9.67. Transient (or unsteady state) heat transfer is important in reactor safety analysis where the thermal behavior as a function of time is of major interest. Generally, the same principles apply as for steady-state heat trans­fer with the addition of time and heat capacity as parameters. In particular, consideration must be given to the heat release after shutdown (§2.215). A typical problem might be to determine the maximum temperature at­tained by the fuel cladding in a water-cooled reactor if the coolant flow is reduced. Even after the reactor is tripped, heat input to the cladding continues; this results from sensible heat stored in the fuel rods which may cause an initial heat-release rate approaching 50 percent of the full power value in a pressurized-water reactor, from fissions by delayed neutrons, and from radioactive decay of the fission products.

9.68. If the coolant-flow rate is decreased, not only will the heat-transfer coefficient decrease, but the thermal transport capacity of the coolant will
decrease since less mass will flow past a given point per unit time. There­fore, for the same heat flux (or heat-flow rate) from the cladding, the coolant will tend to attain a higher temperature. The temperature of the cladding as a function of time is then determined by a balance between the heat input from the fuel and the heat loss to the coolant. Since the temperature-difference driving force for each rate depends on the cladding temperature, the situation is complicated and numerical (computer) meth­ods are required for solution of the problem. Subchannel analysis ap­proaches (§9.135) may be incorporated in these codes to provide a detailed representation of core temperature behavior.