38 resultados para Second Order Parabolic Heat Equation


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This paper presents an achievable second-order rate region for the discrete memoryless multiple-access channel. The result is obtained using a random-coding ensemble in which each user's codebook contains codewords of a fixed composition. It is shown that this ensemble performs at least as well as i.i.d. random coding in terms of second-order asymptotics, and an example is given where a strict improvement is observed. © 2013 IEEE.

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The two-point spatial correlation of the rate of change of fluctuating heat release rate is central to the sound emission from open turbulent flames, and a few attempts have been made to address this correlation in recent studies. In this paper, the two-point correlation and its role in combustion noise are studied by analysing direct numerical simulation (DNS) data of statistically multi-dimensional turbulent premixed flames. The results suggest that this correlation function depends on the separation distance and direction but, not on the positions inside the flame brush. This correlation can be modelled using a combination of Hermite-Gaussian functions of zero and second order, i.e. functions of the form (1-Ax2)e-Bx2 for constants A and B, to include its possible negative values. The integral correlation volume obtained using this model is about 0.2δL3 with the length scale obtained from its cube root being about 0.6δ L, where δ L is the laminar flame thermal thickness. Both of the values are slightly larger than the values reported in an earlier study because of the anisotropy observed for the correlation. This model together with the turbulence-dependent parameter K, the ratio of the root-mean-square (RMS) value of the rate of change of reaction rate to the mean reaction rate, derived from the DNS data is applied to predict the far-field sound emitted from open flames. The calculated noise levels agree well with recently reported measurements and show a sensitivity to K values. © 2012 The Combustion Institute.

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Numerical methods based on the Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) equations are applied to the thermal prediction of flows representative of those found in and around electronics systems and components. Low Reynolds number flows through a heated ribbed channel, around a heated cube and within a complex electronics system case are investigated using linear and nonlinear LES models, hybrid RANS-LES and RANS-Numerical-LES (RANS-NLES) methods. Flow and heat transfer predictions using these techniques are in good agreement with each other and experimental data for a range of grid resolutions. Using second order central differences, the RANS-NLES method performs well for all simulations. © 2011 Elsevier Inc.

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Hybrid large-eddy type simulations for cold jet flows from a serrated nozzle are performed at an acoustic Mach number Ma ac = 0.9 and Re = 1.03×10 6. Since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES) or implicit LES (ILES) reminiscent procedure. To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended to the LES making a hybrid RANS-ILES. The geometric complexity of the serrated nozzle is fully considered without simplification or emulation. An improved but still modest hexahedral multi-block grid with circa 20 million grid points (with respect to 12.5 million in Xia et al.; Int J Heat Fluid Flow 30:1067-1079, 2009) is used. Despite the modest grid size, encouraging and improved results are obtained. Directly resolved mean and second-order fluctuating quantities along the jet centerline and in the jet shear layer compare favorably with measurements. The radiated far-field sound predicted using the Ffowcs Williams and Hawkings (FW-H) surface integral method shows good agreement with the measurements in directivity and sound spectra. © 2011 Springer Science+Business Media B.V.

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The magnetisation of bulk high temperature superconductors (HTS), such as RE-Ba-Cu-O [(RE)BCO, where RE is a rare earth element or Y], by a practical technique is essential for their application in high field, permanent magnet-like devices. Research to-date into the pulsed field magnetisation (PFM) of these materials, however, has been limited generally to experimental techniques, with relatively little progress in the development of theoretical models. This is because not only is a multi-physics approach needed to take account of the heating of the samples but also the high electric fields generated are well above the regime in which there are reliable experimental results. This paper describes a framework of theoretical simulation using the finite element method (FEM) that is applicable to both single- and multi-pulse magnetisation processes of (RE)BCO bulk superconductors. The model incorporates the heat equation and provides a convenient way of determining the distribution of trapped field, current density and temperature change within a bulk superconductor at each stage of the magnetisation process. An example of the single-pulse magnetisation of a (RE)BCO bulk is described. Potentially, the model may serve as a cost-effective tool for the optimisation of the bulk geometry and the magnetisation profile in multi-pulse magnetisation processes. © 2010 IOP Publishing Ltd.

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The dynamic analysis of a deepwater floating platform and the associated mooring/riser system should ideally be fully coupled to ensure a reliable response prediction. It is generally held that a time domain analysis is the only means of capturing the various coupling and nonlinear effects accurately. However, in recent work it has been found that for an ultra-deepwater floating system (2000m water depth), the highly efficient frequency domain approach can provide highly accurate response predictions. One reason for this is the accuracy of the drag linearization procedure over both first and second order motions, another reason is the minimal geometric nonlinearity displayed by the mooring lines in deepwater. In this paper, the aim is to develop an efficient analysis method for intermediate water depths, where both mooring/vessel coupling and geometric nonlinearity are of importance. It is found that the standard frequency domain approach is not so accurate for this case and two alternative methods are investigated. In the first, an enhanced frequency domain approach is adopted, in which line nonlinearities are linearized in a systematic way. In the second, a hybrid approach is adopted in which the low frequency motion is solved in the time domain while the high frequency motion is solved in the frequency domain; the two analyses are coupled by the fact that (i) the low frequency motion affects the mooring line geometry for the high frequency motion, and (ii) the high frequency motion affects the drag forces which damp the low frequency motion. The accuracy and efficiency of each of the methods are systematically compared. Copyright © 2007 by ASME.

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Soil-mix technology is effective for the construction of permeable reactive barriers (PRBs) for in situ groundwater treatment. The objective of this study was to perform initial experiments for the design of soil-mix technology PRBs according to (i) sorption isotherm, (ii) reaction kinetics and (iii) mass balance of the contaminants. The four tested reactive systems were: (i) a granular zeolite (clinoptilolite-GZ), (ii) a granular organoclay (GO), (iii) a 1:1-mixture GZ and model sandy clayey soil and (iv) a 1:1:1-mixture of GZ, GO and model soil. The laboratory experiments consisted of batch tests (volume 900mL and sorbent mass 18g) with a multimetal solution of Pb, Cu, Zn, Cd and Ni. For the adsorption experiment, the initial concentrations ranged from 0.01 to 0.5mM (2.5 to 30mg/L). The maximum metal retention was measured in a batch test (300mg/L for each metal, volume 900mL, sorbent mass 90-4.5g). The reactive material efficiency order was found to be GZ>GZ-soil mix>GZ-soil-GO mix>GO. Langmuir isotherms modelled the adsorption, even in presence of a mixed cations solution. Adsorption was energetically favourable and spontaneous in all cases. Metals were removed according to the second order reaction kinetics; GZ and the 1:1-mix were very similar. The maximum retention capacity was 0.1-0.2mmol/g for Pb in the presence of clinoptilolite; for Cu, Zn, Cd and Ni, it was below 0.05mmol/g for the four reactive systems. Mixing granular zeolite, organoclay and model soil increased the chemisorption. Providing that GZ is reactive enough for the specific conditions, GZ can be mixed to obtain the required sorption. Granular clinoptilolite addition to soil is recommended for PRBs for metal contaminated groundwater. The laboratory experiments consisted of batch tests with a multimetal solution of Pb, Cu, Zn, Cd and Ni. The four reactive materials chosen were granular zeolite, clinoptilolite and model sandy clayey soil, granular organoclay and a mix of clinoptilolite, model soil and organoclay. The reactive material efficiency order was found to be granular clinoptilolite>clinoptilolite-soil mix>clinoptilolite-soil-organoclay mix>granular organoclay. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.