Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

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.

Shell-model calculation of defect energies in alkali halides employing crystal-independent interionic potential parameters

Shell model calculation of defect energies in alkali halides have been carried out using the ion-dependent, crystal-independent potential parameters of Sangster and Atwood (1978). Results indicate that appreciable differences exist between barrier heights for migration of cations and anions. While barrier heights for cations are generally lower than for anions in alkali halides of NaCl structure, the opposite is true in alkali halides of CsCl structure.

Equivalent circuit parameters of the film-covered magnesium/electrolyte interface in Mg/MnO2 dry cells from transient and ac impedance measurements

The electrochemical properties of the film-covered anode/solution interface in the magnesium/ manganese dioxide dry cell have been evaluated. The most plausible electrical equivalent circuit description of the Mg/solution interface with the passive film intact, has been identified. These results are based on the analysis of ac impedance and voltage transient measurements made on the dry cell under conditions which cause no damage to the protective passive film on the anode. The study demonstrates the complementary character of impedance and transient measurements when widely different frequency ranges are sampled in each type of investigation. The values and temperature dependence of the anode-film resistance, film capacitance, double-layer capacitance and charge-transfer resistance of the film-covered magnesium/solution interface have been determined. The magnitude of these values and its implications in understanding the important performance aspects of the magnesium/manganese dioxide dry cell are discussed. The study may be extended, in principle, to Li, Al and Ca batteries.

Equivalent circuit parameters of the film-covered magnesium/electrolyte interface in Mg/MnO2 dry cells from transient and ac impedance measurements

The electrochemical properties of the film-covered anode/solution interface in the magnesium/ manganese dioxide dry cell have been evaluated. The most plausible electrical equivalent circuit description of the Mg/solution interface with the passive film intact, has been identified. These results are based on the analysis of ac impedance and voltage transient measurements made on the dry cell under conditions which cause no damage to the protective passive film on the anode. The study demonstrates the complementary character of impedance and transient measurements when widely different frequency ranges are sampled in each type of investigation. The values and temperature dependence of the anode-film resistance, film capacitance, double-layer capacitance and charge-transfer resistance of the film-covered magnesium/solution interface have been determined. The magnitude of these values and its implications in understanding the important performance aspects of the magnesium/manganese dioxide dry cell are discussed. The study may be extended, in principle, to Li, Al and Ca batteries.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Flocculation, filtration and selective flocculation studies on haematite ore fines using starch

The flocculation and filtration characteristics of typical Indian iron ore fines have been studied using starch as flocculant in the presence of an inorganic electrolyte, namely calcium chloride. The effect of various parameters such as pH, starch and calcium chloride concentrations and pulp density on the settling and filtration rates, turbidity of the supernatant and on residual starch and calcium ion concentrates has been investigated through a statistical design and analysis approach and subsequently optimised on a laboratory scale. The adsorption mechanisms of starch onto haematite have been elucidated through adsorption density measurements, infrared and X-ray photoelectron spectroscopic techniques. The rheological property of the polymer solutions of relevance to flocculations has also been investigated. Further, the role of metal ion-starch interactions in the bulk solution, has been studied. In order to understand the nature of polymer adsorption at the double-layer, electrokinetic studies have been carried out with the iron ore mineral samples using starch and calcium chloride. Based on the above findings, selective floculaation tests on artificial mixtures of iron ore minerals have been carried out to determine the separation efficiencies from the view point of alumina and silica removal from haematite as well as the control of alumina: silica ratio in Indian iron ores.

Temperature dependent optical constants of amorphous Ge2Sb2Te5 thin films

This study focuses on the temperature dependent optical band gap changes in the amorphous Ge2Sb2Te5 (GST) films. The behavior of the amorphous GST thin films at low temperatures has been studied. The band gap increment of around 0.2 eV is observed at low temperature (4.2 K) compared to room temperature (300 K). The band gap changes associated with the temperature are completely reversible. The other optical parameters like Urbach energy and Tauc parameter (B-1/2) are studied for different temperatures and discussed. The observed changes in optical band gap (E-g) are fitting to Fan's one phonon approximation. Phonon energy ((h) over bar omega) corresponding to a frequency of 3.59 THz is derived from Fan's approximation, which is close to the reported value of 3.66 THz. (C) 2010 Elsevier B.V. All rights reserved.

Kinetic studies on the interaction of gold(III) with nucleic acids. I. Native DNA-Au(III) system-spectrophotometric studies

Kinetics of the interaction of Au(III) with native calf thymus DNA has been studied spectrophotometrically to determine the kinetic parameters and to examine their dependency on the concentrations of DNA and Au(III), temperature, ionic strength and pH. The reaction is of the first order with respect to both the nucleotide unit of DNA and Au(III) in the stoichiometry of 2∶1 respectively. The rate constants vary with the initial ratio of DNA to Au(III) and is attributed to the effect of free chloride ions and the existence of a number of reaction sites with slight difference in the rate constants. The activation energies of this interaction have been found to be 14–16 kcal/mol. From the effect of ionic strength the reaction is found to occur between a positive and a negative ion in the rate-limiting step. The logarithm of rate constants are the linear function of pH and the slopes are dependent on ther-values. A plausible mechanism has been proposed which involves a primary dissociation of the major existing species (AuCl2(OH)2)−, to give (AuCl2)+ which then reacts with a site in the nucleotide unit of DNA in the rate-liminting step followed by a rapid binding to another site on the complementary strand of the DNA double helix. There exist a number of binding sites with slight difference in reactivity.

