TEST CASE 11.2 TEMPERATURE DISTRIBUTION IN THE RING UNDER BOUNDARY CONDITIONS OF THE 1st KIND
Reference:
Analytical solution.
Problem description:
A steel ring with inner radius R_{1} and outer radius R_{2} is considered. Temperatures T_{2} and T_{1} are applied along the external and internal circuits, respectively. Find the temperature distribution over the width of the ring between points A (x = 0 mm) and B (x = 20 mm) with a step of 5 mm.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
R_{1} = 20 mm; R_{2} = 40 mm.
Material properties:
Thermal conductivity coefficient of steel: K = 45.4 W/(m·°С).
Boundary conditions:
Inner and outer contour of the ring: X = Y = Z = UX = UY = UZ = 0.
Loads:
Т_{1} = 20 °С; Т_{2} = 40 °С.
Model description:
The system is modeled using 160 eight-node solid elements (FE type is 36). The temperature field analysis is performed.
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
x_{1} = 0 mm |
20.00 |
20.00 |
0.00 |
x_{2} = 5 mm |
26.44 |
26.43 |
0.04 |
x_{3} = 15 mm |
36.15 |
36.14 |
0.03 |
x_{4} = 20 mm |
40.00 |
40.00 |
0.00 |
Temperature distribution in the cross section of the ring, °С