Robin condition

A different set of boundary conditions is that for which the concentration and temperature excess at the edge of the slab are determined by the two fluxes from the pellet. Thus, these Robin conditions have the form... 

The constants g, r and d can take on various values to express any given boundary condition. Thus, if we set g = d = 0, we are left with Co = 0, the Dirichlet (Cottrell) condition if we set r 0 and d 1, we have the Neumann or controlled current condition and setting g = 0 gives us Robin conditions. The constant r expresses the heterogeneous rate constant (this formula only considers a single species, so an irreversible reaction is implied). 

At boundary nodes where the variable values are given by Dirichlet conditions, no model equations are solved. When the boundary condition involve derivatives as defined by Neumann conditions, the boundary condition must be discretized to provide the required equation. The governing equation is thus solved on internal points only, not on the boundaries. Mixed or Robin conditions can also be used. These conditions consist of linear combinations of the variable value and its gradient at the boundary. A common problem does arise when higher order approximations of the derivatives are used at... 

Flux defined in terms of a mass transfer coefficient, k, with an external, known concentration, cq, or a heat transfer coefficient, h, with an external, known temperature, To (called a Robin condition or boundary condition of the third kind) ... 

Robin Condition. The Robin solution given above yields expressions for the instantaneous surface temperature and the instantaneous surface heat flux. They are as follows ... 

The previous expression for the Robin condition can be calculated by the following rational approximation with a maximum error of less than 1.2 percent ... 

P P R point contact constant pressure condition Robin condition solution... 

A study was performed to ascertain the effect of matrix truncation on calculated values of the catalyst effectiveness for both the Dirichlet and Robin conditions. The results are summarized in Table II for a Thiele modulus of 1.0, an external contacting efficiency of 0.5 and for matrices of size N x N. The answers seem to be accurate on the first two decimal places and the results for Bljj = 10 and Bl = computed from two different expressions agree well. 

In the finite element solution of the energy equation it is sometimes necessary to impose heat transfer across a section of the domain wall as a boundary condition in the process model. This type of convection (Robins) boundary condition is given as... 

When round robin tests were performed to test the reproducibility of these standard procedures, large coefficients of variation between laboratories were obtained for tin-free paints (78-80% and 24-32% for the ISO and ASTM methods respectively Haslbeck and Holm, 2005). These discrepancies have multiple sources such as the analytical method (Haslbeck and Holm (2005) report 4-54% deviations when different laboratories measuring samples of known concentration), the sea water conditions both in the holding tank and the measuring tank (Haslbeck and Holm, 2005), the sample preparation for analysis... 

Several laboratory studies have contributed to our understanding of turbulent chemical plumes and the effects of various flow configurations. Fackrell and Robins [25] released an isokinetic neutrally buoyant plume in a wind tunnel at elevated and bed-level locations. Bara et al. [26], Yee et al. [27], Crimaldi and Koseff [28], and Crimaldi et al. [29] studied plumes released in water channels from bed-level and elevated positions. Airborne plumes in atmospheric boundary layers also have been studied in the field by Murlis and Jones [30], Jones [31], Murlis [32], Hanna and Insley [33], Mylne [34, 35], and Yee et al. [36, 37], In addition, aqueous plumes in coastal environments have been studied by Stacey et al. [38] and Fong and Stacey [39], The combined information of these and other studies reveals that the plume structure is influenced by several factors including the bulk velocity, fluid environment, release conditions, bed conditions, flow meander, and surface waves. 

Fig. 9.13. Stationary-state loci for the non-isothermal catalyst pellet (a) three stationary-state branches (b) unique response (c) five stationary-state branches, appropriate to Robin boundary conditions with a < 1.

Stationary-state solutions Robin boundary conditions... 

The idea that light drives the formation of oxidants and reductants was first advanced by C. B. van Niel in the 1920s. It was strengthened through experiments done by Robin Hill in 1939. Hill discovered that isolated chloro-plasts evolved 02 if illuminated in the presence of an added electron acceptor such as ferricyanide, Fe(CN)63-. The electron acceptor became reduced in the process. Because no fixation of C02 occurred under these conditions, this experiment demonstrated that the photochemical reactions of photosynthesis can be separated from the reactions that involve C02 fixation. 

Although calcium arsenates may readily precipitate in acid mine drainage and form in flue gas treatment systems, Robins and Tozawa (1982) warn that the compounds may not have long-term stability, which could lead to disposal and environmental problems. Besides dissolving under acidic conditions, the presence of carbonate, bicarbonate, or CO2 may decompose calcium arsenates. When calcium arsenates react with CO2, calcium carbonate forms and the arsenic could be released into the environment (Ghimire et al., 2003, 4946 Jing, Korfiatis and Meng, 2003, 5055-5056). 

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