Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.     

Transport in the low-temperature limit of a Landau Fermi liquid

The Boltzmann equation for Landau quasiparticles is solved for T 0 by a specialization of a method discussed by Sykes and Brooker. The quasiparticle distribution function is expanded in Legendre polynomials, assuming a boundary condition which imposes axial symmetry, and even-order terms are assumed to relax together with relaxation time _e , odd-order terms with relaxation time _o . By letting wavelength , with finite, one obtains a first-sound solution, and by lettingT 0, and then , one obtains a zero-sound solution. When these solutions are used to calculate the pressure, it is found that the first-sound solution is consistent with hydrodynamics, exhibiting viscosity = _s , while the zero-sound velocityc ₁=[^–1(B₁+4/3_s)]^1/2, so that phenomenologically zero-sound propagates like a longitudinal elastic wave in a glass. A higher zero-sound mode is also predicted, but is heavily damped. The heat flux is calculated and found to obey Vernotte's equation, which contains an intertial term, added to Fourier's law, that becomes significant asT 0.     

The variation of the index of refraction in a vortex tube

Three models of a vortex tube (isentropic, isothermal, and isochoric) are considered as optical inhomogeneities. Expressions relating the index of refraction to the coordinate are obtained. The possibility of obtaining Schlieren pictures of such flows is discussed.Notation a speed of sound - n index of refraction - p pressure - r radius - T absolute temperature - v linear velocity - angular deflection of the beam - x adiabatic exponent - density - angular velocity - ¯v, ¯p etc. dimensionless parameters - v₀, ₀ values at the core bounboundary - p, etc. stagnation values - n_c index of refraction at center of vortex     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

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.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

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.     

Hydrodynamics of a vortex ring

We considered the kinematics and dynamics of a vortex ring in an incompressible fluid in toroidal coordinates. We obtained the change in the pressure difference along the boundary between two flow regions in the case of a moving torus.Notation , , toroidal coordinates - (V ;V ;V ) velocity of a fluid particle and its projections in toroidal coordinates - g ,g ,g metric tensor components - the Jacobian of transition to curvilinear coordinates - V ₀ velocity at the center of a vortex ring on its symmetry axis - x, y, z Cartesian coordinates - z, y, cylindrical coordinates - a distance from the axis of a torus (V=0) to its axis of symmetry (Oz) - angle between the Oy axis and the line that connects a fluid particle on the streamline =const, which represents a circle [16], with the center of this circle - U _z,U _y velocities in the cylindrical system of coordinates - ₀ stream function of a stationary vortex ring - velocity circulation - U V ₁, velocity of a rectilinear flow at infinity - ₁ stream function of a rectilinear flow - = ₀ + ₁ superposition of two flows - n=k ⁴=V ₁/V ₀ velocity ratio coefficient - R radius of a vortical region - U velocity of fluid particles at the boundary in polar coordinates (r, ) with the center at the coordinate origin (point 0) - fluid density - p ₀,p pressure at infinity and at a certain point of flow - pressure difference Polotsk State University, Polotsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 531–536, July–August, 1995.     

Angular dependence of the resistive transitions in superconducting films in a magnetic field

The resistive transitions aboveH _c on Al films with the thicknessd<(0) have been measured as a function of the angle between the film surface and the magnetic field, where (0) is the coherence length at 0 K. An observed broadness in the transitions is considered to be due to fluctuations aboveH _c and is compared with Aoi's theories taking into account the Aslamazov—Larkin (AL) contribution only, or both the AL and an anomalous (Maki) contribution. At all angles the observed electrical conductivity due to fluctuations ' is larger than the theoretical predictions based on the AL contribution alone. Except for angles near =0, the observed ' can be explained by adding the anomalous contribution to that of AL.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

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      

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.     

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     

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     

The mechanism of adhesion of moist powders to solid surfaces in the presence of a temperature field

An examination is made of the basic factors which influence the creation of forces causing powders to adhere to solid surfaces in the presence of a temperature field. An experimental investigation has been conducted on an apatite concentrate.Notation p_c capillary pressure - density of fluid - g acceleration due to gravity - h_cap, h limiting and actual height of capillary rise - surface tension - r radius of equivalent capillary - q specific suction force - k_w water saturation coefficient - V_w volume of water in pores - V_pore volume of pores - Wg humidity by weight - R particle radius - polar angle - _c area of contact - N total adhesive force - _m, _w specific weight of powder and water     

Structure and Diamagnetic Properties of (Pb0.6SnyCu0.4 ? y)Sr2(Y1 ? xCax)Cu2Oz

The effect of Sn doping in (Pb_0.6Sn _y Cu_{0.4 – y} )Sr₂(Y_{1 – x} Ca _x )Cu₂O _z with 0 y 0.3 and 0 x 0.7 was investigated. It was established that a nearly pure 1212 phase can be obtained at 0 y 0.1 and 0 x 0.3. The obtained XRD patterns as well as the results of the EDX and ICP-AES analyses showed that Sn substitution is possible in the (Pb,Cu)-1212 phase. Superconductivity was observed at 0.4 x 0.7. The onset of the diamagnetic transitions varied from 10 to 30 K. The influence of the strong Pb deficiency on the superconducting properties of the samples was discussed.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.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 - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions