yy,_xy components of stress tensor - () mapping function     

Torsional load transfer from a rigid shaft to an elastic plane with a slit

A plane elastostatic problem for an elastic wedge loaded by a concentrated moment at its apex provides an example of violation of the Saint-Venant principle for apex angles 2 larger than . Considering the problem for a truncated wedge, Neuber demonstrated the method of construction of an applicable solution for any apex angles in the range 22, despite the failure of the Saint-Venant principle. In the present paper the particularly important case of the truncated-wedge problem is examined. The truncated wedge degenerates into a slitted elastic plane, while a rigid circular shaft, acted upon by a torsional moment, is inserted into the plane. The analytical solution of the mixed boundary-value problem is obtained. Numerical results turn out to be in complete agreement with Neuber's results for the slitted elastic plane.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

An induced interaction model for arbitrarily polarized Fermi systems

A model for calculating the interactions in arbitrarily spin-polarized Fermi systems is presented. Starting from the four-point vertex functions, the induced part of the interactions is deduced by explicitly treating the one-particle, one-hole irreducible diagrams and using some general crossing symmetry relations. Extrapolation away from the Fermi surface is carried out by replacing the particle-hole phase space by Lindhard functions in the crossed channel; consequently, calculation of the necessary - phase space function is presented. The longitudinal spin-density and density responses for polarized systems are obtained by diagrammatic means. A possible way of treating the direct part of the interactions using Born approximation is also discussed. Finally, the limits of the model for zero and full polarization are given.     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints

The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (=), and those having nonparallel water rays ( ). The = categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two = geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.     

Thermophysical properties data on molten semiconductors

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