On dual solutions occurring in mixed convection in a porous medium

Summary The dual solutions to an equation, which arose previously in mixed convection in a porous medium, occuring for the parameter in the range 0 < < ₀ are considered. It is shown that the lower branch of solutions terminates at =0 with an essential singularity. It is also shown that both branches of solutions bifurcate out of the single solution at =₀ with an amplitude proportional to (₀-)^1/2. Then, by considering a simple time-dependent problem, it is shown that the upper branch of solutions is stable and the lower branch unstable, with the change in temporal stability at =₀ being equivalent to the bifurcation at that point.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

Heat transfer in plane film formation

A mathematical model is obtained for the process of cooling with formation of a planar film. The solution obtained is verified experimentally.Notation mean axial velocity gradient - v_x current axial velocity - v_o initial polymer velocity - v₁ sampling velocity - K draw ratio - deformation rate tensor - x, y, z spatial coordinates - X, Y dimensionless coordinates - L() differential operator - T temperature - T_o initial temperature - T_c temperature of surrounding medium - dimensionless temperature - dimensionless temperature averaged over film thickness - thermal-diffusivity coefficient - 2_o initial film thickness - thermal conductivity - heat-transfer coefficient - f(X) distance function - Bi Biot criterion, Bi_o, Biot criterion calculated for initial film thickness - Gz* modified Graetz criterion - V dimensionless velocity - ₁, ₂, ₃ heat-transfer coefficients produced by radiation, free convection, and forced convection - v_c, _c mean velocity and film half-thickness in formation zone - T₁ calculated temperature value - T₂ experimental temperature value - l formation zone length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 854–858, November, 1979.     

Preferentially orientated precipitation in MnTiO3 single crystals

Preferentially orientated precipitation of -TiO₂ (rutile) needles in single crystals of MnTiO₃ grown by a floating-zone method under a controlled atmosphere of oxygen fugacity was studied. Optical microscopy and X-ray analysis revealed that the orientation relation between the -TiO₂ precipitates and the MnTiO₂ matrix is: {000 1}MnTiO₃// {111}-TiO₂ and 11¯20MnTiO₃// 110-TiO₂. The precipitation phenomenon was explained by introducing a nucleation and growth mechanism which was experimentally supported by heat treating experiments.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

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.     

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.     

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.     

An investigation of the ordered DO19 phase formation in the Ti-Al system

For the Ti-rich, Ti-AI system, the- and- ₂ phase boundaries have been obtained through differential thermal analysis for alloy compositions ranging from 10.2 to 25.2 at% Al (6 to 16 wt% Al). It has been shown that in the above mentioned composition range, a metastable disordered-phase can be quenched in. This metastable then transforms to the ordered ₂(DO)₁₉ phase upon heating and/or isothermal ageing. It has also been observed that the kinetics of this ordering phenomenon is composition dependent.     

Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

---

Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

---

Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

Anisotropic grain growth of R-α-sialon (R = Nd and Er)

Two R--sialon (R_0.6Si_9.3Al_2.7O_0.9N_15.1, R=Nd and Er) compositions were first fired at 1750°C/25 min and 1650°C/2 h respectively for completion of the phase transformation. Elongated -sialon grain morphology was developed in both samples after being re-fired at 1800°C for different periods of time. The growth in width of R--sialon grains is controlled by diffusion in the liquid, while the length growth tends to be interfacial reaction controlled. The anisotropic growth of R--sialon is attributed to the large difference in the growth rate constant between the length and the width directions of the grain.     

The crystal growth and thermoelectric properties of chromium disilicide

Single crystals of chromium disilicide about 8 mm in diameter and 35 mm long were grown using the floating zone technique. Measurements of electrical resistivity , Hall coefficient R and thermoelectric power were carried out in the temperature range from 85 to 1100 K. The values of and showed the anisotropy over the temperature range studied. The ratios parallel and perpendicular to the c-axis were / =1.9 and /=1.7 respectively, at room temperature. It was found to be a degenerate semiconductor having the hole concentration of 6.3×10²⁰ cm^–3 below 600 K. The effective masses of holes parallel and perpendicular to the c-axis determined from the thermoelectric power and the hole concentration near room temperature were estimated to be five and three times as large as a free electron mass, respectively. The calculation on the values of and was made using those effective masses. These values showed good agreement with the observed values in the temperature range from 150 to 1100 K.     

