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: 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: 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:

Temperature distribution across the plate width, °C

Heat flow density, W/m²