In the general case Д/с is function of temperature, control-rod position, and any variable describing the external disturbance which can be cause of an accident (with the exception of the loss of coolant, all accidents appear in Д/с).

The temperature feedback is usually separated in fuel and moderator effect, so that

Д/с = І " Q/(T’) dT’ + " ©„(Т’ЫТ’ + Дкс+Дк. (12.16)

JT/o Jt-c

where 0/(T) = fuel temperature coefficient,

©m(T) = moderator temperature coefficient,

Д/Сс = reactivity given by the control rods,

Д/са = reactivity disturbancy causing the accident.

The integrals appear because the temperature coefficients are usually temperature- dependent.

Equation (12.16) is generally used for the zero-dimensional calculations. If space — dependence is taken into account one can still use this equation for each region in which the reactor is subdivided, or, in a more general way, it is possible to consider the temperature-dependence of the parameters of eqn. (12.1). In this case Д/с will not explicitly appear in the equations and the poisons introduced by the control system appear in 2,. In any case it is necessary to calculate the reactor temperature in zero or more space dimensions.

The explicit solution of eqns. (12.1) [or its simplified versions (12.2) or (12.7)] with
(12.16) and the heat-transfer equations is a formidable, if not impossible task. On the other hand, a numerical solution can be easily programmed on a digital computer.