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Or more directly, it is possible to rewrite (16) as:

By assigning some values to the 8 parameters involved:

converges to 100 ºC. But if by applying a surface treatment to

that busbar surface, the surface emmissivity is increased from 0.4 to
1.0, the heat transfer coefficient equation parameters are changing
to:

And

now converges to 76 ºC reducing the busbar electrical

resistivity by 7%!

The voltage equation is a lot more straightforward as it is the
standard application of the Kirchoff's laws:

It is a linear problem when the temperatures are kept constant.

3D ANSYS

based busbar model

It is quite easy to build a parametric 3D ANSYS

based busbar

model (see figure 3). In such a model, the exact busbar geometry
can be reproduced and the detailed convection and radiation
boundary conditions can be applied i.e. different boundary
conditions for the vertical, horizontal facing up and down surfaces
etc.

Figure 3. Mesh of the 3D ANSYS

based busbar model.

In the 3D model presented here however, in order to be able to
compare with the 1D model results, equation (15) have been used
to compute all the heat transfer coefficients instead of using the
standard COEF macro [11] that computes a series of heat transfer
coefficients tables using the above full set of equations based on
individual surface orientation, typical length etc. So here, for
comparison purpose only, a single heat transfer coefficient equation
is wrongly used for all the busbar external surfaces regardless of
the different surface orientations.

All the busbar surfaces in contact with cathodic flexibles are
defined to be at 0 potential and the surfaces of the 12 risers in
contact with the anode beam have been coupled together in order to
be at the same potential. Figure 4 presents the obtained temperature
and figure 5 presents the obtained voltage.

Figure 4. Thermal solution of the 3D ANSYS

based busbar model.

Figure 5. Voltage solution of the 3D ANSYS

based busbar model.

The maximum temperature reached in the positive or upstream
busbar is 95.1 ºC and in the negative or downstream busbar is
190.2 ºC. The global busbar network voltage drop is 215 mV with
243.3 kA or 48.7% of the total 500 kA passing in the negative or
downstream side and 256.7 kA or 51.3% passing in the positive or
upstream side.