Plane source method

Crete wall and use cylindrical attenuation, a good approximation can be made using the plane-source method (case 41). DJD (actual) = 5 X lOVlO = 5 X 10. JVom Fig. 10-3, using E = 2 Mev for ordinary concrete, = 3.5 ft. If this had been done by cylindrical attenuation (case 31), guess x 3.3 ft, or 40 in. 

In this section, the differences between using CVD hybrid fillers and physically mixed hybrid fillers in polymer composites were studied. It shows an interesting result with regard to the thermal and hardness properties of composites. The synergistic effects of two components in the hybrid fillers helped each other perform as fillers and reinforcements in polymer composites. The thermal conductivities and hardnesses of phenolic/CNT—alumina hybrid composites were studied. The CNT—alumina hybrid (HYB compound) was produced via the CVD method, which was discussed in Section 5.6. The phenolic/CNT—alumina hybrid composites were fabricated using hot-mounted molding. Thermal conductivity was measured using the transient plane source method with a Hot-Disk Thermal Constant Analyzer. Table 5.4 shows the sample description in this study. 

Plane-source Method. In a semi-infinite slab where 0 < a < oo, if at f = 0 a constant heating rate q per unit area is generated at the surface a = 0, it can be shown (27) that the temperature at some later time t at an interior point x, that is, T x, t), is given by... 

The plane-source method was originally applied to the measurement of refractory building materials (24), as was the line-source method. However, the plane source method has been applied with success, at least in one instance, to pol3Tneric systems (4), and its use will probably increase in the future. 

Guidelines on t ualily management and quality system elements Test code for the measurement of airborne noise emitted by rotating electrical machines Engineering method for free field conditions over a reflecting plane Survey method Determination of sound power levels of noise sources 14004/1991 BS EN ISO 9004/1994-1/1994 BS 7458-1/1991 BS 7458-2/1991 B.S 4196 9004/1987 1680-1/1986 1680-2/1986. 3740... 

The mathematical translation of the plane-source problem is as follows. Initially, there is a finite amount of mass M but very high concentration at a = 0, i.e., the density or concentration at a = 0 is defined to be infinite (which is unrealistic but merely an abstraction for the case in which initially the mass is concentrated in a very small region around a = 0). The initial condition is not consistent with that required for Boltzmann transformation. Hence, other methods must be used to solve the case of plane-source diffusion. Because this is the classical random walk problem, the solution can be found by statistical treatment as the following Gaussian distribution ... 

The thin-source method is also referred to as the thin-film method. One surface is cut into a plane surface and polished. A very thin layer is then sprayed or spread onto the surface. The thin layer contains the component of interest, which at high temperature diffuses into the interior of the sample from the polished surface. After the experiment, a section is cut perpendicular to the polished surface. Concentration profile is measured as a function of distance away from this surface. If the length of the concentration profile is much greater than (> 100 times) the thickness of the thin layer on the surface, the problem may be treated as a... 

A comparison of guarded hot plate, transient plane source and modified hot wire methods has been made54 using polyurethane foam, and the strengths and weaknesses of the techniques discussed,... 

Films of metals, produced by evaporation and condensation, will also take up impurities from the vacuum. During the preparation of the films the vacuum produced by the evaporation is very high. Afterward traces of gas, liberated from various parts of the apparatus, form a source of contamination. Owing to their very large surface areas, however, the films can be maintained in a clean state for a far longer time than filaments. Many films seem to have the additional advantage that they consist mainly of one crystallographic plane. The method of preparation provides a unique process of crystallization (339) it may be that the... 

This is the intensity of the exposure radiation in the plane of the wafer. The extended source method, or Hopkins method,is often used to predict the aerial image of a partially coherent, diffraction-limited, low-numerical-aperture-aherrated projection system based on scalar diffraction theory. For very high NA, vector calculations involving the complete solution of Maxwell s equation are used. The illumination may be of a single wavelength or it may be broadband. The illumination source may be a conventional disk shape or other more complicated shapes as in off-axis illumination. ... 

TPS (Transient Plane Source) technique has been shown to be effective method to measure the thermal conductivity, diffusivity of rare earth oxide powder such as gadolinium oxide, samarium oxide, and yttrium oxide. The details of the measutrement are described in Ref 66. The experimental results of effective thermal conductivity as well as thermal diffusivity of the above described three rare earth oxides are tabulated in Table 5-7. 

The time-dependent temperature distribution in a transient experiment is governed by Eq. 4, and usually the related parameter, thermal diffusivity. is obtained. However, under certain circumstanees the solution to the heat equation contains the thermal conductivity as well as the thermal diffusivity, and by choosing a suitable method the diffusivity can be eliminated from the answer. The more important methods are the line and plane source heater methods and arc described below. These arc not Standard methods, but they can be used where speed is more imp .>rtant than absolute accuracy, to give a conductivity value more quickly than the Standard methods. They can also be used to compare a range of materials. 

