Basic model equation

The basic model equations for a description of hydrodynamical flow are the Navier-Stokes equations, representing momentum conservation in the fluid... 

Temperature control in a stirred-tank heater is a common example (Fig. 2.9). We will come across it many times in later chapters. For now, we present the basic model equation, and use it as a review of transfer functions. 

The basic model equations are used to solve for the values of ... 

All conceptual models that have been applied to interpret dissolved noble gases in lakes and ground waters suppose that the measured concentrations are a sum of (some of) the components introduced in the previous section. In a general way, the basic model equation may be written as (compare Figs. 2, 3 and4) ... 

We noted that the sensitivity equations are linear. This property enables a computational approach based on adjoint operators (Koda and Seinfeld, 1982). Adjoint operators are important because they enable differential equations to be expressed as exact differentials, which can be integrated by direct quadrature. To see how adjoint operators can be used in sensitivity analysis, return to the basic model equation (4.A.3). Consider a perturbation in... 

Typical formulation of basic model equations will be summarized later. 

This relation for tangential forces with the correctness accepted for the boundary layer approximation (7) is represented. As boundary condition (30) represents a partial case of surface force r, discussed above in formulas (15-16), it is possible to use the basic model equations (16) for hydrodynamic part of the problem under consideration. We need now to discuss boundary value problem to obtain model equation for a. We follow here the recent investigations( Velarde et al., 2000). 

The analysis of packed-column operations has the same three basic goals we have seen in similar contexts, i.e., design, prediction of equipment performance, and, to a lesser extent, parameter estimation from experimental data. We may, for example, wish to calculate the height of a column required to achieve a certain degree of separation or level of pimfication. Or it may be required to assess the effects of changes in feed concentration or flow rate on column performance. In all these problems, the same basic model equations are applied and manipulated in appropriate ways to extract the desired information. 

The basic model equations for countercurrent continuous mass transfer are the differential mass balances over each phase, which had been derived in... 

The basic model equations for coimtercurrent continuous mass transfer are the differential mass balances over each phase, which were derived in Illustration 2.3, and the companion equilibrium relation (Equation 2.12f). They represent a complete model for tiie system and are reproduced below ... 

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