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      

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.     

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.     

Effects of Orthorhombic Distortion on Magnetic Excitation in t-J Model

Neutron scattering experiments on La_2–x Sr _x CuO₄ (LSCO) have revealed the incommensurate antiferromagnetic peaks do not lie exactly on the symmetry axes (q _x=± and q _y=±), but, are slightly shifted from them. In this paper, a scenario is presented for such shift in terms of the anisotropy of t (next-nearest-neighbor hopping integral on the square lattice) in the slave-boson scheme of the two-dimensional t-J model. Since the predictions of the present theory are different from those based on the spin-charge stripes hypothesis, further studies of the shift may clarify the factor responsible for the incommensurate antifcrromagnetic fluctuations in LSCO systems.     

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     

Dislocation structures in Zr3Al-based alloys

Transmission electron microscopy has been used to investigate dislocation structures in deformed binary and ternary Zr₃Al-based alloys. In the binary alloy deformed at temperatures between 293 and 673 K the dislocations in the Zr₃Al phase consisted of a/31 1 2-type partial dislocations bounding superlattice intrinsic stacking fault on {1 1 1} planes. The {111} a/31 1 ¯2 stacking fault energy was approximately 2mJ m^–2 at 673 K. In binary specimens deformed between 873 and 1073 K cube slip predominated. Dislocations consisted mainly of a/2 1 1 0 pairs separated by antiphase boundary. For this temperature range the {1 0 0} a/201 1 antiphase boundary energy was between 30 and 45 mJ m^–2. Alloying with niobium or titanium was found to increase the {111} a/31 1¯2 stacking fault energy and thus increase the propensity for antiphase boundary-type dissociation.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Landau laminar intermediate state structures: Surface energy between normal and superconducting domains in type I superconductors with small κ values

An expression for the surface energy at the normal-superconducting boundaries of a laminar intermediate state structure is derived as a function of a _s /, where a _s is the width of superconducting domains and the surface energy parameter. Numerical calculations show that the ratio / ( is the coherence length) is almost constant for a _s/ larger than the limit of about 4. This value corresponds to the critical film thickness that separates the regions of type I and type II superconducting behavior.On leave from the Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Hydrodynamic reaction to accelerated onedimensional motion of gas bubbles of variable volume in an unbounded liquid

A solution is given for the problem of the hydrodynamic reaction of an ellipsoidal gas bubble of variable volume to accelerated motion and the relation between the value of the apparent mass and the eccentricity of the bubble.Notation (,) velocity potential - V velocity of motion of the bubble with respect to the liquid - (, ) velocity potential of the near field - T₂ kinetic energy of the liquid due to the variation in bubble volume - F_r reaction force of the liquid - B₁ momentum of the liquid - _e apparent mass of the ellipsoid - density of the liquid - V_e volume of the ellipsoidal bubble Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 47–50, July, 1980.     

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.     

Reversible colour change in Cu-Al-Ni alloy ribbon associated with phase transformation

The colour change behaviour and its relation to phase transformation of Cu-14 wt% Al-4 wt% Ni alloy ribbon produced by the twin-roller type melt-quenching method were investigated by spectral reflectivity and X-ray diffraction, respectively. This ribbon turns copper-coloured around room temperature on quenching it from a temperature above 1020 K, and turns gold-coloured on ageing it between 670 and 970 K. By repeating these heat treatments, either of the two colours can be acquired interchangeably. The spectral reflectivity also changes with respect to the colour change. The copper-coloured alloy shows a DO₃ structure which is the ₁, phase. The gold-coloured alloy shows a mixed phase of ₂ (cubic, Cu₉Al₄ compound), and (fcc, Cu-Al-Ni solid solution) and/or ₁ which is a martensite of the ₁ phase having a (1 21) twinning structure. Therefore, the colour change between copper and gold is due to the solid-state phase transformation between ₁ and ₂ + ( and/or ₁) on heat treatment.     

External heat transfer in polydispersed fluidized beds at elevated temperatures

The authors present results of a theoretical and experimental study of heat transfer in polydispersed fluidized beds of coarse particles at temperatures up to 1273 K.Notation a tube radius - C_f specific heat of the gas - d_i mean diameter of the i-th fraction - g acceleration due to gravity - H height of the fluidized bed - J=fu mass flow rate of gas - ₀ thickness of the gas film on the heat transfer surface - m₀ porosity at the onset of fluidization - m porosity - r radius - R radius of the equipment - tf, °C, T_f, °K gas temperature - T₀ initial gas temperature - T_t8, T_w temperature of the fluidized bed and of the heat transfer surface, u, u₀, speed of filtration and speed at the start of fluidization - a heat-transfer coefficient - _w, _b emissivities of the heat transfer surface, and the fluidized bed - _S emissivity of the particles - _e effective (apparent) emissivity of the fluidized bed - _f viscosity of the gas - _f thermal conductivity of the gas - _f ⁰=_f0 ^c+nc_fJd₂/m thermal conductivity of the gas at t_f=0°C - _f ^c molecular thermal conductivity of the gas - _f ^c at temperature (T_w+T_t8)/2 - _f0 ^c molecular thermal conductivity of the gas at t_f=0°C, =gl_f/gl_f0 ^c - _S, _f density of particles in the gas - Stefan-Boltzmann constant - Ar=gd_1fS-_f)/_f ² Archimedes Number - Pe=c_fJ₀ ²/Hm_f0 ^c Peclet number - Re=ud_1f/_f Reynolds Number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 767–773, May, 1989.     

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.     

