A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials

Summary The problem of heat conduction of thermoelastic cylindrical medium composed of two different materials is considered. The problem is solved in the framework of the generalized thermoelasticity theory with one relaxation time. The solution is obtained in the Laplace transform domain using the potential function approach. Numerical inversion formula is used to obtain the corresponding solutions in the physical domain.Notation T _i absolute temperature - _irr radial component of the stress tensor - _i transverse component of the stress tensor - _izz axial component of the stress tensor - u radial component of displacement vector - _i density - k _i thermal conductivity - t time - _i , _i Lamè's constants - _i coefficient of linear thermal expansion - c _i specific heat for constant strain - _i = (3 _i +2 _i ) _i T ₀ reference temperature chosen such that |(T-T ₀)/T ₀|1 - _i relaxation time - r, ,z cylindrical coordinates - r ₁,r ₂ nondimensional inner and outer radii respectively - f ₁(t),f ₂(t) inner and outer surrounding temperatures - q _i heat flux where - i=1, 2 for inner and outer media, respectively With 5 Figures     

Phase Transitions in the Gross–Neveu Model on a Sphere for High-T c Materials

Phase transitions were studied in the 3D Gross–Neveu model on a sphere at T 0. The zeta function of the Dirac operator of the model was represented with a double sum, and its derivative was calculated using recurrent formulas for generalized Epstein–Hurwitz functions. The effective potential Vwas determined as a function of the field, temperature T, and inverse radius of curvature r. Phase transitions first-order in temperature at R= 0 (T _c = 1/2ln2) and second-order in curvature R= 2/r ² at T= 0 (r _c = 1/1.5) were identified. For the general case, T 0 and R 0, the critical phase dependence T _c(r _c) was obtained, and the V(, T, r) surface was constructed. External stimuli such as temperature and curvature were shown to restore the symmetry of the system in the 3DGross–Neveu model.     

Microwave surface resistance of epitaxial YBa2Cu3O7 thin films at 18.7 GHz measured by a dielectric resonator technique

We used a dielectric resonator technique for highly sensitive measurements of the temperature dependence of the microwave surface resistanceR _s of 1×1 cm² superconducting films at 18.7 GHz. It consists of a sapphire disc positioned on the film under investigation within a copper cavity which is acting as a radiation shield. In the TE₀₁ oscillation mode the highly reproducible quality factor of about 10⁵ results in a sensitivity of ±50 forR _s measurements. The temperature dependence ofR _s can be measured up to values as high as 1 . We have investigated several YBa₂Cu₃O₇ thin films prepared by high oxygen pressure d.c. sputtering on LaAlO₃ and NdGaO₃. Our best films exhibit a pronounced nonlinear behavior of the d.c. resistivity(T) with(300K)/(100K) values of about 3.7. Those films show, besides the initial fall-off just belowT _c , a further strong decrease ofR _s at low temperatures. This was observed both at 18.7 GHz and 87 GHz, as measured by a conventional cavity end plate replacement technique. ForTT_c/2 these films exhibit an exp (–T _c/T) dependence ofR _s with-values around 0.4. These observations may be explained by a superconducting energy gap with 2/kT _c0.8 for charge carriers localized in the CuO chains for YBa₂Cu₃O₇.     

Band-theoretical calculation for the anomalous resistivity of Ni near the Curie temperature

The anomalous resistivity of nickel near the Curie temperature T _c is investigated using the itinerant model of the magnetic electron. The 3d-band wave functions are used to calculate the form factor. The temperature derivative of resistivity diverges positively when T approaches T _c from below and negatively when it approaches from above. The calculation of the correlation function shows that both short-range and long-range orders exist. The critical exponents = 1/2 and = 0 are equal to the Ornstein—Zernike values in the paramagnetic region, but in the ferromagnetic region in addition to these values ₁ = 1/2 and ₁ = 0 there is simultaneously a second set of values ₂ = and ₂ = –1.     

