Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Effect of curve crossing on absorption and resonance Raman spectra: analytical treatment for delta-function coupling in parabolic potentials

We propose an exactly solvable model for the two-state curve-crossing problem. Our model assumes the coupling to be a delta function. It is used to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.

Process Analytical Technology Approach on Fluid Bed Granulation and Drying : Identifying Critical Relationships and Constructing the Design Space

Fluid bed granulation is a key pharmaceutical process which improves many of the powder properties for tablet compression. Dry mixing, wetting and drying phases are included in the fluid bed granulation process. Granules of high quality can be obtained by understanding and controlling the critical process parameters by timely measurements. Physical process measurements and particle size data of a fluid bed granulator that are analysed in an integrated manner are included in process analytical technologies (PAT). Recent regulatory guidelines strongly encourage the pharmaceutical industry to apply scientific and risk management approaches to the development of a product and its manufacturing process. The aim of this study was to utilise PAT tools to increase the process understanding of fluid bed granulation and drying. Inlet air humidity levels and granulation liquid feed affect powder moisture during fluid bed granulation. Moisture influences on many process, granule and tablet qualities. The approach in this thesis was to identify sources of variation that are mainly related to moisture. The aim was to determine correlations and relationships, and utilise the PAT and design space concepts for the fluid bed granulation and drying. Monitoring the material behaviour in a fluidised bed has traditionally relied on the observational ability and experience of an operator. There has been a lack of good criteria for characterising material behaviour during spraying and drying phases, even though the entire performance of a process and end product quality are dependent on it. The granules were produced in an instrumented bench-scale Glatt WSG5 fluid bed granulator. The effect of inlet air humidity and granulation liquid feed on the temperature measurements at different locations of a fluid bed granulator system were determined. This revealed dynamic changes in the measurements and enabled finding the most optimal sites for process control. The moisture originating from the granulation liquid and inlet air affected the temperature of the mass and pressure difference over granules. Moreover, the effects of inlet air humidity and granulation liquid feed rate on granule size were evaluated and compensatory techniques used to optimize particle size. Various end-point indication techniques of drying were compared. The ∆T method, which is based on thermodynamic principles, eliminated the effects of humidity variations and resulted in the most precise estimation of the drying end-point. The influence of fluidisation behaviour on drying end-point detection was determined. The feasibility of the ∆T method and thus the similarities of end-point moisture contents were found to be dependent on the variation in fluidisation between manufacturing batches. A novel parameter that describes behaviour of material in a fluid bed was developed. Flow rate of the process air and turbine fan speed were used to calculate this parameter and it was compared to the fluidisation behaviour and the particle size results. The design space process trajectories for smooth fluidisation based on the fluidisation parameters were determined. With this design space it is possible to avoid excessive fluidisation and improper fluidisation and bed collapse. Furthermore, various process phenomena and failure modes were observed with the in-line particle size analyser. Both rapid increase and a decrease in granule size could be monitored in a timely manner. The fluidisation parameter and the pressure difference over filters were also discovered to express particle size when the granules had been formed. The various physical parameters evaluated in this thesis give valuable information of fluid bed process performance and increase the process understanding.

Investigating physical properties of solid dosage forms during pharmaceutical processing : Process analytical applications of vibrational spectroscopy