Microstructure and mechanical properties of metastable lath martensite wires in the Fe-Ni-Cr-Al-C system produced by melt spinning in rotating water

Metastable lath martensite ( _L ) phase wires with high strengths have been produced in the Fe-Ni-Cr-Al-C alloy system by melt spinning in rotating water. These wires have a circular cross section and a white lustre and the wire diameter is in the range of 100 to 140m. The width and length of each lath in the _L phase are as small as about 0.3 and 2m, respectively. The _y, _f and _p are about 900 and 1650 MPa and 2.0% for the _L wires. The subsequent annealing causes an increase in _p as well as _y and _f and the attained values are about 1000 and 1700 MPa and 3.0% for Fe-10Ni-10Cr-6.5 Al-1.0C wire annealed at 773 K for 1 h owing to the precipitation strengthening of a very fine unidentified carbide and to a high density of dislocations and lath boundaries in the _L phase. Further annealing causes a significant decrease in _p through decomposition of _L to+M₇C₃+M₂₃C₆. Therefore, the high strength combined with relatively good ductility for the _L wires is interpreted as due to the suppression of the phase transformation of _L to a mixed structure of+M₇C₃+M₂₃C₆ by melt quenching.     

Methods of calculating heat transfer in metallurgical plants and control models

Modern deterministic approaches to constructing mathematical models and strategic and tactical control models for a production process with reference to metallurgy and labor activity are considered. Examples of using complete and simplified mathematical models to evaluate optimal conditions of production and technological processes are presented.Notation p medium density - t time - i medium enthalpy - thermal conductivity - T, temperature - q_v intensity of internal heat sources - q_rad vector of heat transferred by radiation; m and n, number of volume and surface zones - A radiation transfer coefficient - g convective transfer coefficient - Q_j heat sources - c heat capacity per unit volume - w_l.s velocity along the x-axis - x, y, z coordinates - q_s.t. source term - s layer thickness - u, v gas velocity components - c_p gas heat capacity at constant pressure - _t turbulent viscosity - Pr_t turbulent Prandtl number - q^ch heat release power due to chemical reactions - q^r heat by radiation - number of nodes - V volume of a zone or node - A _j ^j radiation to answer coefficient proportional to the intrinsic radiation flow leaving the zone h - C concentration of a reagent to be treated - C₂ equilibrium concentration - C _j initial concentration of a reagent in a treating medium - relative initial potential - L₀ theoretical reagent flow rate necessary for complete reaction - efficiency (effectiveness) - _s heat transfer efficiency - _ch physicochemical efficiency - W flow heat capacity - G mass flow - F_x surface - k_ch and k total heat and mass transfer coefficients - Z_ch and Z_enh enhancement density centers of heat and mass transfer processes - Q_L relative potential of the physicochemical and thermal interaction - generalized chemical-thermal efficiency - _t.ch. and _t final physicochemical and thermal efficiencies - q_ch and q_u useful energy expenditures for chemical and thermal processes - _ch and _t effective resistances determined by the extent of using chemical-thermal regeneration, thermal efficiency of an extra modulus and other factors - b_d.r. energy expenditures for direct use of a reagent - F_opt complex optimality criterion - Q_res resultant heat flux - K_non degree of heating nonuniformity - A, B weight coefficients - _loss and _loss coefficients of heat losses by the working space and under chemical and mechanical incomplete combustion - _r regeneration degree - J_F optimality criterion with respect to heat flow rate and capital expenses - b_f specific fuel flow rate - Q output (commercial products) - V₀ and V₁ effective labor potential and current potential per labor product - K labor activity intensity - F_e extensive factor of the labor activity (last labor) - g_out output - =N labor activity capacity - N pure products (national income) - q₁ relative magnitude of useful products - Q useful products - C cost - _ac labor activity effectiveness - complex coefficient of the labor potential effectiveness - complex extensive factor of the labor activity - _p.r. profit rate. Indices - i, j, s, m,l.s. zones transferring and absorbing the heat, surface, material, and lining-setting - b liquid or solid body (lining-setting material) - l laminar boundary layer at the zone-surface boundary - L_f, 1, 2, 0, , inlet temperature parameters of the heating medium, the medium to be treated, the treating medium and the surrounding medium at the inlet and outlet - ch chemical potential - fix assigned potential - node Ural Polytechnic Institute, Ekaterinburg, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 259–270, March, 1993.     

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.     

Asymptotic expansions for constant-composition dew-bubble curves near the critical locus

Explicit functional representations are developed for constant-composition dew and bubble curves near critical according to the modified Leung-Griffiths theory. The pressure and temperature incrementsP=P–P _c andT= T–T _c, where c denotes critical, are linearly transformed to new variablesP andT. In the transformed space, the coexistence curves are no longer double-valued and can be expressed as a nonanalytic expansion, where the coefficients are functions of the critical properties and their derivatives. A similar asymptotic expansion is developed forT in terms of the density increment=– _c. In the approximation that the critical exponents=0 and=1/3, the critical point in temperature-density space is shown to be a point of maximum concave upward curvature, rather than an inflection point as previously conjectured.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Dielectric Properties of Pb(Ti,Zr)O3–∑n=14 (PbB"1-αB""αO3)nSolid Solutions

Dielectric permittivity measurements in Pb(Ti,Zr)O₃–_n=1 ⁴ (PbB^" _{1 -} B^" O₃) _n solid-solution systems demonstrate that the permittivity ^T ₃₃/₀of the solid solutions correlates with the molar ratio of the more soft-electric to the less soft-electric component of PbB^" _{1 -} B^" O₃(). With increasing , ^T ₃₃/₀rises because of the decrease in the uniform cell distortion parameter. The permittivity is also sensitive to structural disordering at > 1 and reduction in the density of the materials at 1.     

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.