code for the transient heat transfer in a rectangular sheet , problem in formulation of for loop for simulation of time steps

I have written a code for the simulation of rectangular sheet and the problem statement is as follows:

1. need to simulate the temperature profile across the thickness of the rectangular sheet
2. the sheet is very long so i am taking differential element of same thickness but length is less
3. speed of the sheet is to be considered which is 10 m/min here
4. the total time for the transient simulation has to be 0 to 10 seconds
5. first the sheet travels in air for a distance of 1 mm(test distance) and convective heat transfer condition applies at both of the boundary
6. then the sheet is exposed to hot roller from end and the contact length is projected to be the length of sector found out by using circumference, wrap angle so in top it is exposed to air having same convective heat transfer condition and from the bottom, conduction is there so i have applied dirichlet boundary condition
7. then it again travels in air for a distance of 0.5 mm where the convective heat transfer will be applied at both of the edges

the problem is regarding the time simulation

i want that for each time increment, the material should move

for example at t=0 s, speed =1 m/s , dt = 1 s

distance = 1*1 = 1

t_old = t

t=t_old+dt = 1+1 = 2 s, speed = 1 m/s

distance = 2*1

so it should go on like from t = 0 to 10 and calculate the corresponding distance travelled

and then at every distance travelled , the model should perform and apply the boundary conditions to get the results

but the problem is in the loop, i cannot figure it out how to correct the loop or should i write double loop instead of one

because the results=solve(model,tlist) or solve(model) is defined only in these forms in matlab and tlist should take two arguements. Also, the dependence of time is there in the model so if time changes, the model should give different results but it cannot be seen explicitly

code for reference and matlab is not allowing to upload the geometry file as it is in STL format

% Define the geometry and mesh (assuming one layer)

model = createpde('thermal', 'transient');

importGeometry(model, '/home/jbagchi/OB_5.stl');

generateMesh(model);

% Define the thermal properties for the PVC body

thermal_conductivity1 = 0.15; % W/m-K

specific_heat1 = 1350; % J/kg-K

density1 = 1250; % kg/m^3

% Define the thermal properties for the steel roller

thermal_conductivity2 = 50; %W/m-K

convective_htc = 500; %W/m2-K

diameter = 0.4; %m

% Convert material speed from m/min to m/s

material_speed = 10 / 60; % m/min to m/s

% Define the element size of your mesh

element_size = 0.001; % Adjust based on your mesh element size

% Calculate the dwell time

dwell_time = element_size / material_speed;

%Calculate the contact length, roller temperature

roller_diameter = 0.4; %metre

contact_angle_deg = 180; %in degree

contact_length = (pi*roller_diameter*contact_angle_deg)/360; %in metre

contact_length_test = 0.001; %m

air_contact_length = 0.5 ;%m

% Define the time parameters

t_end = 10.0; % seconds

dt = min(0.01, dwell_time); % Adjust time step to be smaller or equal to dwell time

% Define the transient heat conduction PDE

thermalProperties(model, "ThermalConductivity", thermal_conductivity1, "MassDensity", density1, "SpecificHeat", specific_heat1);

% Define initial temperature condition

initialTemperature = 25.0; % °C

thermalIC(model, initialTemperature);

% Initialize distance traveled

distance_traveled = 0;

%Define timesteps

tlist = 0:dt:t_end;

% Loop through time steps

for t = 0:t_end

% Update distance traveled based on material speed

distance_traveled = distance_traveled + material_speed * dt; % m/min to m

% Apply boundary conditions based on distance traveled

if distance_traveled < contact_length_test

% Contact with air (no heat transfer)

thermalBC(model, "Edge", 2, "Temperature", 25);

thermalBC(model, "Edge", 4, "Temperature", 25);

elseif distance_traveled < (contact_length_test + contact_length)

% Contact with roller (conduction and convection)

thermalBC(model, "Edge", 2, "Temperature", 100);

thermalBC(model, "Edge", 4, "ConvectionCoefficient", 12, "AmbientTemperature", 25); % Adjust h as needed

else

% Contact with air again (no heat transfer)

thermalBC(model, "Edge", 2, "Temperature", 25);

thermalBC(model, "Edge", 4, "Temperature", 25);

end

end

% Solve for current time step

results = solve(model, tlist);

% Extract the temperature at the end of the time step

temperature = results.Temperature(:, end);

%Set the tolerance of the solver options.

model.SolverOptions.RelativeTolerance = 1.0e-3;

model.SolverOptions.AbsoluteTolerance = 1.0e-4;

% Extract and visualize the temperature field at specific time steps

time_steps_to_plot = [0, 2, 4, 6, 8, 10]; % Time steps to visualize

figure;

for i = 1:length(time_steps_to_plot)

subplot(2, 3, i);

pdeplot(model, 'XYData', results.Temperature(:, i), 'Contour', 'on');

title(['Time = ', num2str(time_steps_to_plot(i)), ' s']);

end

% Add a color bar to the last subplot

h = colorbar;

set(h, 'Position', [0.92, 0.12, 0.02, 0.76]);

could someone please help me with this!

thanks in advance!

[vidyesh]

Hello Joydeep,

I was not able to reproduce the issue at my end. It would be helpful to debug if you could provide the STL file and the expected result. You can upload the STL file by zipping it.

Answer 1

[vidyesh]

Hello Joydeep Bagchi,

I understand that you are facing an issue while creating a loop to solve your equation.

The current ‘for’ loop starts at 't = 0' and increments by 1 until 't' reaches the value of 't_end'. However, to get the desired results, it is necessary for 't' to increment by 'dt' for each iteration instead.

Please make the following change in line 53:

Replace

for t = 0:t_end

with

for t = 0:dt:t_end

Hope this helps resolve the issue.

[Joydeep Bagchi]

yes, I have tried but it doesn't give me the desired result

however, thankyou for the reply