In order to improve and continuously develop the quality of pharmaceutical products, the process analytical technology (PAT) framework has been adopted by the US Food and Drug Administration. One of the aims of PAT is to identify critical process parameters and their effect on the quality of the final product. Real time analysis of the process data enables better control of the processes to obtain a high quality product. The main purpose of this work was to monitor crucial pharmaceutical unit operations (from blending to coating) and to examine the effect of processing on solid-state transformations and physical properties. The tools used were near-infrared (NIR) and Raman spectroscopy combined with multivariate data analysis, as well as X-ray powder diffraction (XRPD) and terahertz pulsed imaging (TPI). To detect process-induced transformations in active pharmaceutical ingredients (APIs), samples were taken after blending, granulation, extrusion, spheronisation, and drying. These samples were monitored by XRPD, Raman, and NIR spectroscopy showing hydrate formation in the case of theophylline and nitrofurantoin. For erythromycin dihydrate formation of the isomorphic dehydrate was critical. Thus, the main focus was on the drying process. NIR spectroscopy was applied in-line during a fluid-bed drying process. Multivariate data analysis (principal component analysis) enabled detection of the dehydrate formation at temperatures above 45°C. Furthermore, a small-scale rotating plate device was tested to provide an insight into film coating. The process was monitored using NIR spectroscopy. A calibration model, using partial least squares regression, was set up and applied to data obtained by in-line NIR measurements of a coating drum process. The predicted coating thickness agreed with the measured coating thickness. For investigating the quality of film coatings TPI was used to create a 3-D image of a coated tablet. With this technique it was possible to determine coating layer thickness, distribution, reproducibility, and uniformity. In addition, it was possible to localise defects of either the coating or the tablet. It can be concluded from this work that the applied techniques increased the understanding of physico-chemical properties of drugs and drug products during and after processing. They additionally provided useful information to improve and verify the quality of pharmaceutical dosage forms

Analytical studies of gain optimization in CO2-N2 gasdynamic lasers employing two-dimensional wedge nozzles

An analytical method has been proposed to optimise the small-signaloptical gain of CO2-N2 gasdynamic lasers (gdl) employing two-dimensional (2D) wedge nozzles. Following our earlier work the equations governing the steady, inviscid, quasi-one-dimensional flow in the wedge nozzle of thegdl are reduced to a universal form so that their solutions depend on a single unifying parameter. These equations are solved numerically to obtain similar solutions for the various flow quantities, which variables are subsequently used to optimize the small-signal-gain. The corresponding optimum values like reservoir pressure and temperature and 2D nozzle area ratio also have been predicted and graphed for a wide range of laser gas compositions, with either H2O or He as the catalyst. A large number of graphs are presented which may be used to obtain the optimum values of small signal gain for a wide range of laser compositions without further computations.

Experimental and Analytical Investigations of the actions taking place in a Synchronous machine during the starting period when the starting Is effected by means of alternating current

The literature on the subject of the present investigation is somewhat meagre. A rotary converter or synchronous motor no! provided with any special starting devices forms, when started from the alternating current side, a type of induction motor whoso Htator is provided with a polyphase winding, and whoso rotor has a single-phase (or single magnetic axis) winding.

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.

A new analytical approach to optimize a generation schedule

Identification of the optimum generation schedule by various methods of coordinating incremental generation costs and incremental transmission losses has been described previously in the literature. This paper presents an analytical approach which reduces the time-consuming iterative procedure into a mere positive-root determination of a third-order polynomial in λ. This approach includes the effect of transmission losses and is suitable for systems with any number of plants. The validity and effectiveness of this method are demonstrated by analysing a sample system.

Geochemistry of meta-anorthosites from Holénarasipur, Karnataka, South India

Geochemical and Rb---Sr isotope studies indicate that the meta-anorthosites of Holénarasipur, occurring as minor differentiates in ultramafic-mafic complex are igneous intrusives with cumulus character, emplaced around 3095 m.y. ago. The fine-grained nature is secondary; relict cumulus features are preserved in less deformed bodies. In major element chemistry, they compare well with other Archean anorthosites. Abundance levels of Ti, Zr, Y and P indicate the evolution through crystal fractionation of a parental magma; cumulus olivine and pyroxenes dominated chemistry for ultramafites, cumulus plagioclase and possibly clinopyroxene controlled chemistry for anorthosite-gabbros and cumulus magnetite in magnetite-gabbros. Magnetite is not an early cumulate. REE geochemistry is dominated by plagioclase with low abundance levels, slightly LREE enriched and variable positive Eu anomaly. Sr and Image values vary with An content in plagioclase. Isotopic studies show low initial Image (=0.7016) indicating that Rb---Sr isochron age represents the time of intrusion rather than the time of metamorphism.

On an analytical-numerical procedure for the analysis of cylindrical-shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

Description of ring puckering of furanose: An analytical approach

An analytical approach for the description of the ring puckerings from the endocyclic ring torsion angles of a five-membered saturated ring is given. This description is independent of any reference conformation. For the description, a revised notation for the endocyclic ring torsion angles has been suggested. The application of this method to the furanose ring is described in detail.