Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

The effect of selected water-soluble excipients on the dissolution of paracetamol and ibuprofen

The purpose of this investigation was to study the dissolution behavior of paracetamol and ibuprofen in the presence of a range of selected potential excipients. First, a pH-solubility profile was generated for both drugs, and the effect of changing hydrodynamic conditions on the intrinsic dissolution rate was investigated. It was established that both drugs dissolved according to the diffusion-layer model. Paracetamol solubility (approximately 20.3 mg mL -1) did not vary from pH 1.2-8.0, corresponding to the in vivo range in the gastrointestinal tract. Ibuprofen had an intrinsic solubility of approximately 0.06 mg mL-1, and pKa was calculated as 4.4. Second, the effects of selected potential excipients (lactose, potassium bicarbonate, sodium bicarbonate, sodium chloride, and tartaric acid) were evaluated by measuring the effect of the inclusion of each additive in the dissolution medium on drug solubility, drug intrinsic dissolution rate, and solution viscosity. The results were evaluated using the diffusion-layer model, and it was determined that for paracetamol, the collected data fitted the model for all the excipients studied. For ibuprofen, it was found that there were differences between the excipients that raised the solution pH above the pK a to those that did not. For the excipients raising the pH above the pKa, the effect on intrinsic dissolution rate was not as high as that expected from the change in drug solubility. It was postulated that this might be due to lack of penetration of the excipient into the drug boundary layer microenvironment. Formulators may calculate the effect of adding an excipient based on solubility increases but may not find the dissolution rate improvement expected. Copyright © 2005 Taylor & Francis Inc.

Diagenetic processes in ore formation with special reference to the Zambian copperbelt and permian marl slate.

This thesis is concerned with the role of diagenesis in forming ore deposits. Two sedimentary 'ore-types' have been examined; the Proterozoic copper-cobalt orebodies of the Konkola Basin on the Zambian Copperbelt, and the Permian Marl Slate of North East England. Facies analysis of the Konkola Basin shows the Ore-Shale to have formed in a subtidal to intertidal environment. A sequence of diagenetic events is outlined from which it is concluded that the sulphide ores are an integral part of the diagenetic process. Sulphur isotope data establish that the sulphides formed as a consequence of the bacterial reduction of sulphate, while the isotopic and geochemical composition of carbonates is shown to reflect changes in the compositions of diagenetic pore fluids. Geochemical studies indicate that the copper and cobalt bearing mineralising fluids probably had different sources. Veins which crosscut the orebodies contain hydrocarbon inclusions, and are shown to be of late diagenetic lateral secretion origin. RbiSr dating indicates that the Ore-Shale was subject to metamorphism at 529 A- 20 myrs. The sedimentology and petrology of the Marl Slate are described. Textural and geochemical studies suggest that much of the pyrite (framboidal) in the Marl Slate formed in an anoxic water column, while euhedral pyrite and base metal sulphides formed within the sediment during early diagenesis. Sulphur isotope data confirm that conditions were almost "ideal" for sulphide formation during Marl Slate deposition, the limiting factors in ore formation being the restricted supply of chalcophile elements. Carbon and oxygen isotope data, along with petrographic observations, indicate that much of the calcite and dolomite occurring in the Marl Slate is primary, and probably formed in isotopic equilibrium. A depositional model is proposed which explains all of the data presented and links the lithological variations with fluctuations in the anoxicioxic boundary layer of the water column.

Exploration of a simple, low cost, micro gas turbine recuperator solution for a domestic combined heat and power unit

For micro gas turbines (MGT) of around 1 kW or less, a commercially suitable recuperator must be used to produce a thermal efficiency suitable for use in UK Domestic Combined Heat and Power (DCHP). This paper uses computational fluid dynamics (CFD) to investigate a recuperator design based on a helically coiled pipe-in-pipe heat exchanger which utilises industry standard stock materials and manufacturing techniques. A suitable mesh strategy was established by geometrically modelling separate boundary layer volumes to satisfy y + near wall conditions. A higher mesh density was then used to resolve the core flow. A coiled pipe-in-pipe recuperator solution for a 1 kW MGT DCHP unit was established within the volume envelope suitable for a domestic wall-hung boiler. Using a low MGT pressure ratio (necessitated by using a turbocharger oil cooled journal bearing platform) meant unit size was larger than anticipated. Raising MGT pressure ratio from 2.15 to 2.5 could significantly reduce recuperator volume. Dimensional reasoning confirmed the existence of optimum pipe diameter combinations for minimum pressure drop. Maximum heat exchanger effectiveness was achieved using an optimum or minimum pressure drop pipe combination with large pipe length as opposed to a large pressure drop pipe combination with shorter pipe length. © 2011 Elsevier Ltd. All rights reserved.