Problem $1(30$ points$)$

A power transistor with three $0\mathrm{.}8$ mm diameter leads of a copper$-$silver alloy $(k=400\frac{W}{m}-K)$ dissipates $3\mathrm{.}5$ Watts of power. The printed circuit board $($PCB$)$ on which the transistor is mounted is maintained at $30$ C $.$ The air temperature is $20$ C and the heat transfer coefficient for the leads is $60\frac{W}{m^2}K.$ The length of the leads from the transistor to printed circuit board is $9\mathrm{.}0$ mm $.$

$($a$)$ Determine the maximum lead temperature neglecting all convection effects.

$($b$)$ Determine the maximum lead temperature if convection is present.