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Applied Mathematics And Modeling For Chemical Engineers, by Richard G. Rice, Duong D. Do

By Richard G. Rice, Duong D. Do

This moment version of the go-to reference combines the classical research and sleek purposes of utilized arithmetic for chemical engineers. The e-book introduces conventional options for fixing traditional differential equations (ODEs), including new fabric on approximate answer equipment comparable to perturbation ideas and user-friendly numerical strategies. it is also analytical the way to take care of very important periods of finite-difference equations. The final part discusses numerical resolution strategies and partial differential equations (PDEs). The reader will then be built to use arithmetic within the formula of difficulties in chemical engineering. just like the first version, there are lots of examples supplied as homework and labored examples

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V. Danckwerts. 83. Dissolution and Reaction of Gas in Liquids Oxygen dissolves into and reacts irreversibly with aqueous sodium sulfite solutions. If the gas solubilà ity is denoted as C A at the liquid–gas interface, derive the elementary differential equation to describe the steady-state composition profiles of oxygen in the liquid phase when the rate of oxygen reaction is represented by RA ¼ kC nA and the local oxygen diffusion flux is described by J A ¼ ÀDA dC A =dz, where DA is diffusivity and z is distance from the interface into the liquid.

2 CLASSIFICATION OF ODE The broad classification of equations with which engineers must contend is as follows: (a) Linear equations (b) Nonlinear equations Much is known about linear equations, and in principle all such equations can be solved by well-known methods. On the other hand, there exists no general solution method for nonlinear equations. However, a few special types are amenable to solution, as we show presently. We begin this chapter by studying first order ODE, classifying techniques based on certain properties.

N ð1:126Þ Like the Jacobi method, the Gauss–Seidel method requires diagonal dominance for the convergence of iterated solutions. 3 Successive Overrelaxation Method In many problems, the iterated solutions approach the exact solutions in a monotonic fashion. Therefore, it is useful in this case to speed up the convergence process by overrelaxing the iterated solutions. 13 MODEL HIERARCHY AND ITS IMPORTANCE IN ANALYSIS for the overrelaxation scheme is modified from the Gauss–Seidel equation ðkþ1Þ xi ðkÞ ¼ xi  þ w aii bi À iÀ1 X ðkþ1Þ aij xj j¼1 for i ¼ 1; 2; .

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