The example is constrained as shown in the following figure. Thermal conductivity (k) of the material is 5 W/m*K and the block is assumed to be infinitely long. Also, the density of the material is 920 kg/m^3 and the specific heat capacity (c) is 2.040 kJ/kg*K.
It is beneficial if the Thermal-Conduction tutorial is completed first to compare with this solution.
For this example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4 nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensional steady-state or transient thermal analysis.
At this point, the model should look like the following:
The window shown below will pop up. We will use the defaults, so click OK.
The following window will pop up.
A) Set Time at end of loadstep to 300 and Automatic time stepping to ON.
B) Set Number of substeps to 20, Max no. of substeps to 100, Min no. of substeps to 20.
C) Set the Frequency to Write every substep.
Click on the NonLinear tab at the top and fill it in as shown
D) Set Line search to ON .
E) Set the Maximum number of iterations to 100.
For a complete description of what these options do, refer to the help file. Basically, the time at the end of the load step is how long the transient analysis will run and the number of substeps defines how the load is broken up. By writing the data at every step, you can create animations over time and the other options help the problem converge quickly.
For thermal problems, constraints can be in the form of Temperature, Heat Flow, Convection, Heat Flux, Heat Generation, or Radiation. In this example, 2 sides of the block have fixed temperatures and the other two are insulated.
The following window will appear:
Orange triangles in the graphics window indicate the temperature contraints.
Fill in the IC window as follows to set the initial temperature of the material to 100 K:
Plot Temperature
Animate Results Over Time
Fill in the window as shown, with 8 contours, user specified, from 100 to 500.
Fill in the following window as shown (20 frames, 0 - 300 Time Range, Auto contour scaling OFF, DOF solution > TEMP)
You can see how the temperature rises over the area over time. The heat flows from the higher temperature to the lower temperature constraints as expected. Also, you can see how it reaches equilibrium when the time reaches approximately 200 seconds. Shown below are analytical and ANSYS generated temperature vs time curves for the center of the block. As can be seen, the curves are practically identical, thus the validity of the ANSYS simulation has been proven.
Analytical Solution
ANSYS Generated Solution
If it does not open automatically, select Main Menu > TimeHist Postpro > Variable Viewer
in the upper left corner of the window to add a variable.
in the Time History Variables window.
Note how this plot does not exactly match the plot shown above. This is because the solution has not completely converged. To cause the solution to converge, one of two things can be done: decrease the mesh size or increase the number of substeps used in the transient analysis. From experience, reducing the mesh size will do little in this case, as the mesh is adequate to capture the response. Instead, increasing the number of substeps from say 20 to 300, will cause the solution to converge. This will greatly increase the computational time required though, which is why only 20 substeps are used in this tutorial. Twenty substeps gives an adequate and quick approximation of the solution.
