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Poroelastic and poroplastic modelling of a deep spherical gallery submitted to ventilation
Published in J.-L. Auriault, C. Geindreau, P. Royer, J.-F. Bloch, C. Boutin, J. Lewandowska, Poromechanics II, 2020
A. Blaisonneau, A. Giraud, F. Homand, D. Hoxha, T. Lassabatère
where E¯¯ is the matrix for which columns are the eigenvectors associated with the two eigenvalues δi of the matrix H¯¯. The eigenfunctions for the spherical geometry vi¯ are: vi¯=Ai[s]exp[−ωir]r+Biexp[ωir]r
Immobilized Enzymes
Published in Debabrata Das, Debayan Das, Biochemical Engineering, 2019
For spherical geometry, () φ2=(43πR34πr2)2vmaxDeskm=R29vmaxDeskm () 9φ2=R2vmaxDeskm
Production Methods
Published in H. Angus Macleod, Thin-Film Optical Filters, 2017
A slightly better arrangement that can sometimes be used is a spherical geometry where the substrates lie on the surface of a sphere. A point source will give uniform thickness of deposit on the inside surface of a sphere when the source is situated at the center. It can be shown that the directed surface source will similarly give uniform distribution when it is made part of the surface itself. In fact, it was the evenness of the coating within a sphere that led Knudsen [53] to first propose the cosine law for thin-film deposition. The method is often used in machines for simple antireflecting of components such as lenses where the uniformity need not be better than, say, 10% of the layer thickness at the center of the component. However, for precise work, this uniformity is still not adequate.
Numerical study on spark ignition of laminar lean premixed methane-air flames in counterflow configuration
Published in Combustion Science and Technology, 2023
Chunkan Yu, Detlev Markus, Robert Schießl, Ulrich Maas
Moreover, the variation of the with the for the planar geometry (blue line in Figure 12) is also the same as those in the cylindrical and spherical geometry in Maas and Warnatz (1988a). Namely the increases rapidly with smaller spark width, while it is nearly independent of the spark width at sufficient large spark width. This can be attributed to the fact that at small , one has a high-temperature gradient, leading to large heat dissipation and the decrease of the temperature in the ignition volume. Therefore, the should be sufficient large to compensate the heat dissipation. At large spark width, more mixture will be heated and the heat dissipation is less important. In the limit of no gradient of temperature, the total energy provided by spark is used to heat up the mixture as:
Transport Calculation of the Multiplicity Moments for Cylinders
Published in Nuclear Science and Engineering, 2022
Before turning to the quantitative work, there is one more point to consider. Similarly to the discussion in Ref. 7, the results will be compared with those of the point model. For a correct comparison of the results of the space-dependent transport theory results with those of the point model, the first collision probability must be the same for both models. To this order, the first collision probability is needed for each particular cylinder geometry. This was easy to obtain in the case of spherical geometry since a simple analytic expression exists for the first collision probability as a function of the radius of the sphere.12,13 For cylinders, there also exists an analytical expression,14 but it is rather complicated, and it contains singular integrals.
Treatment of Double Heterogeneity in the Resonance and Thermal Energy Regions in High-Temperature Reactors
Published in Nuclear Science and Engineering, 2018
Indrajeet Singh, S. B. Degweker, Anurag Gupta
The method for obtaining the Dancoff factor and the equivalent shell method for treating self-shielding effects in epithermal and thermal groups, respectively, have been incorporated in the BOXER3 code. The BOXER3 code,40 developed at Bhabha Atomic Research Centre during the 1980s as a three-dimensional (3-D) code for the analysis of a pressurized heavy water reactor (PHWR) supercell, was recently converted41 into a LWR assembly-level lattice and burnup code by coupling it to the WIMS-D library. The code primarily uses the collision probability method, but it also has an option to use the method of characteristics. An option for handling spherical geometry for the treatment of spherical geometry of pebble bed lattice cells has also been added in the code.