Numerical methods for chemical engineers with matlab applications solution manual

Edited by: Vasilios N. Steps in Engineering Problem Solving Table 1. Designed for multi-level use, this text explores in detail the derivation of a variety of numerical methods and their application to the solution of engineering problems—with special attention to problems in chemical engineering. Includes bibliographical references and index. Our solutions Application, Gilat and Subramaniam, Wiley.

A copper sphere of diameter 5 cm is initially at temperature … These equations arise, for instance, in heat and mass transfer, dynamics of particles, vibrations of systems, electrical circuitry, and chemical kinetics.

Although analytical methods may be employed for the solution of some ODEs, numerical techniques are generally needed for most of the equations that arise in engineering applications. Muller and Theodore I. Here are the first few steps. The remainder of the computation would be implemented in a similar fashion and the results displayed in the plot below.

Here are the first few steps along with the analytical solution. A plot of all the values can be developed and indicates the same close agreement. The first program shown below is strictly developed to solve 2 equations. Here is the test of the solution of Prob. This is also illustrated by a state-space plot y versus x : 16 12 8 4 0 0 4 8 12 16 b RK4.

Here is the first step in detail. Although the pattern might appear random, an underlying pattern emerges when we look at the state- space plots. For example, here is the plot of y versus x. However, the state-space representation looks much more consistent. Thereafter, they abruptly begin to diverge.

The reason for this behavior is that these equations are highly sensitive to their initial conditions. After a number of steps, because they all employ different algorithms, they begin to diverge slightly. When the discrepancy becomes large enough which for these equations is not that much , the solution will tend to make a large jump. Thus, after awhile, the various solutions become uncorrelated.

Such solutions are said to be chaotic. It was this characteristic of these particular equations that led Lorenz to suggest that long-range weather forecasts might not be possible. The second step can then be implemented with the non-self-starting Heun method: Predictor: y 0. A plot of the entire solution is also displayed t y 0 0 0. The best way to do this is with LU decomposition since we will have to solve the system repeatedly.

For the present case, because its easier to display, we will use the matrix inverse to obtain the solution. Very tiny round off errors in the numerical solutions bring it to the fore. Hence all of the following solutions eventually diverge from the analytical solution. The plot shows the numerical solution bold line along with the exact solution fine line. First, because the displacement is small, the linear solution provides a decent approximation of the more physically realistic nonlinear case.

Second, the two solutions diverge as the computation progresses. After 10 iterations, the relative error falls to 0. First, the matrix can be put into the proper form for an eigenvalue analysis by bringing all terms to the left-hand-side of the equation.

First, the matrix can be put into the proper form by dividing each row by 0. After 9 iterations, the method does not converge on the highest eigenvalue. Rather, it converges on the second highest eigenvalue of 7. Related Papers. By Leger Fernandez. By Not Arian. By Suemy Villalobos. Metodos Numericos para Ingenieros Solucionario Chapra 5ed. By Jeaxs Deyfrus. By Majd Hammad. Download pdf. Log in with Facebook Log in with Google. Physical description xxv, p.

Series Prentice-Hall international series in the physical and chemical engineering sciences. Available online. Full view. Science Library Li and Ma. Stacks Library has: 1 v. More options. Find it at other libraries via WorldCat Limited preview. Contributor Mostoufi, Navid. Bibliography Includes bibliographical references and index. Programs on the website. Numerical Solution of Nonlinear Equations.