During a short circuit there will be electromagnetic forces which determine the required busbar size and the support size. In addition to that we need to be careful about the extreme overheating of the busbars due to the high current, which leads to softening of the material and damage to the support structure.
At the time of a fault, short circuit current will be many times higher than the normal operating current. This current will continue until protective device operates. Since the time duration is small it assumes adiabatic heating, plus the busbar temperature rise can simplify as linear due to negligible cooling effect.
Since, we know specific heat of the copper (385 J kg-1 K-1) the temperate rise can be calculated as follows.
Q is the amount of heat added to the bar (J)
S is the specific heat of the bar material (Jkg-1K-1)
m is the mass of the bar (kg)
tr is the temperature rise (K)
The amount of energy dissipated in the bar is:
Q = PT
P is the power dissipated in the bar (W)
T is the time for which the power is dissipated (seconds).
However, here specific heat of the bar material (S) and the resistivity of the bar material ( will change with the temperature. Resistivity increases with temperature and while specific heat decreases with the temperature.
Using room temperature values, and adjusting to use convenient units, gives the initial rate of temperature rise as: