Assignment:
For this assignment, you will mainly reproduce the results obtained in Lab 3 for Parts 1, 2, 4, and
5 (we cannot easily control the relaxation parameter for the iteration so we will skip Part 3). You
should be able to get the same answers within the limit of machine precision. For Parts 1, 2, 4
and 5 include a PDE toolbox script file and for Part 3 include an automatically generated
SolidWorks Simulation Report. For all five parts write 2-3 sentences to describe if the results are
consistent with your expectations.
For your comparisons complete the following:
1. Using the PDE toolbox solve for the temperature distribution using the appropriate boundary
condition for the thermal symmetry line at x = L
x
/2 for the case given in Lab 3, Part 1. Include a
figure of the PDE toolbox solution. Also, include a figure plotting temperature at x = y = 0.4 m
versus total number of elements for both the PDE toolbox solution and FD method. On the figure
add the analytical solution from Lab 1. This figure is similar to the one from Lab 2, Part 2 except
for the addition of the FEM solution and using the number of elements for the x-axis. For the
PDE toolbox solution, use the tri2grid function referred to in the Post-Processing section to
find the temperature at the indicated location and use the t matrix referred to in the Mesh section
to determine the number of triangles (or elements). For both methods obtain data for at least 4
different meshes. Determine the number of elements required by both methods to get within
0.01% of the analytical solution.
2. Using the PDE toolbox solve for the temperature distribution for the fin from Lab 3, Part 2,
but only for the case of k = 50 W/m•K. Include a figure of the PDE toolbox solution. Include a
figure plotting temperature at x = y = 0.01 m versus total number of elements for both the PDE
toolbox solution and FD method. For both methods obtain data for at least 4 different meshes.
Determine the number of elements required by both methods to get agreement within 0.01% of
the converged solution of 181.09 ˚C. NOTE: h for the fin sides in the x-y plane is different than
for the front and back faces in the z-dimension, where h = 0 for wide fins, as noted on page 1.
3. Using SolidWorks Simulation solve for the two-dimensional temperature distribution for the
fin from Lab 3, Part 2, again only for the case of k = 50 W/m•K, and with a Global mesh size of
5 mm. Verify that the temperature at x = y = 0.01 m is 181.1 ˚C using either a probe or by
exporting the data into MATLAB for post-processing.
Next, solve for the three-dimensional temperature distribution for a fin width of w = L
y
= 0.20 m
in the z-direction. Use the same convection boundary condition from the two-dimensional case
for both ends (at z = 0 and z = w) as for the sides and tip. Once again, make sure to take
advantage of thermal symmetry for your simulation (HINT: your simulation fin width will be
w/2 in the z-direction with a convection boundary condition on one end and zero heat flux on the
other end for the thermal symmetry plane). Verify that the temperature at x = y = 0.01 m drops to
180.9 ˚C at the center (corresponding to the thermal symmetry plane) and 171.9 ˚C at the ends
due to 3D effects. Include figures of both the two and three-dimensional SolidWorks Simulation
solutions.
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