I need to solve the series for two different cases D1 and D2 specified

The original question:

(C(x,t) -C0 )/(Cb- C0) = 1- 4/pi ∑ (-1)^n /(2*n +1) exp [ -(2*n+1)^2 *(pi)^2 *D*t/4*l^2] * cos((2*n+1)*pi*x)/2*l) . Plot C/Cb on the same plot for the two cases ; D1= 6.0*10^-7 , D2= 3.0*10^-6, C0=2, Cb=0 , l=3 mm . Also label the curve and use minute for time. Solve this problem in matlab .

Matlab code

% Given parameters

D1 = 6.0e-7; % Diffusion coefficient for Case 1

D2 = 3.0e-6; % Diffusion coefficient for Case 2

C0 = 2; % Initial concentration

Cb = 0; % Boundary concentration

l = 0.003; % Length scale (in meters)

% Define x and t (adjust as needed)

x = linspace(0, l, 100); % Spatial domain (from 0 to l)

t_minutes = linspace(0, 60, 100); % Time domain (in minutes)

% Initialize matrices to store results

R1 = zeros(length(x), length(t_minutes));

R2 = zeros(length(x), length(t_minutes));

% Calculate R(x,t) for both cases

for i = 1:length(x)

for j = 1:length(t_minutes)

R1(i, j) = (C(x(i), t_minutes(j), D1, C0, Cb, l) - C0) / (Cb - C0);

R2(i, j) = (C(x(i), t_minutes(j), D2, C0, Cb, l) - C0) / (Cb - C0);

end

end

% Plot R(x,t) for both cases

figure;

surf(t_minutes, x, R1, 'DisplayName', 'Case 1');

hold on;

surf(t_minutes, x, R2, 'DisplayName', 'Case 2');

xlabel('Time (minutes)');

ylabel('Position (meters)');

zlabel('C(x,t) / C_b');

title('Concentration Ratio: C(x,t) / C_b');

legend;

grid on;

% Concentration function (you can adjust this based on your specific problem)

function C_val = C(x, t, D, C0, Cb, l)

C_val = 1 - (4/pi) * sum((-1).^((0:1000)) ./ (2*(0:1000) + 1) ...

.* exp(-(2*(0:1000) + 1).^2 * pi^2 * D * t / (4*l^2)) ...

.* cos((2*(0:1000) + 1) * pi * x / (2*l)));

end

The code yields weird results. Need some help correcting the code . Thanks

[Torsten]

Plot C/Cb on the same plot for the two cases ; D1= 6.0*10^-7 , D2= 3.0*10^-6, C0=2, Cb=0 , l=3 mm .

You cannot plot C/Cb since Cb = 0. Or did you copy your assignment incorrectly ?