$($a$)$ Determine the temperatures at nodes $1\frac{,}{{?}_{?}},$ and $.$

$($b$)$ Calculate the heat transfer rate per unit length

$(\frac{W}{m})$ from the rod using the nodal tempera$-$

tures. Compare this result with the heat rate cal$-$

culated from knowledge of the volumetric gen$-$

eration rate and the rod dimensions.