Shell Conduction

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Shell Conduction

The following example illustrates how to build and solve a model using the Heat Transfer in Thin Shells interface. This example is a 2D NAFEMS benchmark (Ref. 1), which was transformed to 3D.

Model Definition

Figure 1 describes the 2D benchmark example.

Figure 1: A 2D benchmark example for a thin conductive shell.

The 3D model bends this plate so that it becomes a quarter of a cylinder (Figure 2).

Figure 2: The 3D geometry based on the 2D model.

The temperature at point A in Figure 2 (291.40 K) is in agreement with that from the NAFEMS benchmark (Ref. 1). Figure 3 shows the temperature distribution.

Figure 3: The resulting temperature field of the 3D model.

1. J.A. Casey and G.B Simpson, “Two-dimensional Steady State,” Benchmark Tests for Thermal Analysis, NAFEMS, Test 10, p. 2.9, 1986.

Heat_Transfer_Module/Tutorials,_Thin_Structure/shell_conduction

Modeling Instructions

From the menu, choose .

In the window, click .

1

In the window, click .

2

In the tree, select .

3

4

5

In the tree, select .

6

Global Definitions

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
T_edge	373.15[K]	373.15 K	Edge temperature
T_ext	273.15[K]	273.15 K	External temperature
ht	750[W/(m^2*K)]	750 W/(m²·K)	Heat transfer coefficient

Cylinder 1 (cyl1)

1

In the toolbar, click .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. In the text field, type 2/pi.

5

In the text field, type 0.6.

6

Delete Entities 1 (del1)

1

In the window, right-click and choose .

2

On the object , select Boundaries 1–3 only.

3

In the window for , click .

4

Click the button in the toolbar.

1

In the toolbar, click and choose .

2

In the window for , locate the section.

3

In the text field, type (2/pi)*cos(pi*18/180).

4

In the text field, type (2/pi)*sin(pi*18/180).

This step embeds the point where you compare the calculated solution with the benchmark.

5

Single Layer Material 1 (slmat1)

1

In the toolbar, click .

2

In the window, under right-click and choose .

3

In the window for , locate the section.

4

From the list, choose .

5

Locate the section. From the list, choose .

Material 1 (mat1)

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	52	W/(m·K)	Basic
Density	rho	8800	kg/m³	Basic
Heat capacity at constant pressure	Cp	420	J/(kg·K)	Basic

Heat Transfer in Shells (htlsh)

1

In the toolbar, click and choose .

2

Select Edge 5 only.

3

In the window for , locate the section.

4

In the T0 text field, type T_edge.

1

In the toolbar, click and choose .

2

Select Edges 1, 2, and 4 only.

3

In the window for , locate the section.

4

Click the button.

5

In the h text field, type ht.

6

In the Text text field, type T_ext.

1

In the toolbar, click and choose .

2

Select Boundary 1 only.

3

In the window for , click .

In the toolbar, click .

Temperature (htlsh)

The default plot is the surface plot of the temperature and the arrow plot of the conductive heat flux; compare with Figure 3.

Follow the steps below to obtain the temperature at the benchmark verification point.

Point Evaluation 1

1

In the toolbar, click .

2

Select Point 3 only.

3

In the window for , click .

The result shown in the window below the window should be approximately 290.4 K.