Nonsimilar solutions for free convection in non-Newtonian fluids along a vertical plate in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of free convection in power-law type non-Newtonian fluids along a permeable vertical plate with variable wall temperature or heat flux distribution. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

Synthesis of metastable, wurzite-based zinc oxide-cobalt(II) oxide solid solutions by spray pyrolysis

Aqueous solutions of acetates and nitrates of zinc and cobalt have been spray decomposed to study the production of extended solid solutions in the ZnO-CoO system. Examination of the products of a variety of synthesis conditions indicates that up to 70% CoO may be retained in the solid solution in the wurzite phase, even though a comparison of the equilibrium solubility in the phase diagram might be expected to favor the formation of a rock-salt-based solid solution.

Synthesis of single-walled carbon nanotubes using binary (Fe, Co, Ni) alloy nanoparticles prepared in situ by the reduction of oxide solid solutions

Passing a H-2-CH4 mixture over oxide spinels containing two transition elements as in Mg0.8MyMz'Al2O4 (M, M' = Fe, Co or Ni, y + z = 0.2) at 1070 degrees C produces small alloy nanoparticles which enable the formation of carbon nanotubes. Surface area measurements are found to be useful for assessing the yield and quality of the nanotubes. Good-quality single-walled nanotubes (SWNTs) have been obtained in high yields with the FeCo alloy nanoparticles, as evidenced by transmission electron microscope images and surface area measurements. The diameter of the SWNTs is in the 0.8-5 nm range, and the multiwalled nanotubes, found occasionally, possess very few graphite layers. (C) 1999 Elsevier Science B.V. All rights reserved.

An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory. (C) 2011 Elsevier Ltd. All rights reserved.

Microwave heating in multiphase systems: evaluation of series solutions

The 1D electric field and heat-conduction equations are solved for a slab where the dielectric properties vary spatially in the sample. Series solutions to the electric field are obtained for systems where the spatial variation in the dielectric properties can be expressed as polynomials. The series solution is used to obtain electric-field distributions for a binary oil-water system where the dielectric properties are assumed to vary linearly within the sample. Using the finite-element method temperature distributions are computed in a three-phase oil, water and rock system where the dielectric properties vary due to the changing oil saturation in the rock. Temperature distributions predicted using a linear variation in the dielectric properties are compared with those obtained using the exact nonlinear variation.

Peroxo-bridged divanadate as selective bromide oxidant in bromoperoxidation

Diperoxovanadate is effective only in presence of free vanadate in vanadium-dependent bromoperoxidation at physiological pH. Peroxide in the form of bridged divanadate complex (VOOV-type), but not the bidentate form as in diperoxovanadate, is proposed to be the oxidant of bromide. In order to obtain direct evidence, peroxo-divanadate complexes with glycyl-glycine, glycyl-alanine and glycyl-asparagine as heteroligands were synthesized. By elemental analysis and spectral studies they were characterized to be triperoxo-divanadates, [V2O2(O-2)(3)(peptide)(3)]. H2O, with the two vanadium atoms bridged by a peroxide and a heteroligand. The dipeptide seems to stabilize the peroxo-bridge by inter-ligand interaction, possibly hydrogen bonding. This is indicated by rapid degradation of these compounds on dissolving in water with partial loss of peroxide accompanied by release of bubbles of oxygen. The V-51-NMR spectra of such solutions showed diperoxovanadate and decavanadate (oligomerized from vanadate) as the products. Additional oxygen was released on treating these solutions with catalase as expected of residual diperoxovanadate. The solid compounds when added to the reaction mixtures showed transient, rapid bromoperoxidation reaction, but not oxidation of NADH or inactivation of glucose oxidase, the other two activities shown by a mixture of diperoxovanadate and vanadyl. This demonstration of peroxide-bridged divanadate as powerful, selective oxidant of bromide, active at physiological pH, should make it a possible candidate of mimic in the action of vanadium in bromoperoxidase proteins.

