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      

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.     

Temperature and randomness dependence of the pair-breaking parameter in superconducting aluminum films

Magnetoconductance and excess conductance due to superconducting fluctuations in aluminum films are measured in order to study the temperature dependence of the pair-breaking parameter at temperatures nearT _c . The parameter _M is estimated from the relation =/8k _B T_in, where _in is the inelastic scattering time deduced from the analysis of the magnetoconductance. The parameter _F is determined by fitting theories to data on the excess conductance at zero magnetic field. It is shown that: (1) For films with a wide range of the sheet resistanceR , 12R 200 /, the temperature dependence of _M nearT _c agrees well with the theory of Brenig et al. (2) For clean films withR 100 /, the value of _F analyzed with theories including the correction term to the Maki-Thompson contribution shows almost the same temperature dependence as _M . In a film withR 200 /, however, a discrepancy between _M and _F remains.On leave from College of General Education, Kyushu University, Ropponmatsu, Fukuoka, Japan.     

Chebyshev approximation for the roots of the equation BiWГ(μ)=μVГ(μ)

A minimax approximation, uniform for Bi [0, ), is developed for the roots of the equation BiW()=V(), by means of Chebyshev polynomials.Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 28, No. 4, pp. 710–715, April, 1975.     

Resonance-valence-bond superconductivity in CuO2 planes

We find the exact ground state of a system of 4 × 4 unit cells described by an effective model for cuprate superconductors. The model has the form of the t - J one, but includes a three-site term t like that derived from the Hubbard model in the large U limit, but of opposite sign for realistic or large O-O hopping. For t > t_c (where t_c/t 0.1 for realistic J and doping) the system undergoes a transition to a phase in which the ground state has a significant overlap with a very simple superconducting resonance-valence-bond (RVB) wave function. In the RVB phase there is a large increase of the d-wave superconducting susceptibility. We calculate the boundary of the RVB phase.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

The influence of antimony-additions on the creep behaviour of a 25wt% Cr-20wt% Ni austenitic stainless steel

The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate, , decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature _a Creep stress in a constant load creep test without stress-drop - _A Initial applied stress in stress-drop tests - Stress decrement - ( _A-) Applied stress after a stress decrement, - t _i Incubation time after stress drop (by the positive creep) - _C Strain-arrest stress - _i Internal stress - _{s s}-component (= _i- _c) - Steady state creep rate (average value) in a constant load creep test - Strain rate at time,t, in a constant load creep test - New steady state creep rate (average value) after stress drop from _A to ( _A-) - Strain rate at time,t, after stress drop.     

Numerical method for solving heat-conduction problems for two-dimensional bodies of complex shape

A finite-difference scheme is described for a curvilinear orthogonal net which permits the use of a single algorithm for calculating bodies of various shapes.Notation x, y independent variables - u, v orthogonal coordinates - F(w)=F(u + iv) function of a complex variable - g(u,v)= F(w)/w Jacobian of transformation from (u,v) to (x,y) - thermal conductivity - c volumetric heat capacity - Q heat release per unit volume - T temperature - f value of temperature on boundary of region - time - L, L₁, L₂ differential operators - (u,v) solution of differential problem in canonical region - ^j, ₁ ^j , ₂ ^j , t^J, t ₁ ^j , t ₂ ^j network functions in canonical region - ^j, t^*j solutions of difference problems using rectangular and orthogonal nets respectively - {u_i, v_k} rectangular net in canonical region G - {x_i,k, y_i, k} orthogonal net in given region G^* - u_i, v_k dimensions of cell of rectangular net - u_i,v _i,k dimensions of cell of orthogonal net - h, maximum dimension of cell for rectangular and orthogonal nets respectively - ₁, ₂, difference operators for rectangular and orthogonal nets - A, B, C, D, A^*, B^*, C^*, D^* coefficients of difference scheme for rectangular net - D, Ã, B coefficients of difference scheme for orthogonal net Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 503–509, March, 1981.     

Crystallization kinetics in glassy Ge20Se80−x In x alloys

Crystallization kinetics is studied in glassy Ge₂₀Se_80–xIn_x (0 x 20) using isothermal annealing at temperatures between the glass transition and melting. D.c. conductivity is taken as a parameter to estimate the extent of crystallization (). The activation energy of crystallization (E) and the order parameter (n) are calculated by fitting the values of in the Avrami equations of isothermal crystallization. The results indicate that E is highly composition-dependent, which is explained in terms of the stable phases in the Ge-Se-In system.     

