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Nonisothermal diffusion

A diffusion measurement at the temperature To is made by annealing a diffusion couple comprised of two semi-infinite bars. However, there is a complication after the completion of the isothermal anneal, carried out at To for the time to, the specimen must be cooled to room temperature at a finite rate. During this cooling period, a small amount of additional nonisothermal diffusion occurs. If an expression can be found for the amount of time, At, required to produce this same additional increment of diffusion at the constant temperature To, the specimen could be analyzed very simply at the end of the experiment by assuming that it was annealed at To for the time to + At. Assume that D = D0 exp —E/(kT)] and that the temperature during the cooling period is... [Pg.93]

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. [Pg.592]

Graphical interpretation of the factors influencing the critical distance from air supply to the linear obstacle with a height for air supply through a slot diffuser with height Ioq and for air supply through a round nozzle with outlet diameter are presented in Fig. 7.43. Nonisothermal flow has an influence on... [Pg.483]

I learned about chemical reactors at the knees of Rutherford Aris and Neal Amundson, when, as a surface chemist, I taught recitation sections and then lectures in the Reaction Engineering undergraduate course at Minnesota. The text was Aris Elementary Chemical Reaction Analysis, a book that was obviously elegant but at first did not seem at all elementary. It described porous pellet diffusion effects in chemical reactors and the intricacies of nonisothermal reactors in a very logical way, but to many students it seemed to be an exercise in applied mathematics with dimensionless variables rather than a description of chemical reactors. [Pg.549]

The special form of second-order equation in which the right-hand side is a function only of the dependent variable also turns up in the theory of diffusion and reaction in a slablike particle. Corresponding to equations (123-125) for the sphere, we would have, thanks to the reduction described in Chapter 2 and the example of a first-order nonisothermal reaction given by Eq. (129),... [Pg.51]

Most of the models assume that neutral-species transport can be represented with either a well-mixed model or a plug flow model. The major drawback to these assumptions is that important inelastic rate processes such as molecular dissociation are usually localized in space in the reactor and are often fast compared with rates of diffusion or convection. As a result, the spatial variation of fluid flow in the reactor must be accounted for. This variation introduces a major complication in the model, because the solution of the nonisothermal Navier-Stokes equations in multidimensional geometries is expensive and difficult. [Pg.414]

It should be understood that this rate expression may in fact represent a set of diffusion and mass transfer equations with their associated boundary conditions, rather than a simple explicit expression. In addition one may write a differential heat balance for a column element, which has the same general form as Eq. (17), and a heat balance for heat transfer between particle and fluid. In a nonisothermal system the heat and mass balance equations are therefore coupled through the temperature dependence of the rate of adsorption and the adsorption equilibrium, as expressed in Eq. (18). [Pg.39]

Since thermal diffusion is a nonisothermal process and thus cannot be considered as driven by chemical potential gradients, we must go directly to the solute flux equations to understand the capacity of thermal diffusion for separation. The basic law expressing the flux density caused by thermal diffusion [46-48] is... [Pg.174]

Assuming a steady state, for first-order reaction-diffusion system A -> B under nonisothermal catalyst pellet conditions, the mass and energy balances are... [Pg.456]


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See also in sourсe #XX -- [ Pg.212 , Pg.213 , Pg.214 , Pg.215 ]




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