QUESTION $1(50\%)$

A smooth hole of diameter $D=0\mathrm{.}25m$ is drilled through the center of a square $(W=2m)$ solid block of commercial bronze $(k=52\frac{W}{m}K)$ with length $($into the page$)L=10m.$ Hot air at atmospheric pressure flows through the hole at a mass flow rate of $m^{}=2k\frac{g}{s}$ and mean inlet temperature $T_{mi}=550K.$ The outer surface is cooled by water in cross flow at$,V=5\frac{m}{s},T_{}=300K.$ You may assume that the outer of the block and drilled hole have a constant surface temperatures $($schematic below for your reference$)$

You may assume the following fluid properties:

Water