Remarks on wave solutions of the nonlinear heat-conduction equation

Wave solutions of the nonlinear heat-conduction equation are analyzed and their relation to self-similar solutions is established. Solutions of the hyperbolic and the nonlinear heat-conduction equations are compared.Notation k(T) thermal diffusivity coefficient - relaxation parameter - g²=₀/c_v@ square of the heat wave velocity - ₀ and k₀ heat-conduction and thermal diffusivity constant - density - c_v specific heat at constant volume - T temperature - t time - x, y, z space coordinates Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 907–913, May, 1981.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Precise measurements of critical parameters of sulfur hexafluoride by laser interferometry

A laser interferometry has been applied, in the present study, for determination of the critical temperature and critical exponents of sulfur hexafluoride (SF₆). By means of laser holographic technique by real-time method, a series of Fraunhofer diffraction patterns due to the density fluctuation of the sample fluid in the very vicinity of the critical point has been successively photographed and analyzed. A dual-thermostat system which was designed and constructed for the present purpose has made the sample temperature constant within 15 K for several days. We have obtained 107 data for ( _L– _v)/ _c along the vapor-liquid coexistence curve in the reduced temperature range 10^–6¦T ^*¦7×10^–5 and additional 34 data for the isothermal compressibility in the single phase region. By analyzing these measurements with the aid of the simple power law, the critical temperature and the critical exponents of SF₆ have been determined as T _c=318.708±0.001 K, =0.350±0.004, and =1.24±0.02, respectively.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Resistivity of Lightly Doped Ferromagnetic Semiconductors

In metallic magnets with a low carrier density, scattering from magnetic fluctuations above and near the transition temperature T _c provides a large contribution to the electrical resistance. Because the fluctuations can be suppressed by a magnetic field, a large negative magnetoresistance ensues. In a simple model, we find the low field magnetoresistance scales with the ratio of field induced magnetization m(H) to the saturation magnetization m _sat: /=((T, 0)–(T, H))/(T, 0)C(m/m _sat)². At very low carrier densities magnetic polarons should form in a range of temperatures above T _c. The CMR perovskite manganites cannot be explained without strong coupling of the magnetic order to lattice distortions (of the Jahn–Teller type) above T _c.     

Question of determining the composition of composites by a tomographic method

One possible method of determining the volume content of composite components by using x-ray calculational tomography is examined.Notation , _T, _fi, P_b, _b, _w, _im material densities, theoretical, fiber, binder, pore, water, impregnating fluid - _fi, _b, _p fiber, binder, pore volume contents - f_fi, f_b, f_p, f_di, f_di ^*, f_cij, f_im linear coefficients of attenuation of the fiber, binder, air of the i-th layer of the dry specimen - n quantity of cells in the i-th layer, m_fi, m₁ m₂, weight of the dry and impregnated specimens in air and in water - C_cl closed porosity - S_f rms deviation of the linear attenuation coefficients - volume closed pore content Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 738–745, May, 1989.     

Fast adiabatic heating and temperature relaxation in near-critical fluids under zero gravity

Heat transport in supercritical CO₂ is studied under microgravity conditions. A large temperature and density region around the critical point is explored (CO₂ cells were filled at critical density= _c and off-critical densities= _c±0.18 _c). Local heating is obtained by using a small thermistor located in the bulk fluid. Through interferometric observations, a new mechanism of thermalization has been evidenced. Thermal expansion of a warm diffusing boundary layer around the heating thermistor is responsible for rapid adiabatic heating of the bulk fluid through the emission of pressure waves at the border. The scaled thickness of the thermal boundary layer follows a power law. When the heat flow stops, the bulk adiabatic heating instantaneously vanishes and the temperature relaxation inside the thermal boundary layer follows locally a diffusive process.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Anisotropic Electrical Transport in MgB2 Single Crystals

We report on study of transport properties of MgB₂ single crystals. The normal state resistivity has been found to be anisotropic with resistivity ratio _c / _ab =3.5. In agreement with the results of band structure calculations the normal state Hall effect measurements with H//ab-planes and H//c-axis show two type carrier behavior. Below T _c, the in-plane as well as the out-of-plane Hall resistivity, _xy and _zx , display no sign change anomaly. Furthermore, both _xy and _zx have been found to scale with corresponding longitudinal resistivity with the same exponent =1.5.     

Decay rate of critical fluctuations in steam and in dilute steam-NaCl mixtures

The decay rate of critical fluctuations in steam and in a steam-NaCl mixture has been investigated experimentally with the aid of photon correlation spectroscopy. For pure steam, the measurements have been performed along seven isochores [(¦– _c¦)/_c<0.09] as a function of the temperatureT for (T–T_t)<1 K. The results have been compared with the values predicted by the renormalization-group theory written as a modification of the classical mode coupling theory. The agreement between experiment and theory is satisfactory along the critical isochore, but larger deviations are noted for _c when approching the transition temperatureT _t. The decay rate of a 0.1% (molar) dilute mixture of NaCl in H₂O has been measured along some near-critical isochores as a function of temperature. Its behavior, which is very different from that observed for pure steam, is dicussed.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Joule-Thompson effect in a disperse medium

An expression for the Joule-Thompson coefficient of a polydisperse medium subject to throttling is derived in the relaxation approximation of thermodynamics of irreversible processes, with both temperature and velocity relaxation in the phases taken into account.Notation A_qk, A_fk thermal and momentum interphase exchange affinities - _qk, _fk relaxation parameters - T, w temperature and velocity of a phase relaxation in the mixture - density of the mixture - T_o, T_k temperature of the carrier phase and of the k-th group of solid particles - p pressure of the carrier phase - h enthalpy of the mixture - W _o ² /2 specific kinetic energy of the carrier phase - _o, _k volume concentration of the carrier phase and of the k-th group of solid particles - _o, _k true density of the carrier phase and of the k-th group of solid particles - c_v and c_p constant-volume and constant-pressure specific heats of the mixture - c_k specific heat of the k-th group of solid particles - c_v, c_p constant-volume and constant-pressure specific heats, respectively, of the mixture referred to volume - _qk, _fk temperature and velocity relaxation times, respectively, of the k-th group of solid particles - t times - frequency in the Fourier series expansion - differential Joule-Thompson coefficient (adiabatic throttle effect) - N number of groups of particles in the mixture Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 825–829, November, 1979.     

