Do problem 22.19 in your text. Use ode45. Plot the results. Find the maximum tem

Question

Do problem 22.19 in your text. Use ode45. Plot the results. Find the maximum temperature and corresponding time.

                    A nonisothermal batch reactor can be described by the following equations:                 

                

                

                    where C is the concentration of the reactant and T is the temperature of the reactor. Initially, the reactor is at 16

Do problem 22.19 in your text. Use ode45. Plot the results. Find the maximum temperature and corresponding time. A nonisothermal batch reactor can be described by the following equations: where C is the concentration of the reactant and T is the temperature of the reactor. Initially, the reactor is at 16 A degree C and has a concentration of reactant C of 1.0 gmol/L. Find the concentration and temperature of the reactor as a function of time.

Explanation / Answer

create the following function script to define the equations. Save it.

% ---------------------------------------------------------------------------------

function dy = my_ode(t,y)

dy = zeros(2,1);

dy(1) = -exp(-10/(273+y(2))) * y(1);
dy(2) = 1000* exp(-10/(273+y(2))) * y(1) - 10*(y(2) - 20);

% -------------------------------------------------------------------------------------

now save the following script and run it.

% ------------------------------------------------------------------------------------

% initial conditions
T0 = 16;     % in centigrade
C0 = 1;      % in gmol/lit
% initial and final time
t0 = 0;
tf = 5;    % this is not given, we have to choose

% calling the solver ode45
[t y] = ode45(@my_ode,[t0 tf], [C0; T0]);

figure
plot(t,y(:,2))
title('Temp vs time')
xlabel('t')
ylabel('T')
figure
plot(t,y(:,1))
title('Conc vs time')
xlabel('t')
ylabel('C')

% --------------------------------------------------------------------------------------

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