Transient-state or unsteady-state methods make nse of either a line source of heat or plane sources of heat. In both cases, the usual procedure is to apply a steady heat flux to the specimen, which mnst be initially in thermal eqnUibrinm, and to measnre the tanperatnre rise at some point in the specimen, resnlting from this applied flux [83]. The Fitch method is one of the most common transient methods for measuring the thermal conductivity of poor conductors. This method was developed in 1935 and was described in the National Bureau of Standards Research Report No. 561. Experimental apparatus is commercially available. 

ABSTRACT The mean flow features of two types of wall jets used often in hydraulic engineering are analyzed. They include the results of a plane jet and a three-dimensional wall jet. The required flow field was obtained from CFD simulations, the point source method and some limited experiments. These are compared with the available equations in vogue, which predict the growth of the jet, the decay of the maximum mean velocity and concentration of tracers. The variation of the wall shear stress along the flow is also analyzed. The CFD results for the distribution of the mean velocity and the tracer concentration exhibit self-similarity . However, the predicted growth rate of the jets differs from the available data. 

Numerous analytical solutions exist. A fairly complete set of solutions by the method of images is presented by Prakash (73), as modified by Benedict (J). Typical of the solutions is the one for an instantaneous plane source, shown in Eq. (51). 

The use of multichannel recording systems provides more quantitative analysis of source mechanisms utilizing the digitally stored AE signals. Two methods are in eommon use in source mechanism studies on rock specimens, fault-plane solution method and moment tensor analysis. In earthquake seismology, the classical method is the fault-plane solution... 

On the contrary, in the case of laboratory investigations on rock specimens under uniaxial or triaxial load, volume changes in the source play an important role. Dilatancy can be explained as volume expansion caused by tensile opening. In contrast to the fault-plane solution method, the more complex moment tensor method is capable of describing sources with volumetric components like tensile cracks, deviatoric sources like shear cracks, or a mixture of both source types. The volumetric source components can be easily obtained using the isotropic part, or one-third of the moment tensor trace. With the moment tensor method, the source mechanisms are estimated in a least-squares inversion calculation from amplitudes of the first motion as well as from full waveforms of P and S waves. This method requires additional knowledge about the transfer function of the medium (the so-called Green s function) and sensor response. 

Both methods have been applied in the field of AE in rocks. Some examples of the application of the fault-plane solution method are given by Sondergeld and Estey [1982], Kuwahara et al. [1985], Zang et al. [1998]. Because of an insufficient number of sensors these authors investigated only polarities of P-wave first motion to classify AE events recorded during uniaxial loading of rock specimens into shear and tensile types. A source with a imiform compressional polarity pattern was interpreted as a tensile t) e and one with eompressional as well as dilatational first motions as a shear type. It was not possible to determine the source orientation or to quantify the volume ehange of the mieroeracks. 

Various other methods have been described for the determination of thermal conductivity. Capillarity has been used to measure the thermal conductivity of LDPE, HOPE and PP at various temperatures and pressures [30]. A transient plane source technique has been applied in a study of the dependence of the effective thermal conductivity and thermal diffusivity of polymer composites [31]. 

E. Eremina, Y. Eremin and T. Wriedt, Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method. Optics Communications, 273(1), 278-285 (2007). 

In order to demonstrate the application of this general method to neutron diffusion in infinite media, the plane-source and line-source distribution problems (Secs. 5.2a and 5.2c) will be treated using (5.97). 

We treat the present problem by the method of images. Thus we take the infinite-medium solution for the slowing-down density due to a plane source and, by constructing a system of alternating sources outside the slab, reduce the flux at the extrapolated boundaries to zero so... 

Transient-state or unsteady-state methods make use of either a line source of heat or plane sources of heat. 

In addition to the MMP code, the DSM (discrete sources method) code developed by Eremin and Orlov [61] will be used for computer simulations. This DSM code is devoted to the analysis of homogeneous, axisymmetric particles using distributed vector spherical wave functions. For highly elongated particles, the sources are distributed along the axis of symmetry of the particle, while for highly flattened particles, the sources are distributed in the complex plane (see Appendix B). 

In this section, we present scattering results for an axis3nnmetric particle situated on or near a plane surface. For this purpose we use the TPARTSUB routine and a computer program based on the discrete sources method [59,60]. 

Transient Plane Source Thermal Conductivity Test Method... 

The Mathis Instruments Hot Disk Thermal Constants Analyzer is an emerging technology that can measme the in-plane and through-plane TC of an anisotropic material in the same test, using the transient plane source technique [13-17]. The saisor used in this test method is a 10 micron thick nickel foil embedded between two 25.4 micron thick layas of Kapton polyimide film. The nickel foil is wound in a double spir pattern with a radius of 3.189 mm. The thomal eonductivities were measmed at 23"C. 

Using the theorem that the sufficiency condition for mathematical correctness in 3D-reconstruction is fulfilled if all planes intersecting the object have to intersect the source-trajectory at least in one point [8], it is possible to generalise Feldkamp s method. Using projection data measured after changing the sotuce-trajectory from circular to spiral focus orbit it is possible to reconstruct the sample volume in a better way with the Wang algorithm [9]. 

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