A cylindrical nuclear fuel rod contains a core of active, fissionable material and a cladding formed from a high-temperature metal (Figure P5.26). The heat generation rate within this core is a function of position that we will approximate via a parabolic function.

\[\dot{q}=q_{o}\left[1+\alpha\left(\frac{r}{r_{i}}\right)^{2}\right]\]

The fuel rod is exposed to a coolant that circulates at a temperature of \(T_{\infty}\) and provides a heat transfer coefficient of \(h_{o}\left(\mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\right)\). Determine:

a. The temperature profiles in the fuel and cladding.

b. The heat flow through the fuel rod.

c. The critical cladding thickness yielding maximum heat transfer.

Transcribed Image Text:

FIGURE P5.26 h kf