Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

A parameter characterizing plowing nature of surfaces close to Gaussian

A non-dimensional parameter descriptive of the plowing nature of surfaces is proposed for the case of sliding between a soft and a relatively hard metallic pair. From a set of potential parameters which can be descriptive of the phenomenon, dimensionless groups are formulated and the influence of each one of them is analyzed. A non-dimensional parameter involving the root-mean square deviation (R-q) and the centroidal frequency (F-mean) deducted from the power-spectrum is found to have a high degree of correlation (as high as 0.93) with the coefficient of friction obtained in sliding experiments under lubricated condition.

Comparative study of some constitutive equations characterising non-Newtonian fluids

This paper compares, in a general way, the predictions of the constitutive equations given by Rivlin and Ericksen, Oldroyd, and Walters. Whether we consider the rotational problems in cylindrical co-ordinates or in spherical polar co-ordinates, the effect of the non-Newtonicity on the secondary flows is collected in a single parameterα which can be explicitly expressed in terms of the non-Newtonian parameters that occur in each of the above-mentioned constitutive equations. Thus, for a given value ofα, all the three fluids will have identical secondary flows. It is only through the study of appropriate normal stresses that a Rivlin-Ericksen fluid can be distinguished from the other two fluids which are indistinguishable as long as this non-Newtonian parameter has the same value.

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear couple differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Nonsimilar boundary layers for non-Darcy mixed convection flow about a horizontal surface in a saturated porous medium

The nonsimilar non-Darcy mixed convection flow about a heated horizontal surface in a saturated porous medium has been studied when the surface temperature is a power function of distance (Tw = T∞ ± Axλ). The analysis is performed for the cases of parallel and stagnation flows with favourable induced pressure gradient. The partial differential equations governing the flow have been solved numerically using the Keller box method. The heat transfer is enhanced due to the buoyancy parameter and wall temperature, but the non-Darcy parameter reduces it. For non-Darcy flow, the similarity solution exists only for the case of parallel flow.

Mechanism of vapour phase oxidation of anthracene over cobalt molybdate catalyst

Vapour phase oxidation of anthracene over cobalt molybdate catalyst was investigated in an isothermal flow reactor in the temperature range of 280—340°C. Fifteen different models based on redox, Langmuir—Hinshelwood and Rideal mechanisms were tested in order to elucidate the mechanism of the above reaction. These models were compared on the basis of three criteria and were finally discriminated employing the non-intrinsic parameter method. Two-stage redox mechanism was found to explain the data satisfactorily.

Mechanism of vapour phase oxidation of anthracene over cobalt molybdate catalyst

Vapour phase oxidation of anthracene over cobalt molybdate catalyst was investigated in an isothermal flow reactor in the temperature range of 280—340°C. Fifteen different models based on redox, Langmuir—Hinshelwood and Rideal mechanisms were tested in order to elucidate the mechanism of the above reaction. These models were compared on the basis of three criteria and were finally discriminated employing the non-intrinsic parameter method. Two-stage redox mechanism was found to explain the data satisfactorily.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (gamma H/c(o)) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; gamma = unit weight, H., height of the excavation and c(o) = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.(C) 2009 Elsevier Ltd. All rights reserved.

Communication: Evidence of dynamic heterogeneity in glassy polymer monolayers from interface microrheology measurements

We have developed a novel nanoparticle tracking based interface microrheology technique to perform in situ studies on confined complex fluids. To demonstrate the power of this technique, we show, for the first time, how in situ glass formation in polymers confined at air-water interface can be directly probed by monitoring variation of the mean square displacement of embedded nanoparticles as a function of surface density. We have further quantified the appearance of dynamic heterogeneity and hence vitrification in polymethyl methacrylate monolayers above a certain surface density, through the variation of non-Gaussian parameter of the probes. (C) 2010 American Institute of Physics. [doi:10.1063/1.3471584].

Synergistic use of thermogravimetric and electrochemical techniques for thermodynamic study of TiOx (1.67 <= x <= 2.0) at 1573 K

A thermodynamic study of the Ti-O system at 1573 K has been conducted using a combination of thermogravimetric and emf techniques. The results indicate that the variation of oxygen potential with the nonstoichiometric parameter delta in stability domain of TiO2-delta with rutile structure can be represented by the relation, Delta mu o(2) = -6RT In delta - 711970(+/-1600) J/mol. The corresponding relation between non-stoichiometric parameter delta and partial pressure of oxygen across the whole stability range of TiO2-delta at 1573 K is delta proportional to P-O2(-1/6). It is therefore evident that the oxygen deficient behavior of nonstoichiometric TiO2-delta is dominated by the presence of doubly charged oxygen vacancies and free electrons. The high-precision measurements enabled the resolution of oxygen potential steps corresponding to the different Magneli phases (Ti-n O2n-1) up to n = 15. Beyond this value of n, the oxygen potential steps were too small to be resolved. Based on composition of the Magneli phase in equilibrium with TiO2-delta, the maximum value of n is estimated to be 28. The chemical potential of titanium was derived as a function of composition using the Gibbs-Duhem relation. Gibbs energies of formation of the Magneli phases were derived from the chemical potentials of oxygen and titanium. The values of -2441.8(+/-5.8) kJ/mol for Ti4O7 and -1775.4(+/-4.3) kJ/mol for Ti3O5 Obtained in this study refine values of -2436.2(+/-26.1) kJ/mol and-1771.3(+/-6.9) kJ/mol, respectively, given in the JANAF thermochemical tables.

Irreversibility-to-reversibility crossover in transient response of an optically trapped particle

We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system's time evolution shows dramatically different behaviors. Starting from the short-time reversible to long-time irreversible transition, a stationary reversible state with zero net dissipation can be achieved as the release point energy is decreased. If the system starts with even lower energy, it progressively extracts useful work from thermal noise and exhibits an anomalous irreversibility. In addition, we have verified the Transient Fluctuation Theorem and the Integrated Transient Fluctuation Theorem even for the non-ergodic descriptions of our system. Copyright (C) EPLA, 2011

Low oxygen potential boundary for the stability of YBA2Cu3O7−δ

On lowering the oxygen potential, the tetragonal phase of YBa2Cu3O7−δ was found to decompose into a mixture of Y2BaCuO5, BaCuO2 and BaCu2O2 in the temperature range 773–1173 K. The 123 compound was contained in a closed crucible of yttria-stabilized zirconia in the temperature range 773–1073 K. Oxygen was removed in small increments by coulometric titration through the solid electrolyte crucible at constant temperature. The oxygen potential was calculated from the open circuit e.m.f. of the solid state cell after successive titrations. Pure oxygen at a pressure of 1.01 × 105 Pa was used as the reference electrode. The decomposition of the 123 compound manifested as a plateau in oxygen potential. The decomposition products were identified by X-ray diffraction. At temperatures above 1073 K there was some evidence of reaction between the 123 compound, solid electrolyte crucible and platinum. For measurements above 1073 K, the 123 compound was contained in a magnesia crucible placed in a closed outer silica tube. The oxygen potential in the gas phase above the 123 compound was controlled and measured by a solid state cell based on yttria-stabilized zirconia which served both as a pump and sensor. The lower oxygen potential limit for the stability of the 123 compound is given by View the MathML source The oxygen non-stoichiometric parameter δ for the 123 compound has a value of 0.98 (View the MathML source) at dissociation.