Boundary and initial conditions for

The absorption is assumed to occur into elements of liquid moving around the bubble from front to rear in accordance with the penetration theory (H13). These elements maintain their identity for a distance into the fluid greater than the effective penetration of dissolving gas during the time required for this journey. The differential equation and initial and boundary conditions for the rate of absorption are then... 

Figure 2. Description of the initial and boundary conditions for the hydrogen diffusion problem in the pipeline. The parameter / denotes hydrogen flux and C,(P) is normal interstitial lattice site hydrogen concentration at the inner wall-surface of the pipeline in equilibrium with the hydrogen gas pressure P as it increases to 15 MPa in 1 sec. At time zero, the material is hydrogen free,...

Figure 5. Description of (a) boundary conditions for the elastoplastic problem and (b) initial and boundary conditions for the hydrogen diffusion problem at the blunting crack tip in the MBL formulation. The parameter bCl denotes the crack tip opening displacement in the absence of hydrogen. The parameter C, (P) denotes NILS hydrogen concentration on the crack face in equilibrium with hydrogen gas pressure P. and / is hydrogen flux.

Consider a case where the initial and boundary conditions for a diffusion couple are... 

The following example illustrates the method. Consider a one-dimensional diffusion problem with the initial and boundary conditions for the domain 0 < x < L ... 

The initial and boundary conditions for the fluid and solid phases are given for k = 1, N by ... 

To complete the mathematical description it is necessary to state initial and boundary conditions. For illustration purposes, it will be assumed that the initial temperature (T0) is uniform in the mold, the wall temperature... 

The understanding of more detail and fine features of BSGC requires much more data of direct current observations and higher quality and spatiotempo-ral resolution of the initial and boundary conditions for numerical models. 

The appropriate initial and boundary conditions for the transport of solute-humic substances in the two-dimensional, homogeneous, water saturated formation considered here are the following ... 

Now, the averaged hyperbolic model, Eq. (52), defines a characteristic initial-value problem (Cauchy problem). To complete the model, we need to specify Cm only along the characteristic curves x = 0 and f — 0. Thus, the initial and boundary conditions for the averaged model are obtained by taking the mixing-cup averages of Eqs. (31) and (32) ... 

Initial and boundary conditions for the absorption of refrigerant vapor by solution droplets are as follows ... 

Initial and Boundary Conditions for the Diffusion Process Stimulated by a Constant Current (or Flux)... 

Fig. 3. Initial and boundary conditions for two-dimensional simulations. Top Simulation begun with a 4-layer flyer plate. Bottom Simulation begun with a steadily moving piston.

A spherical metal ball of radius r<, is heated in an oven to a temperature of SOO C throughout and is then taken out of the oven and allowed to cool in ambient air at = 2T C, as shown in Fig. 2-38. The thermal conductivity of the ball material isk = 14.4 W/m K, and the average convection heat transfer coefficient on the outer surface of the ball is evaluated to be h = 25 W/m K. The emissivity of the outer surface of the ball is e = 0.6, and the average temperature of the surrounding surfaces is 7, = 290 K. Assuming ] the ball is cooled uniformly from the entire outer surface, express the initial and boundary conditions for the cooling process of Ihe ball. 

The reactions considered were simultaneous CO oxidation and NO reduction, using a kinetic model for rhodium catalyst [25]. Initial and boundary conditions for the concentrations of reactants were the same as given by Lie et al., NO oscillating in phase with oxygen. Kinetic and reactor parameters used were mentioned in Section 8.IV.A. 

Fig. 2.27 Diagram explaining the initial and boundary conditions for the cooling of a plate of thickness 2R, a long cylinder and a sphere, each of radius R...

Mathematically, all models form a system of (partial) differential and algebraic equations. For the solution of those systems initial and boundary conditions for the chromatographic column are necessary. The initial conditions for the concentration and the loading specify their values at time t = 0. Generally, zero values are assumed ... 

At the begirming of the second period (time t + Jf), the feed and the draw-off points are switched simultaneously to their next positions in the direction of the liquid phase flow. The evolution of the concentration profiles during this period depends on the new initial and boundary conditions for each column. These conditions are illustrated in Figure 17.4a, which shows the concentration profiles just after the columns have been switched (i.e., at the very beginning of the third period). In the following we describe qualitatively the phenomenon and then we derive the equations giving the new positions of the shocks (see later, Eqs. 17.20a to 17.20e) and the heights of the new concentration plateaus. 

This equation is to be solved under the appropriate initial and boundary conditions. For the simple case of infinite solution volume, where the aqueous-phase concentration does not change because of sorption or desorption, fractional attainment of equilibrium, F, is given by ... 

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