Q$3.$ Air blows at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ over the top surface of a circuit board at $\backslash (4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The components mounted on the circuit board provide a combined thermal energy output of $65$ W $.$ The circuit board measures $\backslash (25\backslash$times $25\backslash$mathrm$\{$~cm$\}\backslash ).$ Assuming no radiational effects and the back is sufficiently insulated. For the purpose of these calculations, assume a film temperature of $\backslash (45^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and that the components induce a fully turbulent flow. Calculate:

A$)$ The surface temperature of the circuit board when operating under steady state conditions.

$[8$ marks$]$

B$)$ Comment on whether the assumed film temperature is an acceptable one.

$[2$ marks$]$

C$)$ What is the minimum velocity the fan can apply before the board temperature exceeds $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )?$

$[10$ marks$]$