Novel phase-transition behavior near liquid/liquid critical points of aqueous solutions: Formation of a third phase at the interface

We report a novel phase behavior in aqueous solutions of simple organic solutes near their liquid/liquid critical points, where a solid-like third phase appears at the liquid/liquid interface. The phenomenon has been found in three different laboratories. It appears in many aqueous systems of organic solutes and becomes enhanced upon the addition of salt to these solutions.

Analytical solutions for heat transfer during cyclic melting and freezing of a phase change material used in electronic or electrical packaging

In this paper we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each subdomain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.

Minimum error solutions of the Boltzmann equation for shock structure

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

Novel ABO(3) oxides related to perovskite and YAlO3 structure types in the La-B-V-O (B = Ni, Cu) systems

The synthesis, structure and magnetic properties of mixed-metal oxides of ABO(3) composition in the La-B-V-O (B = Ni, Cu) systems are described in the present paper. While the B = Ni oxides adopt GdFeO3-like perovskite structure containing disordered nickel and vanadium at the octahedral B site, La3Cu2VO9 crystallizes in a YAlO3-type structure. A detailed investigation of the superstructure of nominal La3Cu2VO9 by WDS analysis and Rietveld refinement of powder XRD data reveal that the likely composition of the phase is La13Cu9V4O38.5, where the Cu and V atoms are ordered in a root13a(h) (a(h) = hexagonal a parameter of YAlO3-like subcell) superstructure. Magnetic susceptibility data support the proposed superstructure consisting of triangular Cu-3 clusters. At low temperatures, the magnetic moment corresponds to S = 1/2 per Cu-3 cluster, while at high temperatures the behavior is Curie-Weiss like, showing S = 1/2 per copper. The present work reveals the contrasting behavior of La-Cu-V-O and La-Ni-V-O systems: while a unique line-phase related to YAlO3 structure is formed around La3Cu2VO9 Composition in the copper system, a continuous series of perovskite-GdFeO3 solid solutions, LaNi1-xVxO3 for 0 less than or equal to x less than or equal to 1/3 seems to be obtained in the nickel system, where the oxidation state of nickel varies from 3+ to 2+.

Accurate Parameter Estimation of Contaminant Transport Inverse Problem using Paartaicle Swarm Optimization

Swarm Intelligence techniques such as particle swarm optimization (PSO) are shown to be incompetent for an accurate estimation of global solutions in several engineering applications. This problem is more severe in case of inverse optimization problems where fitness calculations are computationally expensive. In this work, a novel strategy is introduced to alleviate this problem. The proposed inverse model based on modified particle swarm optimization algorithm is applied for a contaminant transport inverse model. The inverse models based on standard-PSO and proposed-PSO are validated to estimate the accuracy of the models. The proposed model is shown to be out performing the standard one in terms of accuracy in parameter estimation. The preliminary results obtained using the proposed model is presented in this work.

Novel Algorithm for estimation of Swell Pressure of Fine Grained Soils Based on Diffuse Double Layer (DDL) Theory

Use of engineered landfills for the disposal of industrial wastes is currently a common practice. Bentonite is attracting a greater attention not only as capping and lining materials in landfills but also as buffer and backfill materials for repositories of high-level nuclear waste around the world. In the design of buffer and backfill materials, it is important to know the swelling pressures of compacted bentonite with different electrolyte solutions. The theoretical studies on swell pressure behaviour are all based on Diffuse Double Layer (DDL) theory. To establish a relation between the swell pressure and void ratio of the soil, it is necessary to calculate the mid-plane potential in the diffuse part of the interacting ionic double layers. The difficulty in these calculations is the elliptic integral involved in the relation between half space distance and mid plane potential. Several investigators circumvented this problem using indirect methods or by using cumbersome numerical techniques. In this work, a novel approach is proposed for theoretical estimations of swell pressures of fine-grained soil from the DDL theory. The proposed approach circumvents the complex computations in establishing the relationship between mid-plane potential and diffused plates’ distances in other words, between swell pressure and void ratio.