Heat transfer by natural convection and hydrodynamics on a vertical plate with a discontinuity in the heat flux

It is observed that the temperature distribution in the boundary layer changes qualitatively and the heat transfer in the upper part of a plate intensifies substantially in comparison with a surface with a continuous heat flux. For the case of substantial heat flux density in the initial stage of formation of a free convective flow a two-dimensional vortex is found to appear.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. 2, pp. 179–183, March–April, 1995.     

Thermophysical Properties of Molten Germanium Measured by a High-Temperature Electrostatic Levitator1

Thermophysical properties of molten germanium have been measured using the high-temperature electrostatic levitator at the Jet Propulsion Laboratory. Measured properties include the density, the thermal expansivity, the hemispherical total emissivity, the constant-pressure specific heat capacity, the surface tension, and the electrical resistivity. The measured density can be expressed by _liq=5.67×10³–0.542 (T–T _m ) kg·m^–3 from 1150 to 1400 K with T _m=1211.3 K, the volume expansion coefficient by =0.9656×10^–4 K^–1, and the hemispherical total emissivity at the melting temperature by _{T, liq}(T _m)=0.17. Assuming constant _{T, liq}(T)=0.17 in the liquid range that has been investigated, the constant-pressure specific heat was evaluated as a function of temperature. The surface tension over the same temperature range can be expressed by (T)=583–0.08(T–T _m) mN·m^–1 and the temperature dependence of the electrical resistivity, when r _liq(T _m)=60·cm is used as a reference point, can be expressed by r _{e, liq}(T)=60+1.18×10^–2(T–1211.3)·cm. The thermal conductivity, which was determined from the resistivity data using the Wiedemann–Franz–Lorenz law, is given by _liq(T )=49.43+2.90×10^–2(T–T _m) W·m^–1·K^–1.     

Nonstationary concentration polarization in laminar ultrafiltration in a plane channel

A semiintegral method of determination of concerntration polarization is suggested and specific features of the latter in laminar ultrafiltration in a plane channel are discussed.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 1–2, pp. 103–107, July–August, 1994.     

Heat exchange between a fluidized bed and small-sized bodies

On the basis of the two-zone model, a procedure is developed for calculating the complex heat exchange of a probe of small dimensions (comparable with the diameter of the bed particles). The procedure takes into account the influence of the fluidizing agent pressure.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. 67, Nos. 5–6, pp. 428–432, November–December, 1994.     

Compressibility measurements of β- and β″ -alumina

The compressibilities of the a- and c-axes for sodium - and -aluminas were determined up to 10 GPa from the pressure dependence of powder X-ray diffraction measured at room temperature using synchrotron radiation as an X-ray source. Powders of sodium - and -aluminas which were prepared from grinding synthesized single crystals were used as the specimens for X-ray diffraction. The compressibilities of - and -aluminas are 1.5 ± 0.2 ×10^–12 and 1.7 ± 0.2 × 10^–12 Pa^–1 for the a-axis and 2.9 ± 0.2x10^–12 and 1.6 ± 0.2 ×10^–12 Pa^–1 for the c-axis, respectively. For the c-axis, the compressibility of -alumina is larger than that of -alumina. This experimental fact is explained by the different stacking of oxygen layers and the different content in sodium ion between - and -aluminas.     

Mathematical model of least cost planning of regional energy supply

A number of simple mathematical models for least cost planning of energy supply are considered. Optimum plans have been found and ranking of energy sources is suggested.Institute of Mathematics, Academy of Sciences of Belarus; 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. 1, pp. 149–155, January–February, 1995.     

