TEST CASE 11.1 DISTRIBUTION OF ONE-DIMENSIONAL TEMPERATURE FIELD FOR FLAT STEEL WALL UNDER BOUNDARY CONDITIONS OF THE 1st AND 2nd KIND
Reference:
Analytical solution.
Problem description:
Consider a steel plate clamped at the edges. At one end, the plate is in contact with liquid, at the other end with gas. Find the temperatures at gas-plate interface (T_{gas-plate}) and liquid-plate interface (T_{liquid-plate}). Determine also the heat flow density.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
L = 1 m; H = 500 mm.
Material properties:
Thermal conductivity coefficient of steel: K = 45.4 W/(m·°С);
Heat transfer coefficient of the wall surface with liquid: α_{1} = 240 W/m^{2}·°С;
Heat transfer coefficient of the wall surface with gas: α_{2} = 12 W/m^{2}·°С.
Boundary conditions:
Top and bottom plate edge: X = Y = Z = UX = UY = UZ = 0.
Loads:
Liquid temperature: Т_{с1} = 100 °С;
Gas temperature: Т_{с2} = 20 °С.
Model description:
The system is modeled using 10 shell elements (FE type is 44) and 2 bar surface heat transfer elements (FE type is 168). The temperature field analysis is performed.
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
T_{liquid-plate}, °С |
96.62 |
96.62 |
0.00 |
T_{gas-plate}, °С |
87.67 |
87.67 |
0.00 |
q, W/m^{2} |
812.07 |
812.07 |
0.00 |
Temperature distribution across the plate width, °C
Heat flow density, W/m^{2}