Models boundary conditions

In the formulation of the boundary conditions, it is presumed that there is no dispersion in the feed line and that the entering fluid is uniform in temperature and composition. In addition to the above boundary conditions, it is also necessary to formulate appropriate equations to express the energy transfer constraints imposed on the system (e.g., adiabatic, isothermal, or nonisothermal-nonadiabatic operation). For the one-dimensional models, boundary conditions 12.7.34 and 12.7.35 hold for all R, and not just at R = 0. 

To describe the fully compactified model, with Euclidean coordinates, say Xi, restricted to segments of length Li (i = 1,2,. D) and the field tp(x) satisfying anti-periodic (bag model) boundary conditions, the Feynman rules should be modified following the Matsubara prescription... 

Boundary condition 1 occurs because the pulse is instantaneously mixed only into the primary reactor in the model. Boundary condition 2 indicates that, as the dead zone disappears, the reactor becomes a standard complete mix reactor. Applying boundary condition 1 gives... 

When the stack is modeled, boundary conditions are set only for the boundary cells in the case of the other cells, the nodes at the interconnections are linked together when two cells are connected in series. Figure 7.24 also shows the connections between the cells in a stack. 

To solve the model, boundary conditions are needed atX = 1, on the membrane side. If rf and cR° at X = 1 are given, we solve the model by using the boundary conditions... 

Penetration theory equations for the mass transfer model (boundary conditions as usual in penetration theory [6 ]). ... 

Mathematical modelling is the important stage at designing HHP. At a successful choice of model of processes in HHP and at approach of modelled boundary conditions real conditions developers have an effective tool for fast check of constructive decisions. 

As mentioned in Section 6.2.2, with general rate models, boundary conditions for the adsorbent phase are necessary in addition to the conditions at the column inlet and outlet (Section 6.2.7). The choice of appropriate boundary conditions is mathematically subtle and often a cause for discussion in the literature. The following is restricted to the form of the boundary condition derived by Ma et al. (1996) for a complete general rate model. 

Defining the model by specifying physical models, boundary conditions, and initial conditions... 

Besides selecting a model, boundary conditions have to be applied, and the preferred one will depend upon the properties of interest. The most common ones are a spherical cell containing one macroion, a cylindrical cell containing two macroions, and a cubic box with periodic boundary conditions. The first is most frequently used to examine the distribution of small ions near a macroion and approximate thermodynamic results, the second to determine the force between two macroions mediated by the small ions, and the last boundary condition provides full structural and thermodynamic properties of a bulk system. 

Model boundary conditions quiet (viscous) boundary is set to the bottom, and free-field boundaries are utilized on four lateral sides of the slope model. 

Strengthening Techniques Code-Deficient Steel Buildings, Fig. 12 End plate model boundary conditions (Shen... 

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