Transient Thermal Analysis (TTA) is performed in some nuclear codes such as ASME NB or Class 1.
In the transient thermal analysis, a flow curve Vs time and another of the fluid temperature vs time are defined. These curves are made for both the water in the critical cooling systems of the reactors and the steam systems.
Based on the thermal capacity of the pipes (including accessories and thermal insulation capacity), the program calculates how each node of the pipe will heat up over time. Based on these temperatures, the program calculates the stresses due to thermal expansion at each time the pipes are heated.