Structure and decomposition behaviour of rapidly solidified AI-Cu-Li-Mg-Zr alloys

The microstructural characteristics of AI-Cu-Li-Mg-Zr alloys have been studied after rapid solidification by melt spinning and after subsequent annealing at temperatures in the range 160 to 500°C, by using a combination of optical microscopy, scanning and transmission electron microscopy, X-ray diffraction, differential scanning calorimetry and microhardness measurements. The as-melt-spun alloys consist of a cellular microstructure with fine scale precipitates and icosahedral particles distributed within the cells and at cell boundaries. The icosahedral structure is equivalent to the T₂ phase reported by Hardy and Silcock. Annealing the melt-spun alloys leads to a complex precipitation sequence: + I + + I + S + + I + + T₁ + T₂ (bcc) + two other phases. The icosahedral particles coarsen progressively during annealing, especially at higher annealing temperatures. Fine-scale precipitates grow during annealing at low temperature, dissolve at higher annealing temperatures below 500°C, and then reprecipitate during cooling after annealing at 500°C. During annealing at low temperature, plates of and S precipitate and then dissolve, providing solute atoms for icosahedral particle growth. Stable T₁, T₂ (bcc) and two other phases precipitate after decomposition of the icosahedral particles during annealing at 500°C.     

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     

Free convective flow in an enclosure with a cooled inclined upper surface

Natural convective air flow in an enclosure with a horizontal lower wall, vertical side-walls and a straight inclined top wall has been numerically studied. The lower wall is at a uniform high temperature while the top wall is cooled to a uniform lower temperature. The temperature of the side-walls varies in a prescribed way between the temperatures of the bottom and top walls. This flow situation is related to that occurring in a proposed system for use in developing countries for drying crops such as corn and rice. It has been assumed that the flow is steady, laminar, and two-dimensional and that the fluid properties are constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations have been expressed in terms of stream function and vorticity and written in dimensionless form. The finite element method has been used to obtain the solution to these dimensionless equations. Results have been obtained for enclosures with aspect ratios of between 0.25 and 1 for top surface angles of inclination of between 0 and 45° and for Rayleigh numbers, based on the enclosure width, of between 1000 and 10⁷. The results have been used to study the effect of changes in the governing parameters on the flow pattern in the enclosure and on the mean heat transfer rate to the upper surface.List of symbols A aspect ratio, h/w - h mean height of cavity - k thermal conductivity - Nu local Nusselt number based on w - mean Nusselt number for top surface based on w - n n/w - n coordinate measured normal to boundary surface considered - p pressure - Pr Prandtl number - q local dimensionless heat transfer rate - mean heat transfer rate to top surface - Ra Rayleigh number based on w - T dimensionless temperature - T temperature - T _H temperature of bottom surface - T _C temperature of top surface - u velocity component in x direction - v velocity component in y direction - w width of cavity - x dimensionless x coordinate - x horizontal coordinate position - y dimensionless y coordinate - y vertical coordinate position - thermal diffusivity This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

Heat and mass transfer effects on flow past an impulsively started vertical plate

Summary An exact solution to the problem of lfow past an impulsively started infinite vertical plate in the presence of uniform heat and mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown graphically. The rate of heat transfer, the skin-friction, and the Sherwood number are also shown on graphs. The effect of different parameters like Grashof number, mass Grashof number, Prandtl number, and Schmidt number are discussed.List of symbols C species concentration near the plate - C species concentration in the fluid far away from the plate - C dimensionless concentration - C _p specific heat at constant pressure - D mass diffusion coefficient - g acceleration due to gravity - Gr thermal Grashof number - Gc mass Grashof number - j mass flux per unit area at the plate - K thermal conductivity of the fluid - Nu Nusselt number - Pr Prandtl number - q heat flux per unit area at the plate - Sc Schmidt number - t time - t dimensionless time - T temperature of the fluid near the plate - T temperature of the fluid far away from the plate - T _w temperature of the plate - u velocity of the fluid in thex-direction - u ₀ velocity of the plate - u dimensionless velocity - x coordinate axis along the plate - y coordinate axis normal to the plate - y dimensionless coordinate axis normal to the plate - volumetric coefficient of thermal expansion - ^* volumetric coefficient of expansion with concentration - coefficient of viscosity - kinematic viscosity - density - skin-friction - dimensionless skin-friction - dimensionless temperature - er fc complementary error function - similarity parameter     

