Stationary heat propagation in an L-shaped plate under boundary conditions of the first kind (given temperature)
Verification of the LIRA-FEM software / Stationary heat propagation in an L-shaped plate under boundary conditions of the first kind (given temperature) / Analytical solution: G.T. Symm-, National Physical Laboratory Division of Numerical Analysis and Computing, Treatment of singularities in solution of Laplace's equation by an integral equation method, NPL Report NAC 31, jan. 1973.
Type of analysis: stationary thermal.
Analytical solution: G.T. Symm-, National Physical Laboratory Division of Numerical Analysis and Computing, Treatment of singularities in solution of Laplace's equation by an integral equation method, NPL Report NAC 31, jan. 1973.
Material characteristics:
Thermal conductivity coefficient: λ=1W/m0C
Boundary conditions:
For segment AF: T=10°C.
For segment DE: Т= 0°С
CALCULATION RESULTS:
|
х(м) |
z(м) |
The desired value |
Analytical solution |
Calculation results (LIRA-SAPR) |
Accuracy, % |
|
0 |
0 |
Т (0С) |
10 |
10 |
0 |
|
0 |
0.2 |
Т (0С) |
10 |
10 |
0 |
|
0 |
0.4 |
Т (0С) |
10 |
10 |
0 |
|
0 |
0.6 |
Т (0С) |
10 |
10 |
0 |
|
0 |
0.8 |
Т (0С) |
10 |
10 |
0 |
|
0.2 |
0 |
Т (0С) |
9.316 |
9.294 |
0.236 |
|
0.2 |
0.2 |
Т (0С) |
9.001 |
9.015 |
0.156 |
|
0.2 |
0.4 |
Т (0С) |
8.514 |
8.505 |
0.106 |
|
0.2 |
0.6 |
Т (0С) |
8.018 |
8.025 |
0.087 |
|
0.2 |
0.8 |
Т (0С) |
7.869 |
7.861 |
0.102 |
|
0.4 |
0 |
Т (0С) |
9.009 |
8.996 |
0.144 |
|
0.4 |
0.2 |
Т (0С) |
8.640 |
8.661 |
0.243 |
|
0.4 |
0.4 |
Т (0С) |
6.667 |
6.667 |
0.000 |
|
0.4 |
0.6 |
Т (0С) |
5.680 |
5.669 |
0.194 |
|
0.4 |
0.8 |
Т (0С) |
5.495 |
5.502 |
0.127 |
|
0.6 |
0.4 |
Т (0С) |
2.972 |
2.99 |
0.606 |
|
0.6 |
0.6 |
Т (0С) |
2.881 |
2.959 |
2.707 |
|
0.6 |
0.8 |
Т (0С) |
2.816 |
2.845 |
1.030 |
|
0.8 |
0.4 |
Т (0С) |
0 |
0 |
0 |
|
0.8 |
0.6 |
Т (0С) |
0 |
0 |
0 |
|
0.8 |
0.8 |
Т (0С) |
0 |
0 |
0 |
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