Fatigue of metallic glasses

The fatigue behaviour of Ni₄₉Fe₂₉P₁₄B₆Si₂, Ni₄₈Fe₂₉P₁₄B₆Al₃ and Pd_77.5Cu₆Si_16.5 metallic glasses is examined. In the finite lifetime regime the relationship between stress amplitude ( _a), fracture stress ( _f), mean stress ( _m) and cycles to failure (N _f) is _a=A( _f–_m) (2N _f) ^b , whereA andb are 16.9 and –0.40 respectively for reduced gauge section Ni₄₉ strips (for _m 140 kg mm^–2) and 27.0 and –0.44 for Pd base wires. These results are unusual in thatA 1. Consequently, a sharp discontinuity exists near _a( _f– _m) –1. In a simple tensile test failure occurs at _f(=_y) and 2N_f=1; for peak stresses only a percent or so less than _f the sample will withstand hundreds of cycles of stress. For uniform cross-section glassy metal filaments, a fatigue limit is observed at stress ratios ( _a/ _f) in the vicinity of 0.07 to 0.15. The fatigue limit for reduced section specimens is a factor of 2 higher. Fatigue failure of the Ni-Fe strips may occur under partially or fully plane stress or plane strain conditions, depending on sample thickness and stress. Final failure of the Pd_77.5Cu₆Si_16.5 wires always occurs by general yielding of the remaining section.     

Mass transfer of a single bubble in a minimally fluidized granular bed

The transfer of a gas admixture through the boundary of a cloud of closed circulation of gas is examined with a view to both molecular and convective dispersion.Notation a particle radius - c concentration of the admixture - D, D _c tensors of effective diffusion coefficients and of coefficients of convective dispersion, respectively - D parameter in (14) - D₀, D_m coefficients of molecular diffusion, respectively not taking and taking compressibility into account - F, f functions in (17) and (18), respectively - f fraction of the volume of the sphere with radius R_B occupied by the wake of the bubble - g acceleration of gravity - K mass-transfer coefficient determined in (22) - k coefficient in (7) - L coefficient in (22) - p, s functions determined in (13) - Q, q flow of admixture for the entire bubble and local flow, respectively - r_B, R_c radii of bubble and of cloud of closed circulation, respectively - r radial coordinate - U lift velocity of the bubble - u=v-w; u₀=u_*/u_* minimum velocity of fluidization - V volume of bubble - v, w mean gas velocities in the gaps between particles and of the particles, respectively - parameter determined in (8) - , parameters from (14) - porosity of the dense phase and of the cloud - polar angle - independent variable introduced in (12) - p = 1 - flow function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 323–333, August, 1980.     

Structural Changes in the Surface Layers of PdHx Alloys Caused by the Hydride Phase Decomposition

By the method of optical microscopy, we perform the in-situ investigation of the plane polished surfaces of PdH _x alloys (with video recording of the processes of transformation) in the case of their rapid cooling at a rate of 11–20°C·sec^–1 from T _c = 292°C ( = 1.97MPa) with simultaneous lowering of the pressure of hydrogen within the temperature range 100–160°C. In the course of decomposition of the PdH_0.24 alloy according to a scheme ₀ + , the formation of nuclei of the - and -phases and their growth were not detected. However, we observe a simultaneous coherent transformation of the entire surface accompanied by the formation of a surface topography similar to the modulated structures formed as a result of the spinodal decomposition. We discuss the possibility of realization of spinodal decomposition under the described experimental conditions.     

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.Notation u temperature - k coefficient of thermal conductivity - t time - x spatial variable - x₊ a point on the thermal wave front - a ² generalized coefficient of thermal diffusivity - , , , and s parameters of the process - (x^s) Dirac delta-function - B[, ] a beta function - v(, x), (t) auxiliary functions - A, C, T_o, T_m, T*, R, r, p, and _m constants and parameters Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.     

Heat transfer of a semitransparent plate under conditions of a regular regime of the second kind

The kinetics of the cooling of a plane semitransparent layer under conditions of a regular regime of the second kind is analyzed.Notation time - T temperature - T_e temperature of the surrounding medium (the ambient temperature) - T° initial temperature of the layer - h_e coefficient of convective heat exchange - x coordinate - coefficient of absorption of the substance - n index of refraction - B(, T) surface density of radiation of a black body - C bulk specific heat - K thermal conductivity - wavelength of the radiation - _t range of wavelengths in which the material is partially transparent - _op range of wavelengths in which the material is opaque - degree of blackness of the surfaces in the range of _op - R() coefficient of reflection from the inner surfaces of the layer - ⁺ intensity of the rays consisting of acute angles with the inner normal to the surface x = 0 - ^– intensity of rays in the opposite direction - q thermal flux - angle measured from the inner normal to the surface x = 0 Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 541–546, September, 1981.     