Eutectoid decomposition mechanisms in hypoeutectoid Ti-X alloys

A TEM study has been made of the bainite reaction in five hypoeutectoid Ti-X alloys, where X was successively cobalt, chromium, copper, iron and nickel. Rational orientation relationships were demonstrated amongst eutectoid , eutectoid intermetallic compound and the matrix in Ti-Ni, Ti-Co and Ti-Cr. Formation of Ti₂Co at : boundaries was observed. Eutectoid in bainite was found to be slightly misoriented with respect to proeutectoid , indicating that it is separately nucleated, perhaps sympathetically, rather than the result of the continued growth of proeutectoid . Eutectoid Ti₂Co and Ti₂Cu crystals in bainite were approximately equiaxed whereas Ti-Cr₂ crystals were elongated, a result ascribed to a ledge height-to-spacing ratio / at intermetallic compound crystal: boundaries approaching that of eutectoid (: boundaries in Ti-Cr but not in the other two systems. In the Ti-Fe alloy, eutectoid and eutectoid TiFe were directly observed to have ledged interphase boundaries with their matrix, but with different inter-ledge spacings and growth directions. Observation of pearlite lamellae growing normal to the broad faces of proeutectoid plates in the Ti-Ni alloy indicates that this mode of eutectoid decomposition, like that of bainite, can develop from partially coherent interphase boundaries. The suggestion was offered that pearlite forms when approachesh at the nucleating proeutectoid : interface and that bainite develops when h at this interface.     

Dielectric relaxation in polychlorotrifluoroethylene

The effect of increasing lamellar thickness in bulk polychlorotrifluoroethylene (PCTFE) by various methods (annealing and increasing time and temperature of crystallisation) on the parameters of the and relaxations has been studied.For the a relaxation consistent increase in temperature of maximum loss and activation energy with increasing lamellar thickness confirms the strong suggestion of earlier work [6] on oriented specimens and shows that the relaxation arises mainly in the interior of the lamellae with little contribution from the chain folds.No systematic changes in these parameters with increasing lamellar thickness was found for the relaxation and this is explained by the presence of _c and _a components in crystalline and amorphous regions respectively. The component _a (as well as the _c one) shows a marked anisotropy in magnitude with respect to the draw direction in oriented specimens relative to the direction of the applied electric field. This implies a lining up of the chain molecules parallel to one another in amorphous regions.The non-existence of analogous short chain compounds and experimental scatter prevented detailed checking of the consistency of the data for the relaxation with the theory for the _c-C _c model [5].     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

Supercarrier Effective Mass Isotope Effect by Interband Scattering

Supercarrier effective mass isotope effect (exponent ) is investigated using a two-band model with interband pair scattering. The corresponding repulsive interaction incorporates besides the dominating electronic (Coulomb) part an electron-phonon contribution inversely proportional to the ionic mass factor. Calculations illustrating the behaviour of T _c , its isotope exponent , and with doping in La _2–x Sr _x CuO ₄ type underdoped system reflect the observed tendencies. ² Both and diminish with doping, the sign of is opposite to . A typical estimation gives || 0.2.     

Vibrational properties of wood along the grain

The dynamic Young's modulus (E_L) and loss tangent (tan _L ) along the grain, dynamic shear modulus (G_L) and loss tangent (tan _S) in the vertical section, and density () of a hundred spruce wood specimens used for the soundboards of musical instruments were determined. The relative acoustic conversion efficiency ( ) and a ratio reflecting the anisotropy of wood (, (E_L/G_L)(tan _S/tan _L)) were defined in order to evaluate the acoustic quality of wood along the grain. There was a positive correlation between and , and the variation in was larger than that in . It seemed logical to evaluate the acoustic quality of spruce wood by a measure of . By using a cell wall model, those acoustic factors were expressed with the physical properties of the cell wall constituents. This model predicted that the essential requirement for an excellent soundboard is smaller fibril angle of the cell wall, which yields higher and higher . On the other hand, the effects of chemical treatments on the and of wood were clarified experimentally and analyzed theoretically. It was suggested that the and of wood cannot be improved at the same time by chemical treatment.     

Experimental evaluation of relative mode parameters in the irregular earth-to-ionosphere waveguide

Conclusions A model for representing the propagation of superlong waves was selected. Certain relative mode parameters ()₁, ()₂, ()₃, (V)₁, (V)₂, (V)₃, C₁, C₂, and C₃ can be used in order to account for the time-measurement error produced as a resuit of the double-mode signal propagation, to determine in a semiempirical manner the ionosphere's effective reflection height at night and in the daytime, to calculate and apply signal-propagation corrections which take into account phase velocity changes due to variations in the ionosphere height from day to day, and to calculate the fields of transition paths.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 75–78, August, 1974.