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.     

Charged defects-controlled conductivity in Ge-ln-Se glasses

The variation of the d.c. electrical conductivity, , with composition and temperature was investigated for glasses of the Ge-In-Se system. The results indicate a decrease in the activation energy for electrical conductivity, E, and an increase in on introduction of indium into Ge-Se glasses. The changes in E and with composition (selenium content in the glasses) are identical for the Ge_x In₅ Se_95–x and Ge_x In₈Se_92–x families. The results have been traced to the conduction controlled by charged defects in these chalcogenide glasses. The changes in E and have been explained by a shift in the Fermi level, being brought by the introduction of indium.     

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.     

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.     

Electronic and two-magnon light scattering in oxide superconducting crystals

From investigations of two-magnon Raman scattering (RS) under high pressures up to 430 kbar in Eu₂CuO₄ and YBa₂Cu₃O_6.2 crystals, it was shown that the dependence of the superexchange integralJ on the distance between Cu and O atoms in CuO₂ planesa is anomalously weak (Ja^–n, n=3±0.5). The large value ofJ indicates strong initial overlapping of Cu and O wave functions in high-T _c , materials. It was found that an increase in free carrier concentration results in a rapid increase of magnon damping and the disappearance of the two-magnon peak from RS spectra. A detailed study of electron Raman scattering has been carried out in superconducting and insulating YBa₂Cu₃O_6–x , single crystals. The spectral redistribution at frequencies<600 cm^–1 in different polarizations indicate that the superconducting gap is strongly anisotropic. In the normal (metallic) phase the behavior of the imaginary part of the response functionR() in the polarization (xx) corresponds to the model of a marginal Fermi liquid, and in the polarization (xx), this behavior is independent of the temperature. In insulating crystals,R() is independent of temperature toT200 K in both polarizations.     

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.     

Single-Mode As–S Glass Fibers

Single-mode As–S glass fibers with a core diameter from 3 to 20 m and a clad diameter of 125 m are prepared by the double-crucible method. The cutoff wavelength of the fibers is 0.9–6 m. The lowest transmission losses in the fibers at 2.2–2.3 m are 100 dB/km, and their mean bending strength is 800–1000 MPa.     

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.     

Geometrical factors for parts of an infinite cylindrical surface

A method is described for calculating geometrical factors, allowing for attenuation of radiation by the medium, and computing radiative heat transfer between coaxial strips forming part of a cylinder.Notation mean generalized geometrical factor - local generalized geometrical factor for a closed infinite cylindrical surface - F surface area - l length of ray between elements dF_m - D and H diameter and length of cylinder - k ray attenuation coefficient - equivalent solid angle [1] determined from the condition _mm=1 at =0 for a closed surface - f () indicatrix of the specific radiation intensity (a quantity analogous to the specific luminous intensity [1]) - angle between the normal to an element of surface and the ray linking the surface elements - and angles in a section of the surface - angle between the radius and the chord subtending the projections of dF_mon the section - angle between the radius and the chord subtending the projection of element dF_mon the section and the edge of the surface - acute angle between rayl and the generator of the cylinder - ₀ half subtended angle for the arc of a section of the surface - S₂ and M generalized local geometrical factors in the notation of [2] (s₂ and is shown in Table 2 - M local factor for an infinite cylinder with a semicircular cross section for a point in the middle of the plane part of the surface; a table of values of M is given in [2]) - n number of strips     

Normal-State Gap, Supercarrier Mass Anisotropy and Isotope Effects in La2?xSrxCuO4

Magnetization measurements have been performed on the oxygen-isotopeexchanged samples (¹⁶O and ¹⁸O) of the one-layer cuprate superconductorsLa_2–x Sr _x CuO₄ (0.06x0.20). We find that there is an oxygen-isotopeeffect on the effective supercarrier mass m**, which is huge for x=0.06,and reduced to a smaller value for x=0.15. We also find that there coexistsmall (bi)polarons and free carriers for x0.09, but only small (bi)polaronsare present for x0.09. The normal-state gap is related to the bipolaronbinding energy which is inversely proportional to x for 0.05x0.15. Theobserved isotope effects, supercarrier mass anisotropy, normal-state gap,and mid-infrared spectra for x0.09 can be quantitatively explained by the small(bi)polaron theory of superconductivity proposed by Alexandrov, Kabanov, andMott (AKM).