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      

Grain-boundary sliding and intergranular cavitation during superplastic deformation of α/β brass

Intergranular and interphase cavitation in binary alpha/beta brass has been investigated in tension at 600° C under conditions of superplastic deformation. The sites for nucleation of cavities has been studied by quantitative metallography and the cavities are observed to nucleate preferentially at- interfaces. The process of cavitation is associated with grain boundary sliding and cavity nucleation occurs at points of stress concentrations in the sliding interfaces. Measurements of grain and phase boundary sliding at various interfaces demonstrate that sliding occurred on- boundaries more readily than on- and-gb interfaces. The predominance of- interface cavitation is believed to be as a result of greater sliding at the- boundary and of an unbalanced accommodation of sliding adjacent to this type of boundary.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

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.     

Subcritical region of laminar adiabatic gas flow in a two-dimensional channel

It is shown that so-called developed laminar gas flow in a two-dimensional channel cannot continue beyond values of 0.74. At > > 0.74 the flow is accompanied by considerable deformation of the velocity profiles in the direction of greater fullness, while the resistance coefficient increases.     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Eutectic solidification characteristics of Bridgman grown AI-3Fe-0.1V alloy

Eutectic solidification characteristics of Al-2.85 wt%Fe-0.12 wt% Valloy have been investigated by steady-state growth over the range of solidification front velocity from 51 to 1030m/s and temperature gradient 8 to 15 K/mm. Increasing growth velocity displaced the Al-Al3Fe eutectic by Al-AlxFe eutectic rather than by the Al-Al6Fe eutectic obtained for the binary Al-3 wt%Fe alloy. A fully Al-AlxFe eutectic structure has been obtained for the first time in the vanadium-containing alloy over the growth velocity range from 71 to1030m/s except at 100 and 510m/s where some Al dendrites were present in the eutectic matrix. TheAl-AlxFe eutectic was observed to undergo a morphological transition from lamellar to rod-like with increasing growth velocity concurrently with formation of a cellular eutectic structure. It was found that the relationship = Av–1/2, between eutectic spacing and growth velocity v, was applicable with A = 22.4 ± 1.8 and 13.8 ± 2.1 m3/2s–1/2 for lamellar and rod-like Al-AlxFe eutectics, respectively.     

Numerical calculation of a generalized thermal model of radio-electronic apparatus

A method is proposed for numerical calculation of the temperature field of a generalized model of electronic equipment with high component density.Notation x,y,z,x,y spatial coordinates, m - time, sec - L_x, L_v, L_z dimensions of heated zone, m - _x, _y, _z effective thermal-conductivity coefficients of heated zone, W/m·deg - ₂ thermal conductivity of chassis, W/m·deg - a _z thermal diffusivity of heated zone along z axis, m²/sec - c₁ effective specific heat of heated zone, J/kg·deg - ₁ effective density of heated zone, kg/m³ - c₃, ₃, c₂, ₂ thermophysical characteristics of cooling agent and chassis, J/kg·deg·kg/m³ - q_v(x, ), q(x, y) volume heat-source distribution, W/m³ - q_s (x) surface heat-source distribution, W/m² - p number of cooling agent channels - Fo Fourier number - Bi Biot number - Uⁱ coolant velocity in i-th channel, m/sec - T₁(x, ), T₂(x, ), T₃(x, ) temperature distribution of heated zone, chassis, and coolant, °K - T₃₀, T₁₀(x), T₂₀(x) initial temperatures, °K - T_3in coolant temperature at input to channel, °K - T_T(x) effective temperature distribution of heat loss elements, °K - T_C temperature of external medium, °K - dimensionless heated zone temperature - _v(x) local volume heat exchange coefficient, W/m³·deg - ₁₂(x), _1C(x), _1T(x) heat liberation coefficients - W/m²·sec; ₂₁(x, y), _2c(x, y), _2T(x, y) volume heat-exchange coefficients of chassis with heated zone, medium, and cooling elements, W/m³·deg Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 876–882, May, 1981.     

Coaxial variable-length resonator for determining the electromagnetic parameters of materials at normal and higher temperatures

Conclusions It is possible by means of the above resonator, according to our analysis and in the absence of air gaps between the sample and the line, to evaluate the real components and of permeability and permittivity respectively in the range of 2 to 100 with an error between ±3% and ±10% in the temperature range from room temperature to +400°C, and the imaginary components and (for tan and tan in the range of 0.001 to 2) with an error of 7 to 20% over the same temperature range.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

A calorimetric study of S′ and θ′ precipitation in Al2O3 particle-reinforced AA2618

Differential scanning calorimetry (DSC) was used to study the kinetics of S and precipitation in AA2618 and its composite containing 15 vol % Al₂O₃ particles . The unreinforced alloy and the composite were fabricated by a proprietary casting method, followed by extrusion. The DSC studies were carried out on as-quenched samples of the test materials. The precipitation of the S and phases in both materials was found to be kinetically controlled and obey the modified Avrami-Johnson-Mehl equation. The growth mechanisms for S and formation in AA2618 seemed unaffected by the addition of Al₂O₃ particles. The growth parameters obtained for the precipitation of these phases in the matrix alloy and the composite were not significantly different.     

Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole

Summary The flow of a viscous ferrofluid over a stretching sheet in the presence of a magnetic dipole is considered. The fluid momentum and thermal energy equations are fomulated as a five-parameter problem, and the influence of the magneto-thermomechanical coupling is explored numerically. It is concluded that the primary effect of the magnetic field is to decelerate the fluid motion as compared to the hydrodynamic case, thereby increasing the skin friction and reducing the heat transfer rate at the sheet.Nomenclature a distance - c constant - c _p specific heat at constant pressure - C _f wall friction coefficient - e 2.71828 ... - f dimensionless stream function - H magnetic field - k thermal conductivity - K constant - M magnetization - Nu _x local Nusselt number - p pressure - P dimensionless pressure - Pr Prandtl number, c _p/k - Re _x local Reynolds number, cx ²/ - T temperature - u velocity component along the sheet - v velocity component normal to the sheet - x coordinate along the sheet - y coordinate normal to the sheet - dimensionless distance - ferrohydrodynamic interaction parameter - constant - dimensionless Curie temperature - dimensionless coordinate - dimensionless temperature - viscous dissipation parameter - dynamic viscosity - ₀ permeability - dimensionless coordinate - density - shear stress - magnetic potential - stream function     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

The interdependence between the incidence angles associated with quasi-stable intersections during ion erosion

A general discussion, which is valid for any angular dependence of sputtering yieldS=S(), concerning the interdependence between the incidence angles _e and ₀, associated with quasi-stable intersections during ion erosion, is given. The object was firstly to establish the location of _e roots as a function of ₀ and secondly to identify the stationary points and general trend for the complex dependence _e= _e( ₀). The results obtained are applied to a quasi-stability analysis of some specific surface features during ion erosion. Various possible types of quasi-stable intersections (surface-surface, plane-surface, plane-plane) are reviewed from the point of view of their evolution caused by ion bombardment.     

Singularity parametersε andκ for interface cracks in transversely isotropic piezoelectric bimaterials

Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Hot electrons in metals at low temperatures

Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density ( 10⁶ A/cm²) through thin, narrow (~1 m wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when _D, where is the average electron energy and _D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S() ² F() and g() _tr ² F(). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.     

Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

Influence of stabilizers on Na-β′′-Al2O3 phase formation in Li2O(MgO)-Na2O-Al2O3 ternary systems

The influences of stabilizers on - and -Al2O3 phase formations in Li2O(MgO)-Na2O-Al2O3 systems were investigated. When stabilized with 4MgCO3Mg(OH)25H2O, most of the -Al2O3 phase formed below 1200°C and further - to -Al2O3 transformation with an increase of temperature was not observed. On the other hand, when stabilized with Li2CO3,-Al2O3 formation occurred by two steps. First, -Al2O3 was partly formed below 1200°C, and, second, noticeable transformation from -Al2O3 to -Al2O3 occurred at higher temperature ranges. It was shown that transient eutectic liquid in the Li2O-Na2O-Al2O3 system promoted the - to -Al2O3 transformation at higher temperatures. Uniform distribution of both Mg2+ and Li+ stabilizing ions enhanced -Al2O3 formation at low temperatures. In the Li-stabilized systems, however, homogeneous distribution of Li+ ions hindered both the formation of transient eutectic liquid and the second - to -Al2O3 phase transformation at high temperatures.     

Rheological factor and Fahraeus-Lindqvist effect

Human blood flow in a microvessel with regard for the fahraeus-Lindquist effect is considered in an approximation of a two-layer model. The blood flow curve is described by the generalized equation of a nonlinear viscoplastic medium. Analytical expressions are derived for the volume blood flow velocity, effective blood viscosity, maximum flow velocity, and mean shear rate.Notation shear stress - ₀ limiting shear stress (yield stress) - ₀ analog of plastic viscosity - _pl human plasma viscosity - shear rate - m, n nonlinearity parameters of the rheological model - R vessel radius - thickness of the wall layer of human plasma - r current radius - u _p velocity of human plasma - P/L pressure gradient in vessel - Q _p volume flow rate of human plasma - Q _b volume flow rate of blood - u ₀ quasisolid core velocity - shear stress at the plasma-blood interface - _w =₀/ _w relative thickness of the quasisolid core of a viscoplastic flow - _e total effective viscosity of human plasma and blood - f, , functions accounting for blood plasticity - _b mean velocity of blood flow - _b mean velocity of plasma flow - c _f drag coefficient - Re Rcynolds number - l characteristic size - density - mean velocity of blood flow and the wall plasma layer - $$ " align="middle" border="0"> mean shear rate - _a asymptotic value of the viscosity at a high shear rate Academic-Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 416–426, May–June, 1995.