1.3.38 Simple load tests for thermal-electrical elements

Product: ABAQUS/Standard

Elements tested

DC1D2E DC1D3E

DC2D3E DC2D4E DC2D6E DC2D8E

DCAX3E DCAX4E DCAX6E DCAX8E

DC3D4E DC3D6E DC3D8E DC3D10E DC3D15E DC3D20E

Problem description

The problem illustrated in Figure 1.3.38–1 consists of a 1-m-long conductor through which a constant current density of 6.58E5 Am^–2 is established by creating a potential difference across the ends of the conductor or by prescribing a concentrated current. The electrical energy generated by the flow of current is converted into heat, which results in a temperature distribution through the conductor. Only a steady-state solution is considered for each test. A reasonable mesh is used in each case to obtain the quadratic distribution of heat.

Figure 1.3.38–1 Model of conductor.

Material:

Thermal conductivity = 45 W/m°C; electrical conductivity = 6.58E6 1/ m.

Boundary conditions:

Zero potential ( 0 V) and zero temperature gradient ( 0°Cm^–1) at 0 m.

Potential 0.1 V and temperature 100°C, or current density of 6.58E5 Am^–2 and temperature 100°C at 1 m.

With these boundary conditions the problem is one-dimensional. It is assumed that all electrical energy is converted into heat.

Reference solution

In this uniaxial problem the exact solution for the temperature is of the form , where , , and are real constants. Application of the above material properties and boundary conditions leads to the exact solution

where

–1462.2.

Results and discussion

The tests are composed of three steps.

In Step 1 the proper temperature boundary conditions are applied, and the flow of current is obtained by a potential difference between the two ends of the conductor. The coupled thermal-electrical procedure is used to obtain the desired temperature distribution across the conductor. For first-order elements the results are a function of y and z when the mesh generated is skewed in the x–y plane and/or the x–z plane. For the different test cases studied, the temperature may vary by as much as 3% in the y–z plane for a given x-value. Therefore, special care is needed when using triangular and tetrahedral elements. The exact solution is recovered in most test cases, with a maximum deviation of 1.5% from the exact solution observed with the DC3D6E elements. For second-order elements the exact results are obtained since the results are at most a quadratic function of the variable x. Moreover, skewed meshes do not affect the results.

Step 2 is a heat transfer step in which the conductor is allowed to cool down.

Step 3 invokes a coupled thermal-electrical procedure in which the same amount of electrical energy as that of Step 1 is provided to the specimen. However, energy is now supplied by specifying a prescribed current at 1 m instead of a potential of 0.1 V. Here again, the temperature results are identical to those obtained in Step 1, and the potential distribution that served as input for Step 1 is retrieved as output in this step.