4 resultados para separation of variables

em Repositório Científico do Instituto Politécnico de Lisboa - Portugal


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: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

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We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau-de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.

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This work addresses the treatment by nanofiltration (NF) of solutions containing NaCN and NH(4)Cl at various pH values. The NF experiments are carried out in a Lab-Unit equipped with NF-270 membranes for model solutions that are surrogates of industrial ammoniacal wastewaters generated in the coke-making processes. The applied pressure is 30 bar. The main objective is the separation of the compounds NaCN and NH(4)Cl and the optimization of this separation as a function of the pH. Membrane performance is highly dependent on solution composition and characteristics, namely on the pH. In fact, the rejection coefficients for the binary model solution containing sodium cyanide are always higher than the rejections coefficients for the ammonium chloride model solution. For ternary solutions (cyanide/ammonium/water) it was observed that for pH values lower than 9 the rejection coefficients to ammonium are well above the ones observed for the cyanides, but for pH values higher than 9.5 there is a drastic decrease in the ammonium rejection coefficients with the increase of the pH. These results take into account the changes that occur in solution, namely, the solute species that are predominant, with the increase of the pH. The fluxes of the model solutions decreased with increased pH. (C) 2010 Elsevier B.V. All rights reserved.

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This paper describes preliminary work on the generation of synthesis gas from water electrolysis using graphite electrodes without the separation of the generated gases. This is an innovative process, that has no similar work been done earlier. Preliminary tests allowed to establish correlations between the applied current to the electrolyser and flow rate and composition of the generated syngas, as well as a characterisation of generated carbon nanoparticles. The obtained syngas can further be used to produce synthetic liquid fuels, for example, methane, methanol or DME (dimethyl ether) in a catalytic reactor, in further stages of a present ongoing project, using the ELECTROFUEL® concept. The main competitive advantage of this project lies in the built-in of an innovative technology product, from RE (renewable energy) power in remote locations, for example, islands, villages in mountains as an alternative for energy storage for mobility constraints.