Chapter 2, Problem 2.29P

In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation

${\stackrel{.}{q}}_G={\stackrel{.}{q}}_1\left[1-{\left(\frac{r}{r_o}\right)}^2\right]$

where $q_G$ = local rate of heat generation per unit volume at r

$r_o$ = outside radius

${\stackrel{\cdot }{q}}_1$ = rate of heat generation per unit volume at the centerline

Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of $\text{26 W/}\left(\text{m K}\right)$ if the rate of heat removal from its surface is 1.6 ${\text{MW/m}}^{\text{2}}$.