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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 (Tgas-plate) and liquid-plate interface (Tliquid-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: α1 = 240 W/m2·°С;

Heat transfer coefficient of the wall surface with gas: α2 = 12 W/m2·°С.

 

Boundary conditions:

Top and bottom plate edge: X = Y = Z = UX = UY = UZ = 0.

 

Loads:

Liquid temperature: Тс1 = 100 °С;

Gas temperature: Тс2 = 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, %

Tliquid-plate, °С

96.62

96.62

0.00

Tgas-plate, °С

87.67

87.67

0.00

q, W/m2

812.07

812.07

0.00

 

Temperature distribution across the plate width, °C

 

Heat flow density, W/m2