Transient thermal stress analysis of multilayered hollow cylinder

Summary This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.Nomenclature Lame's constant - density - C _v specific heat - k _r ,k radial and circumferential thermal conductivity - _r , linear radial and circumferential thermal expansion coefficient - E _r ,E radial and circumferential Young's modulus - v _r Poisson's ratio - ₀ reference temperature - ,T dimensional and nondimensional temperature - r ^*,r dimensional and nondimensional radial coordinate - ,t dimensional and nondimensional time - _r ^* , _r dimensional and nondimensional radial stress - ^* , dimensional and nondimensional circumferential stress - U, u dimensional and nondimensional radial component of displacement     

Penetration depth and related properties of Al films with enhanced superconductivity

Using combined resistivity, susceptibility, critical field, and NMR measurements it was found that Al films with enhanced superconductivity can be divided into two separate categories depending on their residual resistivities ₀. Films with resistivities smaller than 10 ^–3 ·cm are metallic (_(300K)/ ₀ is larger than but very close to unity); the experimentally measured penetration depth, the upper critical field H, and the penetration field H_p are in good agreement with theoretically calculated values using an experimental value of the mean free path1 _eff. The density of states for such films as inferred from NMR measurements is very close to that of bulk. On the other hand, films with ₀ larger than 10 ^–3 ·cm have a semiconducting behavior ( ₃₀₀ K/ ₀ 1) and are grossly inhomogeneous. The experimental values of H no longer agree with the theoretical estimates using1 _eff. In such films ₀ is no longer a meaningful parameter that can be related to1 _eff, for it is to a large extent a tunneling resistivity as shown by the fact that films not superconducting down to 0.95 K, when measured resistively, are superconducting at 1.2 K, as shown by a susceptibility measurement. These experiments seem to indicate that in a homogeneous film1 _eff has a lower limit of approximately 1 Å.     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

An isothermal theory of anisotropic rods

Summary To provide an isothermal, deterministic theory of anisotropic rods is the primary objective of this paper. Our starting point is the 3-D linear theory of micropolar elastodynamics. First, the governing equations of the theory are established by the use of a suitable averaging procedure together with a separation of variables solution for kinematic variables. Next, without making the usual definiteness assumption for the strain energy density, a dynamic uniqueness theorem is constructed for the solutions of the governing equations. Logarithmic convexity arguments are then used to enumerate a set of conditions sufficient for uniqueness. The theory includes the effects of warping and shearing deformations, and in fact, it incorporates as many higher order effects as deemed necessary in any special case. Also, the application of the theory is illustrated in a sample example.Nomenclature Euclidean 3-space - X_k, X₁z, X a system of right-handed Cartesian coordinates in, rod axis, lateral coordinates; k=1, (=2, 3) - , , a regular region of space in , its closure and boundary surface - L _d,L complementary subsets of, on which deformations and stresses are prescribed, respectively;L _d L =L,L _d L = 0 - L length of rod - A area of cross-section of rod - C a Jordan curve which boundsA - V, L entire volume of rod and its boundary surface - L ₁,L _t lateral surface of rod, surface portion ofL ₁ on which stresses are prescribed - A _r,L ₁ right and left faces of rod - dv, dA, ds element of volume and area onA, and line element alongC - n_i,v _i unit exterior normal vectors toL andC - t time - t_kl, m_kl components of stress and couple stress tensors - f_i, l_i body force and body couple vectors per unit volume - , J_kl mass density, components of microinertia tensor - u_i, _i displacement and microrotation vectors - prescribed steady temperature increment - _kl, _klm components of Kronecker's delta and alternating tensor - t_i, m_i stress and couple stress vectors - _kl, e_kl components of strain and infinitesimal strain tensors - C_klmn, D_klmn components of isothermal elastic stiffnesses - B_kl thermal coefficients of material - , Lamé's elasticity constants - , , , elastic moduli of microisotropic continuum - B coefficient of linear thermal expansion - d_i, d_kl u_i or _i, _kl or e_kl and/or _kl - T _kl ^(m,n) , M _kl ^(m,n) components of stress and couple stress resultants of order (m, n) - T _k ^(m,n) M _k ^(m,n) components of stress and couple stress vector resultants of order (m, n) - d _k ^(m,n) , d _kl ^(m,n) components of deformation (u _k ^(m,n) , _k ^(m,n) ) and strain ( _kl ^(m,n) , e _kl ^(m,n) , _kl ^(m,n) ) of order (m, n) - F _i ^(m,n) , L _i ^(m,n) body force and body couple resultants of order (m, n) - U _i ^(m,n) , _i ^(m,n) displacement and microrotation resultants of order (m, n) - P _i ^(m,n) , Q _i ^(m,n) effective loads of order (m, n) - N , M, , P, Q, w, T ₁₁ ^(0,0) ,M ₁₁ ^(0,0) , P ₁ ^(0,0) , Q ₁ ^(0,0) , U ₁ ^(0,0) , ₁ ^(0,0) - v₀ rod velocity, (E/)^1/2 - K, W kinetic and potential energy densities - V, U kinetic and potential energies per unit length of rod - total energy of rod - C^(m,n) functions with derivatives of order up to and including (m) and (n) with respect to space coordinates and time, respectively - G (t) logarithmic convexity function - ()^. time differentiation, /t () - () partial differentiation with respect to the axial coordinate, /z () - E,v Young's modulus, Poisson's ratio     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.