Nonlinear Solver
To make this problem non-linear the thermal conductivity will once again be made temperature
dependent. 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 Steady 2D Nonlinear, under Options select Use 2D Simplification, and
then click the green check mark. In the Study Type window insure that Extruded is selected. In
the Section Definition 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.
Similar to before to specify the PDE to solve, in the Simulation Tree right click on Steady 2D
Nonlinear and select Properties from the pop-up menu. In the Thermal window under the
Options tab insure that Steady state is selected. 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. Note that if the problem is highly non-linear you may need to set the
under-relaxation factor to a value much less than one to get convergence.
To change the material properties for your brick, in the Simulation Tree expand the Part folder
and right click on brick and select Apply/Edit Material from the pop-up menu. In the Material
window right click on the Custom Materials\ME 554 Materials folder and select New Material
from the pop-up menu. In the Material window change the name to “ceramic variable” and set
the density to 1 kg/m
3
and specific heat to 1 J/kg•K as before. Next, click the box where the value
for Thermal Conductivity is set and select Temperature Dependent from the pull-down menu.
This should switch you to the Tables & Curves tab. Use Equation (5) to set the thermal
conductivity at 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 ˚C. When finished click Apply and
Close. Note that if you switch back to Steady 2D the original properties for “ceramic” are still
being used and have not been changed in the database.
To set the same constant temperature boundary conditions on all the edges used previously,
select the Steady 2D tab from the bottom. In the Simulation Tree left click on Thermal Loads,
then while holding down the button drag the thermal loads icon on top of the Steady 2D
Nonlinear tab on the bottom and release the button. You should be switched into the new
simulation and the constant boundary temperature conditions should have been copied. To use
the same mesh, copy the mesh from Steady 2D over to your new simulation in a similar way.
Once again to solve the problem, in the Simulation Tree right click on Steady 2D Nonlinear and
select Run from the pop-up menu. Notice that it will take a little longer to solve and that the
solution will change significantly. Save your results to your file.
Transient Problems
We will now solve the same two-dimensional transient problem from the PDE Toolbox tutorial.
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 2D, under Options select Use 2D Simplification, and then click the green
check mark. In the Study Type window insure that Extruded is selected. In the Section Definition
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