Numerical calculation of a generalized thermal model of radio-electronic apparatus

A method is proposed for numerical calculation of the temperature field of a generalized model of electronic equipment with high component density.Notation x,y,z,x,y spatial coordinates, m - time, sec - L_x, L_v, L_z dimensions of heated zone, m - _x, _y, _z effective thermal-conductivity coefficients of heated zone, W/m·deg - ₂ thermal conductivity of chassis, W/m·deg - a _z thermal diffusivity of heated zone along z axis, m²/sec - c₁ effective specific heat of heated zone, J/kg·deg - ₁ effective density of heated zone, kg/m³ - c₃, ₃, c₂, ₂ thermophysical characteristics of cooling agent and chassis, J/kg·deg·kg/m³ - q_v(x, ), q(x, y) volume heat-source distribution, W/m³ - q_s (x) surface heat-source distribution, W/m² - p number of cooling agent channels - Fo Fourier number - Bi Biot number - Uⁱ coolant velocity in i-th channel, m/sec - T₁(x, ), T₂(x, ), T₃(x, ) temperature distribution of heated zone, chassis, and coolant, °K - T₃₀, T₁₀(x), T₂₀(x) initial temperatures, °K - T_3in coolant temperature at input to channel, °K - T_T(x) effective temperature distribution of heat loss elements, °K - T_C temperature of external medium, °K - dimensionless heated zone temperature - _v(x) local volume heat exchange coefficient, W/m³·deg - ₁₂(x), _1C(x), _1T(x) heat liberation coefficients - W/m²·sec; ₂₁(x, y), _2c(x, y), _2T(x, y) volume heat-exchange coefficients of chassis with heated zone, medium, and cooling elements, W/m³·deg Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 876–882, May, 1981.     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Critical phenomena of liquid4He in the vicinity of the upper λ point

We determinedC _p along six isobars near T in the vicinity of the upper superfluid transition point (upper point) from measurements ofC _v and (P/T) _v along six isochores.C _p was analyzed with the functionC _p =(A/)^–(1+D^–)+B for T>T, and the same function with primed coefficients for T, whereD denotes the strength of the effect of the irrelevant variable. The present work clarified the effect of the pressure (irrelevant variable) on the critical behavior of ⁴ He near T, that is, the correction term due to the irrelevant variable increases with pressure even in the small range 3×10^–3. This indicates that the pressure depresses the true critical region. The universality of the amplitude ratioA/A was confirmed even in the vicinity of the upper point by specific heat measurements. With constraints ==–0.02, ==–0.5, andB=B the pressure-independent amplitude ratiosA/A=1.088±0.007 andD/D=0.85±0.2 were obtained.AD/AD=0.93±0.2 implies that the pressure has a similar effect onC _p in the normal fluid and superfluid regions, within experimental errors.     

First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux

Summary A finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented here, taking into account the homogeneous chemical reaction of first order. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.List of symbols C concentration - C species concentration in the fluid far away from the plate - C _w species concentration near the plate - C dimensionless concentration - D mass diffusion coefficient - Gc mass Grashof number - Gr thermal Grashof number - g acceleration due to gravity - j mass flux per unit area at the plate - K dimensionless chemical reaction parameter - K _l chemical reaction parameter - k thermal conductivity - Nu_x dimensionless local Nusselt number - dimensionless average Nusselt number - Pr Prandtl number - q heat flux per unit area at the plate - Sc Schmidt number - Sh_x dimensionless local Sherwood number - dimensionless average Sherwood number - T temperature - T temperature of the fluid far away from the plate - T _w temperature of the plate - T dimensionless temperature - t time - t dimensionless time - u ₀ velocity of the plate - U, V dimensionless velocity components inX,Y-directions, respectively - u, v velocity components inx, y-directions, respectively - X dimensionless spatial coordinate along the plate - x spatial coordinate along the plate - Y dimensionless spatial coordinate normal to the plate - y spatial coordinate normal to the plate - thermal diffusivity - volumetric coefficient of thermal expansion - * volumetric coefficient of expansion with concentration - coefficient of viscosity - kinematic viscosity - _x dimensionless local skin-friction - dimensionless average skin-friction     

