Consider the fuel element of Example 5.11. Initially, the element is at a uniform temperature of 300C with no heat generation. Suddenly, the element is inserted into the reactor core, causing a uniform volumetric heat generation rate of q= 10 W/m'. The surfaces are convectively cooled with T.= 300C and h=1100 W/m K. Using the explicit method with a space increment of 2 mm, determine the temperature distribution 1.5 s after the element is inserted into the core. EXAMPLE 5.11 A fuel element of a nuclear reactor is in the shape of a plane wall of thickness 2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m K and T, = 250C. At normal operating power, heat is generated uniformly within the element at a volumetric rate of = 10' W/m. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change to 4, = 2 x 107 W/m, and use the explicit finite-difference method to determine the fuel element temperature distribution after 1.5 s. The fuel element thermal properties are k = 30 W/mK and a = 5 10-6 m/s.