A kinetic investigation of thermal degradation of poly(vinyl formals)

Several samples of poly(vinyl formal) having the same vinyl alcohol content (8–9%) but varying contents of vinyl acetate (6–22%) and vinyl formol (70–85%) were prepared and subjected to thermogravimetric analysis, in air and nitrogen atmospheres, employing both isothermal and dynamic methods. Kinetic parameters determined from both the isothermal and dynamic TGA data are compared. The activation energy is seen to be largely dependent on the degree of conversion, implying a complex degradation reaction. The activation energy is also much less for degradation in air than in nitrogen, which can be explained by a reaction with oxygen-producing structures favoring degradation. The activation energy is less sensitive to variation in polymer composition for degradation in air than in nitrogen. Thus, in the dynamic process, the activation energy value decreases (from 36 to 23 kcal/mole) with increasing acetate content (from 6 to 22%) in nitrogen atmosphere, while in air the activation energy value increases only moderately (from 21 to 27 kcal/mole) with increasing acetate content (from 6 to 22%). The order of reaction is nearly unity, irrespective of the composition of the polymer, both in air and nitrogen.

A kinetic investigation of thermal degradation of poly(vinyl formals)

Several samples of poly(vinyl formal) having the same vinyl alcohol content (8–9%) but varying contents of vinyl acetate (6–22%) and vinyl formol (70–85%) were prepared and subjected to thermogravimetric analysis, in air and nitrogen atmospheres, employing both isothermal and dynamic methods. Kinetic parameters determined from both the isothermal and dynamic TGA data are compared. The activation energy is seen to be largely dependent on the degree of conversion, implying a complex degradation reaction. The activation energy is also much less for degradation in air than in nitrogen, which can be explained by a reaction with oxygen-producing structures favoring degradation. The activation energy is less sensitive to variation in polymer composition for degradation in air than in nitrogen. Thus, in the dynamic process, the activation energy value decreases (from 36 to 23 kcal/mole) with increasing acetate content (from 6 to 22%) in nitrogen atmosphere, while in air the activation energy value increases only moderately (from 21 to 27 kcal/mole) with increasing acetate content (from 6 to 22%). The order of reaction is nearly unity, irrespective of the composition of the polymer, both in air and nitrogen.

Temperature dependent transport behavior of n-InN nanodot/p-Si heterojunction structures

The present work explores the temperature dependent transport behavior of n-InN nanodot/p-Si(100) heterojunction diodes. InN nanodot (ND) structures were grown on a 20 nm InN buffer layer on p-Si(100) substrates. These dots were found to be single crystalline and grown along 001] direction. The junction between these two materials exhibits a strong rectifying behavior at low temperatures. The average barrier height (BH) was determined to be 0.7 eV from current-voltage-temperature, capacitance-voltage, and flat band considerations. The band offsets derived from built-in potential were found to be Delta E-C=1.8 eV and Delta E-V=1.3 eV and are in close agreement with Anderson's model. (C) 2010 American Institute of Physics. doi:10.1063/1.3517489]

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Analysis of sequence dependent variations in secondary and tertiary structure of tRNA molecules

The double helical regions of the five tRNA(Phe) and two tRNA(Asp) crystal structures have been analyzed using the local basepair step parameters. The sequence dependent effects in the mini double helices of tRNA are very similar to those observed in the crystal structures of oligonucleotides in the A-form, the purine-pyrimidine and purine-purine steps have small roll angles when compared to the fiber models of A-DNA as well as A-RNA, while the pyrimidine-purine doublet steps have large roll angles. The orientation of the basepairs in the D-stem is unusual and invariant i.e. they are different from the other three stems but are very similar in all the five tRNA(Phe) crystal structures, presumably due to tertiary interaction of the Watson-Crick basepairs with other bases, with all bases being highly conserved. The origin of the differences between the tertiary structures of tRNA(Phe) and tRNA(Asp) from yeast has also been investigated. It is found that even though the angle between the acceptor arm and the D-stem is very similar in the two structures, the angle subtended by the acceptor arm and the anticodon arm is smaller in the tRNA(Phe) structure (by more than 10 degrees). This is due to differences in the orientation of the two mini helices constituting the anticodon arm, which are inclined to each other by approximately 25 degrees in tRNA(Phe) and 16 degrees in tRNA(Asp). In addition, the acceptor arm, the D-stem and the anticodon stem are nearly coplanar in tRNA(Phe), while in tRNA(Asp) the anticodon stem projects out of the plane defined by the acceptor arm and the anticodon stem. These two features together lead to a larger separation between the acceptor and anticodon ends in tRNA(Asp) and indicate that the junction between the D-stem and the anticodon stem is quite variable, with features characteristic of a ball-and-socket type joint and determined for each tRNA molecule by the base sequence at the junction.

A Theory of the Lifted Temperature Minimum on Calm Clear Nights

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of $\frac{1}{2}$ m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several hours, and has not so far been satisfactorily explained. We formulate here a theory that considers energy balance between radiation, conduction and free or forced convection in humid air, with surface temperature, humidity and wind incorporated into an appropriate mathematical model as parameters. A complete numerical solution of the coupled air-soil problem is used to validate an approach that specifies the surface temperature boundary condition through a cooling rate parameter. Utilizing a flux-emissivity scheme for computing radiative transfer, the model is numerically solved for various values of turbulent friction velocity. It is shown that a lifted minimum is predicted by the model for values of ground emissivity not too close to unity, and for sufficiently low surface cooling rates and eddy transport. Agreement with observation for reasonable values of the parameters is demonstrated. A heuristic argument is offered to show that radiation substantially increases the critical Rayleigh number for convection, thus circumventing or weakening Rayleigh-Benard instability. The model highlights the key role played by two parameters generally ignored in explanations of the phenomenon, namely surface emissivity and soil thermal conductivity, and shows that it is unnecessary to invoke the presence of such particulate constituents as haze to produce a lifted minimum.