Self-diffusion and the isotope-mass-effect in stearic acid single crystals

Self-diffusion parallel to the molecular axis in melt-grown crystals of the monoclinic c form of stearic acid has been examined in the temperature range 320 to 340 K using the radiotracer serial-sectioning technique. The results are best described by an expression of the form D=4×10³³ exp (–314±4 kJ mol^–1/RT) m²sec^–1. The value of the preexponential factor and activation energy are similar, relatively, to those obtained previously for other organic solids and are consistent with self-diffusion by a vacancy mechanism. Isotope-mass-effect measurements yielded mass factors E _ab=fK=0.3±0.04. For vacancy migration in a simple monoclinic lattice f _v0.6, thus K0.5. This is not an unreasonable value of K. It is argued however that values of f for vacancy diffusion in such anisotropic lattices as stearic acid could be significantly lower than expected.     

Numerical simulation of gasdynamic processes in the case of catastrophic volcanic eruptions

Numerical simulation of the flow of air originating as a result of volcanic eruption is carried out with the parameters corresponding to those figuring in the eruption of the Krakatau volcano in 1883 (with an energy of 100–1000 Mton of TNT equivalent). The results of the calculation are compared with the consequences of the disaster known from the literature.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 3, pp. 263–266, March, 1994.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Ohm resistivity of electroless copper layers as a function of their thicknesses

The electric Ohm resistivity of electroless Cu depositions on dielectric substrates as a function of their thicknesses is studied. Substantial deviations (up to 10–20 times) from the standard resistivity ( = 1.7 cm^–1) below 0.5 (m thicknesses are observed. The experimental data show for the entire region of thicknesses (d 0.07–5 m) a power function between the relative resistivity changes (/) and the inverse thickness of depositions (d )–(/ (1/d )^0.8. This empirical relation is discussed as an effect of the porous structure of the metallic layers deposited on the substrate. A scanning electron micrography was applied in order to visualize the morphology of the depositions. The micrographs clearly show the evolution of the deposition profile: starting from separate islands at the very beginning of the process, and gradually covering the entire area with continuous but porous metal layers.     

Modeling of unsteady wave processes in moving media

Using the nonreciprocity relation a difference scheme is built for the wave equation in a moving medium. Examples are given of solution of the problems of sound propagation in the presence of wind.The work was carried out with financial support from the Fundamental Research Fund of the Republic of Belarus.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus, Institute of Mathematics of the Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 6, pp. 1005–1010, November–December, 1995.     

Determining the convective heat transfer coefficient by the “Half-space period” method

The method of determining the convective heat transfer coefficient by the half-space period, based on the laws of heat propagation through a semiinfinite body, is described and checked out experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 2, pp. 297–301, February, 1973.     

High-temperature creep response of a commercial grade siliconized silicon carbide

Creep studies conducted in four-point flexure of a commercial siliconized silicon carbide (Si-SiC, designated as Norton NT230) have been carried out at temperatures of 1300, 1370, and 1410°C in air under selected stress levels. The Si-SiC material investigated contained 90% -SiC, 8% discontinuous free Si, and 2% porosity. In general, the Si-SiC material exhibited very low creep rates (2 to 10×10^–10 s^–1) at temperatures 1370°C under applied stress levels of up to 300 MPa. At 1410°C, the melting point of Si, the Si-SiC material still showed relative low creep rates (0.8 to 3 × 10^–9 s^–1) at stresses below a threshold value of 190 MPa. At stresses >190 MPa the Si-SiC material exhibited high creep rates plus a high stress exponent (n=17) as a result of slow crack growth assisted process that initiated within Si-rich regions. The Si-SiC material, tested at temperature 1370°C and below the threshold of 190 MPa at 1410°C, exhibited a stress exponent of one, suggestive of diffusional creep processes. Scanning electron microscopy observations showed very limited creep cavitation at free Si pockets, suggesting the discontinuous Si phase played no or little role in controlling the creep response of the Si-SiC material when it was tested in the creep-controlled regime.     

Thermal state of a plasma in a compressed layer

The results of an investigation of the thermal state of a plasma in a compressed layer under retardation conditions of the plasma flow of a coaxial Hall accelerator are reported and compared with analogous data for a free flow.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. 67, Nos. 1–2, pp. 108–111, July–August, 1994.     

