Please do $5\mathrm{.}3($NOT $5\mathrm{.}2),$ thanks!

$5\mathrm{.}2$ A MCHEx has been designed for cooling an electronic chip of size $30$ mm by

$30$ mm $.$ The transition Reynolds number is $800.$ The average Nusselt numbers can

be calculated from the following correlations:

$=0\mathrm{.}0384R{e}^{0\mathrm{.}67}P{r}_{nf}^{0\mathrm{.}33}$ for laminar flow

$=0\mathrm{.}00726R{e}^{0\mathrm{.}8}P{r}_{nf}^{0\mathrm{.}33}$ for turbulent flow

To cool the chips, a square microchannel of $250m$ is chosen where the permis$-$

sible water velocity is $1\frac{m}{s}$ and the fluid temperature is $40C.$

a$.$ Calculate the heat transfer coefficient

b$.$ If the length of the microchannel has been given as $20$ mm $,$ calculate the

friction coefficient and the pressure drop.

$5\mathrm{.}3$ Repeat the problem $5\mathrm{.}2,$ if the permissible water velocity is changed to be $2\frac{m}{s}$

but the fluid temperature is still the same. By using a proper correlation, deter$-$

mine the average heat transfer coefficient.