The primary economic pressure is to maximise the power output from a reactor, because this gives the best return on the capital invested in the reactor plant and the inventory of fuel committed to the reactor and the reprocessing cycle, and also maximises the breeding of fissile material or the consumption of waste products, whichever is required. Whatever the purpose of the reactor the heat generated has to be removed from the reactor core, and the power is limited by heat — transfer considerations. The crucial limits are set by conduction of heat within the fuel elements and by the flow of coolant through the core.

As explained in Chapter 2 in power reactors the fuel elements are in the form of long tubes of cladding, usually steel, containing the fuel in the form of ceramic or metal pellets or powder. If the power density in the fuel material due to fission is Q Wm-3, then q, the linear rating of the fuel element, is given by q = n RfQ, and if ATf is the temperature difference between the centre and the surface of a cylindrical fuel pellet, in the case of constant thermal conductivity, q is given by

q = 4n Kf ATf. (3.1)

As we have seen in Chapter 2 for most fuel materials the maximum acceptable value of q is about 50 kWm-1 .If q is fixed the power density Q = q/пR2f can in principle be increased indefinitely by reducing the radius of the fuel, but a practical limit is set by the cost of manufacture which rises rapidly for very small fuel elements. For this reason the fuel radius cannot be less than about 2.5 mm, which limits the maximum power density in the fuel to about 2.55 GWm-3.