Dielectric properties of chemically vapour-deposited Si3N4

The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si₃N₄ were measured in the temperature range from room temperature to 800° C. The a.c. conductivity ( _a.c.) of the amorphous CVD-Si₃N₄ was found to be less than that of the crystalline CVD-Si₃N₄ below 500° C, but became greater than that of the crystalline CVD-Si₃N₄ over 500° C due to the contribution of d.c. conductivity ( _d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si₃N₄ are smaller than those of the crystalline CVD-Si₃N₄ in all of the temperature and frequency ranges examined. The relationships of ^n-1, (- ) ^n-1 and/(- ) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si₃N₄ were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si₃N₄ was smaller than that of the crystalline CVD-Si₃N₄.     

Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

Prediction of thermal fatigue life of ceramics

On the assumption that the thermal fatigue life of ceramics is determined mainly by the duration over which a crack reaches a small critical length, a prediction of the life was made by application of fracture mechanics to ceramics based on subcritical crack growth. Approximated formulae, such asN/N(T _N /T _N ) ⁿ , were derived, whereN andN are the lives for temperature differences of T _N and T _N , respectively, andn is a material constant. Experimental examination showed that the formulae proved to be valid for glass, sintered mullite under moderate shock severity, and zirconia. Data given by other authors also prove their validity. The deviation of the life from the formulae for sintered mullite under a thermal shock of extremely low severity, suggests that a certain mechanism, for example strengthening, is needed to understand the life of the sintered mullite. Moreover,n determined from the thermal shock experiments is comparable with that given in data determined by a mechanical method.     

Precipitate strengthening mechanisms in magnesium zinc alloy single crystals

The mechanical behaviour of Mg-5.1 wt % Zn alloy single crystals was studied in the 4.2 to 300° K temperature range. Quenched crystals have activation energies and volumes best associated with the cutting of small clusters of Zn atoms by dislocations. Fully hardened crystals contain fine ₁ and occasional ₂ precipitates with an average ₁ interparticle spacing of 330 to 660 Å. Strengthening in these crystals is mainly ascribed to the cutting of ₁ particles by dislocations. In the overaged condition ₁, ₂ and equilibrium particles are present and lead to a considerable temperature-dependence unusual for an overaged condition. Analysis of this temperature-dependence suggests that below 77° K the relatively easy cutting of ₁ particles by dislocations takes place in addition to the cutting of ₂ and particles. Above 77° K the difficult cutting of ₂ and particles alone controls the deformation, ₁ being more easily cut with the aid of thermal fluctuations.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu : Mg ratio alloys the main phases found were , , S and T₁, while fewer T₂ and Al₇Cu₂Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T₁ precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu : Mg ratio alloy the addition of 0.2 wt % Ag resulted in the precipitation of phase simultaneously with , , S and T₁ phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed.     

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     

Intergranular Critical Current Density in Polycrystalline (Bi-Pb)-2223 High Temperature Superconductor by ac Susceptibility Measurements

The field dependence of real () and imaginary () component of ac susceptibility of superconductors within the critical state model can conveniently be used for evaluating the critical current when field amplitude is larger than the penetration field. A method to analyze the real () and imaginary () component of fundamental ac susceptibility with the objective of extracting the temperature dependence of critical current density J _c(T) is reported. The procedure makes use of the ac susceptibility data of two polycrystalline (Bi-Pb)-2223 samples measured with different excitation amplitudes below and close to the critical temperature. The temperature dependence of J _c is extracted using the isothermal scan over and data. Results obtained from this procedure are found to be in fair agreement with J _c(T) calculated from traditional loss-maximum data.