Stationary heat propagation in the plate (ring section) under boundary conditions of the first kind (given temperature)
Verification of the LIRA-FEM software / Stationary heat propagation in the plate (ring section) under boundary conditions of the first kind (given temperature) / Société Fançajse des Mécaniciens, Commission Validation des progiciels de calcul de Structures, groupe de travail Thermique (2D et 3D) et thermoélasticité, Pan‘s, 1989.
Type of analysis: stationary thermal.
Source: Société Fançajse des Mécaniciens, Commission Validation des progiciels de calcul de Structures, groupe de travail Thermique (2D et 3D) et thermoélasticité, Pan‘s, 1989.
Geometry:
Inner radius: Ri=0.3m
Outer radius: Re=0.35m
Length: l=1m
Material characteristics:
Thermal conductivity coefficient: λ=1W/m0C
Boundary conditions:
- Cylinder inner radius: set temperature Ti=100°C.
- Outer radius of the cylinder: set temperature Te=20.0°C.
Calculation method used to obtain the reference solution:
where, ϕ – heat flux (1W = 1 J/s);
φ is the heat flux density (W/m2 = 1 J/(s m2).
CALCULATION RESULTS:
|
r(м) |
The desired value |
Analytical solution |
Calculation results (LIRA-SAPR) |
Accuracy,% |
|
0.30 |
Т (0С) |
100 |
100 |
0 |
|
0.31 |
Т (0С) |
82.98 |
82.98 |
0 |
|
0.32 |
Т (0С) |
66.51 |
66.51 |
0 |
|
0.33 |
Т (0С) |
50.54 |
50.54 |
0 |
|
0.34 |
Т (0С) |
35.04 |
35.04 |
0 |
|
0.35 |
Т (0С) |
20.00 |
20 |
0 |
| [0.3÷0.35] |
|
3260.8 | 3261.63 | 0.025 |
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