Shell Conduction

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Shell Conduction

The following example illustrates how to build and solve a model using the Heat Transfer in 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

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

.

Material 1 (mat1)

1

In the toolbar, 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
Thickness	lth	0.01[m]	m	Shell

Heat Transfer in Shells (htlsh)

1

In the window, under right-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

From the list, choose .

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. 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 291.4 K.