T c enhancement in La2−x Sr x CuO4 under anisotropic pressure

We have measured _c (T) for La _2–x Sr _x CuO ₄ (LSCO) with x=0.15 under anisotropic pressures. The c-axis compression, which decreases _c (T), reduces T _c drastically, whereas the c-axis stretch, which increases _c (T), enhances T _c from 38K at the ambient pressure to 51.6K at 8GPa. The T _c = 51.6K is the highest record so far reported for LSCO. The variation of T _c is well scaled with variations of _c . We deduce that the enhancement of T _c in LSCO is mainly caused by the suppression of interlayer coupling, though two dimensionality is generally known as a destructive factor for conventional superconductivity.     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Behaviour of amorphous poly(ethylene terephthalate) annealed at T<T g by thermally stimulated currents

Thermally stimulated current (TSC) discharges in open circuit of amorphous poly(ethylene terephthalate) (PET) corona-charged electrets show a heteropolar relaxation at 87 °C, ₁ between and peaks. This relaxation tends to become homopolar when the sample is annealed at temperatures below the glass transition temperature. This is due to the formation of a trapped charge density on the surface of the material that originates, during the TSC discharge, a current that counteracts the one that results in ₁ This trapping effect, which initially is null, increases with annealing due to the rise in resistivity. On the other hand, TSC discharges in short-circuited annealed samples result in a heteropolar peak, ^*, that corresponds to ₁ The area of ^* increases with the annealing time in a bounded way. This peak is related to the formation of thermal nuclei (embryos) in the bulk of the material that act as heterogeneities. This suggests that ₁ is associated with a barrier-type polarization. If the annealed sample is heated to temperatures above the glass transition temperature, the tendency to the inversion of ₁ vanishes and ^* disappears, whereas and are modified. This suggests that relaxation is related to a Maxwell-Wagner-Sillars effect.     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

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.     

Hall-Effect in LuNi2B2C and YNi2B2C Borocarbides in Normal and Superconducting Mixed States

It was shown that the Hall resistivity _xy for LuNi ₂ B ₂ C and YNi ₂ B ₂ C is negative in the normal and mixed states and has no sign reversal below T _c . In the mixed state the scaling relation _{xy xx} (_xx is the longitudinal resistivity) was found for both compounds with 2.0. In the normal state a distinct nonlinearity in the _xy(H) dependence, accompanied by a large magnetoresistance, was found below 40 K only for LuNi ₂ B ₂ C. The difference in the behaviour of Lu- and Y-based borocarbides seems to be connected with the difference in the Fermi surfaces of these compounds.     

Crossover equation of state of normal hexane in the critical region

The coefficients of the basic crossover equation of state of n-hexane are determined in the critical region from experimental P, , T and C_p, P, T data. In the reduced density and temperature ranges 0.35_c1.65 and 0.982T/T_c1.23 the root mean square errors of the calculated pressure, isobaric heat capacity, and isochoric heat capacity were 0.115%, 4.87%, and 3.04%, respectively.Academician M. D. Millionshchikov Petroleum Institute, Grozny, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp.185–191, August, 1993.     

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.     

Heat transfer in vapor condensation on laminar and turbulent liquid jets,taking account of the inlet section and variability of the flow rate over the jet cross section

The results of numerical modeling of heat transfer in phase transition at jets are outlined.Notation x, y orthogonal coordinate system related to jet symmetry axis - u, v components of the velocity vector along the coordinates x and y - T temperature - kinematic viscosity - a thermal diffusivity - density - thermal conductivity - c_p specific heat at constant pressure - h_fg latent heat of vaporization - Re=u₀R₀/ Reynolds number - Pr=/a Prandtl number - Fr=u₀ ²/(gR₀) Froude number - We=u₀ ²R₀/ Weber number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 732–735, May, 1988.     

Critical properties of4He in aerogel near the λ-line

We measured the superfluid fraction _s/ and the isobaric thermal expansion coefficient _P of⁴He confined in an aerogel. Data were obtained near the -line along several isobars. Powerlaw fits to the results for _s/ as a function of tT/T_c–1 (T_c is the transition temperature) give a pressure—independent exponent =0.755 when a confluent singular term is included. Fits to the _P data of power laws yield the specific-heat exponents –0.6 and –1.0 above and below T_c respectively. When an analytic background term a×t is included in the fit, the pressure-independent value =–0.59 is permitted, but the amplitude ratio A/A is found to be near zero and the coefficient of the analytic term is large. The measured values for and or are inconsistent with hyperscaling in three dimensions.     

Shock Compression of Porous Aluminum and Nickel at Megabar Pressures

Data are given on shock compression of porous samples of aluminum with the initial density ₀₀= 0.34 g/cm³and nickel with ₀= 0.44 and 0.32 g/cm³. In the case of aluminum, all results are obtained for the first time ever. The range of pressure being investigated is from 0.25 to 76 GPa. For nickel, a shock adiabat is found with the porosity m= ₀/₀₀= 28 (which is the highest porosity for metals) and an adiabat with m= 20 at a pressure of 92 GPa, which is approximately twice the respective values obtained previously. Comparison is made with the results of other researchers.