Register

#### 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 R1 and outer radius R2 is considered. Temperatures T2 and T1 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:

R1 = 20 mm; R2 = 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.

Т1 = 20 °С; Т2 = 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, % x1 = 0 mm 20.00 20.00 0.00 x2 = 5 mm 26.44 26.43 0.04 x3 = 15 mm 36.15 36.14 0.03 x4 = 20 mm 40.00 40.00 0.00

Temperature distribution in the cross section of the ring, °С