The Cyclic Carburization Process by Bi-velocity Method

The paper presents numerical analysis of the cyclic external fluxes on diffusion process. It is shown, that the cycles characteristics strongly affects the concentration profiles and stress distribution in material. Calculations were performed using the bi-velocity method with the stress field factor. Moreover, the more general model describing the cyclic carburization process influenced by self stress was formulated. Numerical solutions were obtained assuming composition dependent diffusion coefficients. The results of simulation were compared with the experimental data. The model proposed in this paper may be applied to other diffusion controlled processes with the external flux of the diffusive component.

Generalized Ballistic-Diffusive Formulation and Hybrid SN-PN Solution of the Boltzmann Transport Equation for Phonons for Nonequilibrium Heat Conduction

A generalized form of the ballistic-diffusive equations (BDEs) for approximate solution of the Boltzmann Transport equation (BTE) for phonons is formulated. The formulation presented here is new and general in the sense that, unlike previously published formulations of the BDE, it does not require a priori knowledge of the specific heat capacity of the material. Furthermore, it does not introduce artifacts such as media and ballistic temperatures. As a consequence, the boundary conditions have clear physical meaning. In formulating the BDE, the phonon intensity is split into two components: ballistic and diffusive. The ballistic component is traditionally determined using a viewfactor formulation, while the diffusive component is solved by invoking spherical harmonics expansions. Use of the viewfactor approach for the ballistic component is prohibitive for complex large-scale geometries. Instead, in this work, the ballistic equation is solved using two different established methods that are appropriate for use in complex geometries, namely the discrete ordinates method (DOM) and the control angle discrete ordinates method (CADOM). Results of each method for solving the BDE are compared against benchmark Monte Carlo results, as well as solutions of the BTE using standalone DOM and CADOM for two different two-dimensional transient heat conduction problems at various Knudsen numbers. It is found that standalone CADOM (for BTE) and hybrid CADOM-P1 (for BDE) yield the best accuracy. The hybrid CADOM-P1 is found to be the best method in terms of computational efficiency.

Isopycnal Averaging at Constant Height. Part II: Relating to the Residual Streamfunction in Eulerian Space

In Part I, the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.

The diffusive component of intestinal glucose absorption is mediated by the glucose-induced recruitment of GLUT2 to the brush-border membrane

We have investigated the mechanism responsible for the diffusive component of intestinal glucose absorption, the major route by which glucose is absorbed. In perfused rat jejunum in vivo, absorption was strongly inhibited by phloretin, an inhibitor of GLUT2. The GLUT2 level at the brush-border membrane increased some 2-fold when the luminal glucose concentration was changed from 0 to 100mM. The phloretin-sensitive or diffusive component of absorption appeared superficially linear and consistent with simple diffusion, but was in fact carrier-mediated and co-operative (n = 1.6, [G1/2] = 56mM; where [G1/2] is the glucose concentration at half Vmax) because of the glucose-induced activation and recruitment of GLUT2 to the brush-border membrane. Diffusive transport by paracellular flow was negligible. The phloretin-insensitive, SGLT1-mediated, component of glucose absorption showed simple saturation kinetics with [G1/2] = 27mM: the activation of protein kinase C (PKC) βII, the isoenzyme of PKC that most probably controls GLUT2 trafficking [Helliwell, Richardson, Affleck and Kellett (2000) Biochem. J. 350, 149–154], also showed simple saturation kinetics, with [G1/2] = 21mM. We conclude that the principal route for glucose absorption is by GLUT2-mediated facilitated diffusion across the brush-border membrane, which is up to 3-fold greater than that by SGLT1; the magnitude of the diffusive component at any given glucose concentration correlates with the SGLT1-dependent activation of PKC βII. The implications of these findings for the assimilation of sugars immediately after a meal are discussed.