Conduction & Convection
Example 3
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Problem Description
A mild steel fin, 300mm long x 25mm wide x 1.5mm thick, is attached to an object held at a constant 100°C. The temperature at the end of the fin is measured as a constant 20°C. Convection occurs at a rate of 10 w/m^2-k. Find the steady-state temperature distribution.
The fin is created as a flat plate and assigned a thickness of 1.5mm mild steel (k=52.019 W/m-K). The meshed fin is 100 elements long and 7 elements wide. Again, to compensate for the fact that boundary conditions are applied element centroids, the fin is made 303.03mm long. Boundary conditions were applied by holding strips of elements at the two ends at constant temperatures.
Boundary Conditions
-
The at x=0 the end is a constant 100°C.
-
The fin end (x=300mm) is a constant 20°C.
-
The ambient temperature TINFINITY is 20°C.
Assumptions
-
Emissivity is set to zero (no radiation).
-
Steady state and one-dimensional.
-
Convection at 10 w/m^2 occurs only on the top and bottom surfaces.
Objective
Predict the steady-state temperature gradient along the fin for several different fin thicknesses.
Analytical Solution
Shown is the 1.5mm solution:
TAI Results
The solution was converged its maximum in each case. The theoretical and TAI results are very closely matched. Observable differences are most likely the result of numerical error.
|
Element # |
X Distance |
Thickness |
Analytical |
RadTherm 5.0 |
WinTherm 5.0 |
MuSES 5.0 |
|
541 |
97.0mm |
1.5mm |
36.9 |
37.3 |
37.3 |
37.3 |
|
229 |
215.2mm |
1.5mm |
22.4 |
22.4 |
22.4 |
22.4 |
|
541 |
97.0mm |
5mm |
53.4 |
53.4 |
53.8 |
53.8 |
|
229 |
215.2mm |
5mm |
29.4 |
29.4 |
29.4 |
29.4 |
|
541 |
97.0mm |
100mm |
72.7 |
72.7 |
72.7 |
72.7 |
|
229 |
215.2mm |
100mm |
41.5 |
41.3 |
41.3 |
41.3 |
Note: Test run by RES 3-2000 using versions 5.0.0.
Learn More about Validation
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