By Norman W. Loney
Targeting the appliance of arithmetic to chemical engineering, utilized Mathematical tools for Chemical Engineers, moment version addresses the setup and verification of mathematical types utilizing experimental or different independently derived data.
An accelerated and up-to-date model of its well-respected predecessor, this ebook makes use of labored examples to demonstrate numerous mathematical equipment which are crucial in effectively fixing approach engineering difficulties. The booklet first offers an creation to differential equations which are universal to chemical engineering, via examples of first-order and linear second-order usual differential equations (ODEs). Later chapters research Sturm–Liouville difficulties, Fourier sequence, integrals, linear partial differential equations (PDEs), and normal perturbation. the writer additionally specializes in examples of PDE purposes as they relate to some of the conservation legislation practiced in chemical engineering. The e-book concludes with discussions of dimensional research and the scaling of boundary worth difficulties and provides chosen numerical equipment and on hand software program packages.
New to the second one Edition
· renowned ways to version improvement: shell stability and conservation legislations balance
· One-dimensional rod version and a planar version of warmth conduction in a single direction
· platforms of first-order ODEs
· Numerical approach to strains, utilizing MATLAB® and Mathematica the place appropriate
This priceless source offers an important creation to mathematical equipment for engineering and is helping in picking out an appropriate software program package deal for computer-based algebraic purposes.
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Additional info for Applied Mathematical Methods for Chemical Engineers, Second Edition
Then CA0 – CB(t) is the concentration of A at time t. Determine CB(t) if CB(0) ¼ CB0. 2006 6:31pm Applied Mathematical Methods for Chemical Engineers dCB (t) ¼ kCB (t)(CA0 À CB (t)) dt (2:38) subject to CB (0) ¼ CB0 where k is the reaction rate coefficient. 34, n ¼ 2. 39 to give dt ÀvÀ2 dv ÀkvÀ1 CA0 ¼ ÀkvÀ2 dt Then multiplying both sides of the resulting equation by Àv2 gives dv þ kCA0 v ¼ k dt ð m(t) ¼ exp kCA0 dt Then [v exp (kCA0 t )]0 ¼ k exp (kCA0 t) Integrating both sides with respect to t gives v exp (kCA0 t) ¼ where m1 is an arbitrary constant.
32. 29. 30, determines the integration constant c uniquely. Sometimes nonlinear equations can be reduced to linear ones by a substitution. One example where such a substitution is helpful is in solving the Bernoulli equations. 34 to a linear equation. 36 gives dx 1 dv 2 1 À vÀ3=2 þ vÀ1=2 ¼ 2 vÀ3=2 2 dx x x following simplification, the differential equation becomes dv 4 2 À v¼À 2 dx x x (2:37) a linear first-order differential equation with new dependent variable v(x). 1. A more engineering-type example is demonstrated below.
Consider a two-stage solvent extraction of the benzoic acid with the previously made assumptions and yi ¼ mxi , i ¼ 1,2 where i denotes the stage . a. 1. b. Use your table to write the time-dependent mass balance of acid for each stage. c. Find the steady state organic (x2) and aqueous (y1) acid concentration profiles. d. If E is the proportion of acid extracted and a ¼ R/ms, what is the relationship between E and a for the steady state process? R, X2 R R, X1 I S, y1 II S, 0 S, y2 3. Give suitable initial conditions for the two first-order differential equations and outline a solution.
Applied Mathematical Methods for Chemical Engineers, Second Edition by Norman W. Loney