Thermodynamic consistency of the ternary functions

A ternary thermodynamic function has been developed based on statistico-thermodynamic considerations, with a particular emphasis on the higher-order terms indicating the effects of truncation at the various stages of the treatment. Although the truncation of a series involved in the equation introduces inconsistency, the latter may be removed by imposing various thermodynamic boundary conditions. These conditions are discussed in the paper. The present equation with higher-order terms shows that the α function of a component reduces to a quadratic function of composition at constant compositional paths involving the other two components in the system. The form of the function has been found to be representative of various experimental observations.

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values

Circular elastic inclusions in cylindrical shells

The problem of a circular elastic inclusion in a cylindrical shell subjected to internal pressure or thermal loading is studied. The two shallow-shell equations governing the behaviour of a cylindrical shell are transformed into a single differential equation involving a curvature parameter and a complex potential function in a non-dimensional form. In the shell region, the solution is represented by Hankel functions of first kind, whereas in the inclusion region it is represented by Bessel functions of first kind. Boundary conditions at the shell-inclusion junction are expressed in a simple form involving in-plane strains and change in curvature. The effect of such inclusion parameters as extensional rigidity, bending rigidity, and thermal expansion coefficients on the stress concentrations has been determined. The results are presented in non-dimensional form for ready use.

Monte carlo simulation for molecular gas dynamics

The dynamics of low-density flows is governed by the Boltzmann equation of the kinetic theory of gases. This is a nonlinear integro-differential equation and, in general, numerical methods must be used to obtain its solution. The present paper, after a brief review of Direct Simulation Monte Carlo (DSMC) methods due to Bird, and Belotserkovskii and Yanitskii, studies the details of theDSMC method of Deshpande for mono as well as multicomponent gases. The present method is a statistical particle-in-cell method and is based upon the Kac-Prigogine master equation which reduces to the Boltzmann equation under the hypothesis of molecular chaos. The proposed Markoff model simulating the collisions uses a Poisson distribution for the number of collisions allowed in cells into which the physical space is divided. The model is then extended to a binary mixture of gases and it is shown that it is necessary to perform the collisions in a certain sequence to obtain unbiased simulation.

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

Unsteady boundary layer flow on a cylinder in a channel

The unsteady laminar incompressible nonsimilar boundary layer flow over a circular cylinder placed symmetrically inside a channel has been studied when the unsteadiness and nonsimilarity are due to the free stream velocity. The nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference in combination with the quasilinearization technique. It is found that the channel blockage parameter controls the transfer of heat from the cylinder and delays separation. The skin friction and heat transfer are significantly affected by the free stream velocity distributions.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

A thermodynamic protocol for explaining subcriticality and other subtle features in self-deflagrating solids

A novel universal approach to understand the self-deflagration in solids has been attempted by using basic thermodynamic equation of partial differentiation, where burning mte depends on the initial temperature and pressure of the system. Self-deflagrating solids are rare and are reported only in few compounds like ammonium perchlorate (AP), polystyrene peroxide and tetrazole. This approach has led us to understand the unique characteristics of AP, viz. the existence of low pressure deflagration limit (LPL 20 atm), hitherto not understood sufficiently. This analysis infers that the overall surface activation energy comprises of two components governed by the condensed phase and gas phase processes. The most attractive feature of the model is the identification of a new subcritical regime I' below LPL where AP does not burn. The model is aptly supported by the thermochemical computations and temperature-profile analyses of the combustion train. The thermodynamic model is further corroborated from the kinetic analysis of the high pressure (1-30 atm) DTA thermograms which affords distinct empirical decomposition rate laws in regimes I' and 1 (20-60 atm). Using Fourier-Kirchoff one dimensional heat transfer differential equation, the phase transition thickness and the melt-layer thickness have been computed which conform to the experimental data.

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the low-conductivity limit. Our treatment is non-perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Re-m), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Re-m. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the 'C' and 'D' terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the space-time integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the cross-shear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Re-m, but to all orders in the shear strength, the D term cannot give rise to a shear-current-assisted dynamo effect; (iv) casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocity-spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shear-current-type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non-helical velocity dynamics at low fluid Reynolds number does not result in a shear-current-assisted dynamo effect.

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number. Untersucht wurde die instationäre laminare Mischkonvektion längs eines vertikalen, in einem porösen Medium eingebetteten Zylinders unter kombinierten Auftriebseffekten von thermischer und spezieller Diffusion. Der Einfluß der Permeabilität des Mediums sowie des magnetischen Feldes wurden in die Betrachtung einbezogen. Die partiellen Differentialgleichungen mit drei unabhängigen Variablen, welche die Strömung beschreiben, wurde numerisch anhand des Schemas der endlichen Differenzen in Verbindung mit der Technik der Quasilinearisation gelöst. Berechnungen für die beschleunigte, verzögerte und oszillierende Geschwindigkeitsverteilung der freien Strömung sind durchgeführt worden. Untersucht wurden ebenfalls die Effekte der Permeabilität des Mediums, der Auftriebskräfte, der transversalen Krümmung, des magnetischen Feldes auf die Oberflächenreibung sowie die Wärmeund Stoffübertragung. Es wurde festgestellt, daß die Geschwindigkeit mehr Einfluß auf die Oberflächenreibung als auf die Wärmeund Stoffübertragung hat. Die Oberflächenreibung sowie die Wärme- und Stoffübertragung werden durch die Auftriebskräfte und die Krümmungsparameter verbessert. Die Wärmeübertragung ist stark abhängig von den Parametern der viskosen Dissipation und der Prandtl-Zahl; die Stoffübertragung von der Schmidt-Zahl.

Solubility of sulfur dioxide at low partial pressures in dilute sulfuric acid solutions

Equilibrium of dissolution of sulfur dioxide at ppm levels in aqueous solutions of dilute sulfuric acid is analyzed, and a general expression is derived relating the total concentration of sulfur dioxide in the liquid phase to the partial pressure of SO2 in the gas and to the concentration of sulfuric acid in the solution. The equation is simplified for zero and high concentrations of the acid. Experiments at high concentrations of sulfuric acid have enabled the direct determination of Henry’s constant and its dependency on temperature. Heat of dissolution is -31.47 kJ/mol. Experiments in the absence of sulfuric acid and the related simplified expression have led to the determination of the equilibrium constant of the hydrolysis of aqueous sulfur dioxide and its temperature dependency.The heat of hydrolysis is 15.69 kJ/mol. The model equation with these parameters predicts the experimental data of the present work as well as the reported data very well.

Persistence Problem in Two-Dimensional Fluid Turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Lambda to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent theta = 2.9 +/- 0.2.

Theoretical estimation of the effect of minor elements on the solubility of oxygen in silicon melt

The effect of fourteen minor elements (Al, As, B, Bi, C, Ga, Ge, In, N, P, Pb, S, Sb and Sn) on the solubility of oxygen in silicon melt has been estimated using a recently developed theoretical equation, with only fundamental physical parameters such as hard sphere diameter, atomic volume and molar heat of solution at infinite dilution as inputs. The results are expressed in the form of interaction parameters. Although only limited experimental data are available for comparison, the theoretical approach appears to predict the correct sign, but underestimates the magnitude of the interaction between oxygen and alloying elements. The present theoretical approach is useful in making qualitative predications on the effect of minor elements on the solubility of oxygen in silicon melt, when direct measurements are not available.