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      

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     

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.     

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     

Amplifier based on a field-effect triode with negative current feedback

Conclusions A field-effect triode amplifier with series negative current feedback allows a voltage gain of the order of 200–300 to be obtained for a load resistance R_s1 M. The coefficient K_u begins to decrease noticeably only for a feedback resistance above 500 .The current gain reaches (8–10)·10³. Increasing the resistances R_s and R_L to hundreds of ohms has practically no effect on K_i. For a further increase of R_s and R_L the coefficient K_i decreases.The power gain reaches its maximum value (of the order of 10⁴ or more) for R_s100 and R_L=10–100 k. An increase in R_s leads to a reduction of K_pmax and to a shift of the extremum of the function K_p=f(R_L) into the range of higher values of R_L.A large input resistance of the amplifier (tens of megohms and higher) is obtained when R_s increases to 10–100 M. The maximum input resistance is obtained for R_L and R_s and may exceed values of from hundreds of megohms to several gigaohms. The minimum input resistance is hundreds of kilohms for R_L and R_s0.The minimum input resistance (5–10 k or less) is ensured for R_g and R_L0. An increase of the output resistance to hundreds of megohms or higher occurs for R_g and R_s.Translated from Izmeritel'naya Tekhnika, No. 9, pp. 67–70, September, 1971.     

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.     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

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.     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

Thermal conductivity and heat capacity of solid silver bromide (AgBr) under pressure

The thermal conductivity, , and the heat capacity per unit volume, c _p , have been measured for solid silver bromide (AgBr) using the transient hot-wire method. Measurements were made at temperatures in the range 100–400 K and at pressures up to 2 GPa. c _p was found to be independent of temperature and pressure over these ranges. of AgBr was found to be similar to that of AgCl, which was measured previously. For AgBr, only acoustic phonons needed to be taken into account up to 340 K, but optic phonons probably carried some heat at higher temperatures. The Leibfried-Schlömann (LS) formula could describe the ratio (AgCl)/(AgBr), but not the ratio (1 GPa)/(0) for either substance. An empirical modification of the LS formula could describe the latter ratios but not the former. Further theoretical developments are required for understanding of (P) for even such relatively simple substances as AgCl and AgBr.     

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.     

Computational thermography: Numerical modeling of the thermal regimes of building structures

We consider numerical methods of simulating thermal regimes of building structures that make it possible to create optimum structures as regards power consumption by using more accurate calculations than those available in existing construction specifications and regulations. Possible means of reducing energy expenditures for formation of an optimum microclimate in living quarters are described.Notation R thermal resistance to heat transfer - _i thermal conductivity - c _i heat capacity - _i moisture content - i number of a layer - S thermal inertia of the material - density of the substance - frequency of harmonic vibrations - t time - Fo Fourier number - thermal diffusivity - t time step - x spatial step - Bi Biot number - h _c coefficient of convective heat transfer - k thermal conductivity - T ambient temperature - T _w wall temperature - Nu Nusselt number - Ra _l Rayleigh number - Gr _l Grashof number - Pr Prandtl number - g free fall acceleration - coefficient of thermal volumetric expansion of air - l characteristic length - coefficient of kinematic viscosity of air - determining temperature - thermal conductivity of the material - q heat flux - s area of the heat transfer surface - perimeter of the heat transfer surface - T free stream velocity - air viscosity Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66 No. 6, pp. 733–738, June, 1994.     

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     

Effect of the elastic factor on the hydrodynamic stability of a structurally viscous medium

The effect of relaxation phenomena on the hydrodynamic stability of the plane gradient flow of a structurally viscous medium is investigated using linear theory.Notation _ij stress tensor deviator - U_i components of the velocity vector - x_i coordinates - t time - P pressure - =₀L/^*V plasticity parameter - _o limiting shear stress - andc dimensionless wave number and the perturbation frequency - Re=VL/* Reynolds number - density - F_ij deformation rate tensor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 868–871, November, 1978.     

Empirical heat-exchange equation for a hydroresistor thermoanemometer

An empirical equation is obtained which well describes the heat-exchange process at the sensor of a hydroresistor thermoanemometer in the range of Reynolds numbers from 3 · 10³ to 10⁵ and with a Prandtl number of 7.5.Notation effective electrical conductivity of water in the averaging volume of the sensor, (·cm)^–1 - ₀ electrical conductivity of the surrounding medium - t effective temperature of water heating at sensor, deg - t₀ temperature of surrounding medium - R active resistance of sensor at the temperature t, - R₀ resistance at the temperature t₀ - I effective value of current through the sensor, A - F area of heating layer on sensor head, cm² - heat-transfer coefficient - D diameter of the sensor head - Nu Nusselt number - Pr Prandtl number - Re Reynolds number - circular frequency of voltage supplied to sensor, sec^–1 - magnetic permeability of the medium - v local stream velocity beyond the limits of the boundary layer at the surface of the sensor head, cm/sec - V velocity of the undisturbed stream, cm/sec - x distance from center of the microelectrode along the surface of the head, cm - f designation of functional dependence - coefficient of thermal conductivity of water - kinematic viscosity - _* electrical conductivity of water at the base temperature t_* - b temperature coefficient of electrical conductivity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 827–833, November, 1978.     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

A boundary layer theory for the end problem of a circular cylinder

Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a mid-surface radius of cylinder - c half-height of cylinder - E, in-plane elastic moduli - E_t, _t, G_t transverse elastic moduli - _z, , _r axial, circumferential, and normal strain - _rz transverse shear strain - h cylinder thickness - _z, , _r axial, circumferential, and normal stress - _rz transverse shear stress - z, r axial and radial coordinates - u_z, u_r axial and normal displacements     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

The piezoresistance coefficients of copper and copper-nickel alloys

This paper attempts to further a better understanding of the piezoresistance coefficients by studying the piezoresistive effects in copper and copper-nickel alloys. The experimental evidence of isotropic piezoresistance coefficients (₁₁=₁₂) has been obtained for the annealed copper and copper-nickel alloys. The piezoresistance coefficients of the cold-worked copper and Cu₆₀Ni₄₀ alloy are of the tensor character (₁₁₁₂). A physical explanation has been given to the change of the ( _ij ) tensor.