KMU-206 Questions for Midterm I

1. Write a MATLAB® script to solve the following Continuous Stirred Tank Reactor (CSTR) problem using Gauss-Siedel iteration. Five CSTR’s are connected in series. Find the exit concentration from each reactor.

Assumptions for the system are:

§

k_i

Steady state system

§ First-order irreversible reaction in liquid phase AàB

§ No change in volume or density of liquid

§ Rate of disappearance of solute in reactor given by: R_i=V_ik_iC_i mol/h

	Reactor 1	Reactor 2	Reactor 3	Reactor 4	Reactor 5
Vi (L)	100	150	75	40	80
ki (h^-1)	0.1	0.2	0.3	0.5	0.3

Hints: First set up the material (mass) balance equations for each of the reactors

Remember: input-output-disappearance by reaction-accumulation=0, where accumulation will be zero for a steady state system.

You will have 5 equations and 5 unknown variables C_i, where i=1:5

Make sure the system of linear equations is diagonally dominant.

2. Write a MATLAB® function to calculate the condition number of a symmetric square matrix of any size by means of Eigenvalues:

§ The power method should be used to calculate the Eigenvalues.

§ The script (function) should give an error message if the matrix is not square and/or is not symmetric.

§ The result of the built-in MATLAB® function “cond” should be displayed in addition to the results of the power method.

For example:

function [condPower,condMatlab]=NameofFunction(A,…)

…

…

condPower=…;

condMatlab=cond(A);

fprintf(‘Condition of matrix calculated using the Power method is %5.2g and using cond(A) is %5.2g \n’, condPower,condMatlab);