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Electrothermics by Javad Fouladgar

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3.4. Nonlinear model

In the case of the nonlinear system, the equation of conservation of energy in the steady state is of the form:

[3.25] images

with boundary conditions:

[3.26] images

[3.27] images

Equation [3.25] can be solved using the finite volumes method:

[3.28] images

where the quantities with the indices w, p, and e represent the values calculated at the left of the current point, those calculated at the current point, and those calculated at the right of the current point, respectively.

Assembling this equation by taking boundary conditions into account, [3.26] and [3.27] result in the following nonlinear equation:

[3.29] images

This equation is solved using the iterative algorithm in Figure 3.11.

Figure 3.11. Nonlinear model algorithm

f0116_001.tif

3.4.1. Nonlinear model results

For a given temperature, if we reduce the electric field, we reduce the power injected in the plasma, defined by the term (T)Ee2. Decreasing ...

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