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.     

The effect of quenching on the martensitic transformation in ß1 phase of Au-Cd alloys

The effect of quenching on the martensitic transformation mechanism in ₁ Au-Cd alloys has been investigated by measurements of the electrical resistivity and X-ray diffraction. In the case of the Au-47.5 at%Cd alloy, the ₂-martensite is the characteristic product under quenching conditions, but it always exists with the equilibrium ₂-martensite phase. Consequently, the _{1 2} and ₂transformations occur simultaneously during the heating and cooling cycles. The corresponding resistivity behaviour is very complicated and extremely sensitive to thermal treatments such as quenching temperature and thermal cycling. On the other hand, in the case of the Au-49.0 at%Cd alloy, only the _{1 2} transformation occurs even when quenched, and the transformation is unaffected structurally by quenching. A distinct resistivity anomaly, which is considered to be due to the disappearance of quenched-in vacancies, is observed in quenched alloys. Some important characteristics of this anomaly are determined. In particular, the quenching effect disappears when the specimen is heated above the temperature at which the resisitivity anomaly begins. This result suggests that the quenched-in vacancies play an essential role in the martensitic transformation process under quenching conditions.     

State space formulation to viscoelastic fluid flow of magnetohydrodynamic free convection through a porous medium

Summary In this work we formulate the state space approach for one-dimensional problems of viscoelastic magnetohydrodynamic unsteady free convection flow through a porous medium past an infinite vertical plate. Laplace transform techniques are used. The resulting formulation is applied to a thermal shock problem and to a problem for the flow between two parallel fixed plates both without heat sources. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.Notation C specific heat at constant pressure - g acceleration due to gravity - density - time - u velocity component parallel to the plate - H _x induced magnetic field - x, y coordinates system - T temperature distribution - T _o temperature of the plate - T temperature of the fluid away from the plate - ₀ limiting viscosity at small rates to shear - v _o ^* / - v _m magnetic diffusivity - Alfven velocity - ^* coefficient of volume expansion - thermal conductivity - ^* thermal diffusivity - G Grashof number - Pr Prandtl number - L some characteristic length - k _o the elastic constant - K permeability of the porous medium     

Method for heat transfer calculation using isothermal coordinates

Equations for steady-state heat transfer are considered in curvilinear coordinates. The equations are shown to be simplest when one of the families of coordinates are isotherms. Conditions are obtained for which these coordinate systems and some exact solutions of the heat conduction equations must satisfy.Notation a ₁, a₂, ..., a_n coefficients determining the temperature dependence of thermal conductivity (see formula (8)) - f() function of the -coordinate (see formula (4)) - H ₁,H ₂,H ₃ coefficients of the first differential form (Lamé coefficients) (see formula (2)) - n number of a term of the series in formula (8) - q heat flux - Q power of volume heat release - x, y, z Cartesian coordinates - , , general curvilinear orthogonal coordinates - ₁, ₂ coordinates of the boundary surfaces on which the temperatures are prescribed - x ₀₁ thermal conductivity att=0 - () function of the -coordinate (see formula (4)) - () -function determining temperature distribution in the case of constant heat flux along the coordinate lines Scientific-Research and Design-Technological Institute of Machine Manufacture, Scientific-Production Subbranch Novator, Kramatorsk, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 651–659, July–August, 1995.     

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     

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.     

On apparent properties of nonlinear heterogeneous bodies smaller than the representative volume

Summary Huet's model for overall properties of specimens smaller than the representative volume is generalized on nonlinear heterogeneous elastic materials with imperfect interfaces. A modified definition for the apparent properties of heterogeneous nonlinear elastic bodies is given. The size effect relationships are established between experimental results obtained on a big specimen and on an appropriate set of smaller specimens. Hierarchies between the apparent properties of the families of specimens of different sizes are constructed.Notation D domain occupied in space by a material body - D boundary ofD - x position of a material point at timet - n outward normal - internal interface of a heterogeneous body - [a]=a ⁺–a^– jump bracket ofa on an interface in the direction of the outward normal - stress tensor - strain tensor - displacement vector - P traction vector density on a surface - a spatial average of the variablea on a domainD - x tensor product (dyadic) - twice contracted tensor product - syma symmetric part 1/2(a+a ^T ) of the tensora - F ,F potential energy and complementary energy functionals, respectively - S ^eff,C ^eff effective compliance and modulus tensors, respectively - S ,C kinematic apparent compliance and modulus tensors, respectively - S ,C static apparent compliance and modulus tensors, respectively     

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.     

Anisotropic model of an emitting electric arc

An analytical procedure is proposed for obtaining exponential dimensionless equations to calculate the characteristics of an electric arc in a plasmatron channel that is based on using an exponential approximation of the temperature dependence of electric conductivity with different exponents for longitudinal and transverse coordinates.Notation density - C _p specific heat at constant pressure - electrical conductivity - thermal conductivity - V velocity - T temperature - E electric-field strength - r, z radial and longitudinal coordinates - thermal conductivity function - G gas flow rate - Q bulk radiation density - R, D radius and diameter of channel - I strength of current - r/R - z/R - m R/r _*=1/r _* - S S–S _* - b _Q Q ₀/S ₀ - a, k,k ,n ,C ₀₀, constants - J ₀,J ₁,Y ₀ Bessel functions - ₁, _n roots of characteristic equations - j current density - q heat flux density - Po, Pe Pomerantsev and Pecklet numbers, respectively - Nu Nusselt number - _K , _U , _q ,K _Q ,K _S similarity numbers - U voltage - heat-transfer coefficient Indexes z longitudinal component - * boundary of conducting band - 0 base value - 1 value on the wall - 00 axial value - I, II conducting and nonconducting bands, respectively Academic Scientific Complex A. L. Luikov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 820–826, September–October, 1995.     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.     

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     

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.     

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     

Pulse determination of thermal diffusivity and thermal conductivity for hemispherical specimens: nickel

A method is described for determining the thermal diffusivity, specific heat, and thermal conductivity in a hemispherical volume on the basis of duration of the reference signal.Notation r radius - R radius - r dimensionless coordinate - dimensionless temperature - time - _i duration of heat pulse - _1/2 time for temperature signal at r to attain half the maximum value - q_o amount of heat - a thermal diffusivity - thermal conductivity - density - c_p heat capacity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 864–869, May, 1981.     

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      

Effects of plasticization on the piezoelectric properties of nylon 11 films

Nylon 11 films (-form) were plasticized by immersion in 2-ethyl 1,3 hexanediol. Two different kinds of studies were performed. In the first study, poled nylon 11 films were plasticized by immersion in the plasticizer for different lengths of time. The piezoelectric strain constant,d ₃₁, initially increased up to a plasticizer content of 14% (by weight) and then decreased. The values of piezoelectric stress constant,e ₃₁, however, decreased with increase in dipping time. In the second study, the films were initially plasticized and then poled. Bothd ₃₁ ande ₃₁ were higher for plasticized films compared to unplasticized films under identical poling conditions. X-ray diffraction studies showed some conversion of -phase to -phase during the process of plasticization.     

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     

Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid