MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1 Manuale Utente Pagina 14

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window for the Section Plane select the front face of the brick (that is normal to the z-axis), set
the Section depth to 0.10 m, and then click the green check mark.
To specify the PDE to solve, in the Simulation Tree right click on Transient 2D and select
Properties from the pop-up menu. In the Thermal window under the Options tab select Transient
and verify that the Total time is set to 1 sec and the Time increment is set to 0.1 sec. Click the
Advanced Options button and set the Convergence tolerance to 0.0001%, insure the Under-
relaxation factor for the iteration is set to Automatic, and click OK. Copy the constant
temperature boundary conditions and mesh from the Steady 2D tab using the same method that
was used above for the Nonlinear Solver section.
In addition to the fixed temperature boundary conditions we now need to add an initial condition
for the temperature for the entire domain. To do this in the Simulation Tree right click on
Thermal Loads and select Temperature from the pop-up menu. In the Type window select Initial
temperature and for the Faces, Edges or Vertices select the front face in the drawing window. In
the Temperature window set the temperature to 0 ˚C and then click the green check mark.
To solve the problem, in the Simulation Tree right click on Transient 2D and select Run from the
pop-up menu. Notice that it will once again take a little longer to solve. When finished a contour
plot of temperature at the final time will be displayed in the drawing window. To see the solution
at a different time, in the Simulation Tree in the Results folder right click on Thermal1 and select
Edit Definition from the pop-up menu. In the Plot Step window enter either a new Time or Plot
step for the plot and click the green check mark.
To extract data at several locations, in the Simulation Tree in the Results folder right click on
Thermal1 and select Show and then Probe from the pop-up menu. In the Options window select
At location and click on the front face in five location starting near the top in middle and going
downwards. To remove a probe at a particular location, in the Results window right click on a
node and select Delete from the pull-down menu. To save these probe locations, in the Report
Options window click the Save as Sensor button. In the Options window if you now select From
sensors you should see that your sensors have been saved as Workflow Sensitive1. To plot out
your data as a function of time, in the Report Options window click the Response button. When
finished verifying the data makes sense, close the Response Graph window and click the green
check mark. Note that in the Feature Manager Design Tree in the Sensors folder you will now
find Workflow Sensitive1 that can be edited from this location. Save your results to your file.
Three-Dimensional Problems
We will now solve the same two-dimensional transient problem from above, but use the three-
dimensional brick geometry. To create a new simulation tab for this case, from the toolbar at the
top of the window use the Simulation pull-down menu to select Study. In the Type window select
the Thermal button, for Name enter Transient 3D, under Options insure that Use 2D
Simplification is NOT selected, and then click the green check mark. In the drawing window you
should now see the 3D brick geometry.
To specify the PDE to solve, in the Simulation Tree right click on Transient 3D and select
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