Please do $5\mathrm{.}4($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.

$5\mathrm{.}4$ If the microchannel from Problem $5\mathrm{.}2$ is changed from the square microchannel

to be the trapezoidal microchannel. The width of the microchannel is $125m,$ the

length of the microchannel is $62\mathrm{.}5m,$ the side angle is $44$ degree, the permissible

water velocity is $1\mathrm{.}5\frac{m}{s},$ and the fluid temperature is $40C.$ By selecting a proper

correlation, calculate

a$.$ The average heat transfer coefficient

b$.$ The pressure drop.