Concentrational polarization in ultrafiltration in a plane channel

We investigated steady-state concentrational polarization in laminar ultrafiltration in a plane channel in relation to the selective properties of the membrane.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. 67, Nos. 3–4, pp. 235–239, September–October, 1994.     

A new formalism for time-dependent electromagnetic scattering from a bounded obstacle

In this paper a time-dependent three-dimensional electromagnetic scattering problem is considered. Let R ³ be the three-dimensional real Euclidean space filled with a medium of electric permittivity , magnetic permeability and zero electric conductivity. The quantities , are positive constants and there are no free charges in the space and the free current is taken to be zero. Let R ³ be a bounded simply connected obstacle with a locally Lipschitz boundary , that is assumed to have a nonnegative constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. An incoming electromagnetic wave packet that hits is considered, and a method that solves the Maxwell equations to compute the corresponding electromagnetic field scattered by as a superposition of time harmonic electromagnetic waves is proposed. These time-harmonic electromagnetic waves are the solutions of exterior boundary-value problems for the vector Helmholtz equation with the divergence-free condition and they are computed with an `operator expansion' method that generalizes the method presented by L. Fatone et al.[J. Math. Phys. 40 (1999) 4859–4887]. The method proposed here is computationally very efficient. In fact, it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from a numerical and a physical point of view. The quantitative character of the numerical experiments shown is established. The website: http://www.econ.unian.it/recchioni/w4/ contains some animations relative to the numerical experiments.     

Modeling the heat transfer process in an infiltrated granular bed with regard for the temperature difference of the phases

Based on the solutions of the internal and external problems of a gas flow in a granular bed, expressions are obtained for calculating the interphase heat transfer coefficient and the degree of gas flow nonuniformity.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. 67, Nos. 3–4, pp. 243–249, September–October, 1994.     

Separable functions in load separation for the ηpl and ηpl CMOD plastic factors estimation

The objective of this paper is to develop the load separation method for evaluating the _pl and _pl ^CMOD plastic factors used in the J estimation approach based on load versus displacement records. Appropriate forms for the geometry and deformation functions have been suggested from the EPRI Handbook solutions to produce the separable form for the load. The obtained functions are applied to evaluate the _pl and _pl ^CMOD plastic factors for center cracked tension specimen. The present load separation method gave results which are somewhat different from the estimated values of _pl given in the literature. For shallow cracks, the _pl and ^CMOD _pl plastic factors show considerable variation with crack size and the strain hardening exponent. For a deeply cracked CCT specimen, the ^CMOD _pl factor tends to the _pl factor and equals approximately unity. Abbreviations: CCT – center cracked specimen; CMOD – Crack Mouth Opening Displacement; EPRI – Electric Power Research Institute; FEM – Finite Element Method; LLD – Load Line Displacement.     

Characterization of deformation processes in a Zn-22% Al alloy using atomic force microscopy

The Zn-22% Al eutectoid alloy was subjected to equal-channel angular pressing at a temperature of 473 K to give an as-pressed grain size of 1.3 m. Subsequent tensile testing of the as-pressed alloy at room temperature revealed a transition from deformation by a dislocation mechanism at the higher strain rates to superplastic flow at strain rates below 5 × 10^–3 s^–1: this corresponds to the transition from region III to region II in conventional superplasticity. Samples were pulled to relatively low total strains, of the order of 0.2–0.5, and the surface topography was then examined using an atomic force microscope (AFM). The AFM observations confirm the transition in deformation mechanisms with decreasing strain rate and they provide direct evidence for the occurrence of grain boundary sliding within the superplastic regime.     

Model of gas bubble breakup in a turbulent liquid flow

A system of equations for evolution of the size spectrum of gas bubbles as a results of their breakup in an isotropic turbulent damped flow of an incompressible liquid is derived and solved numerically.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. 2, pp. 192–204, March–April, 1995.