A resistor element on a circuit board dissipates $0\mathrm{.}15$ W of power in an environment at $35$C

with a heat transfer coefficient of h $=9$ W$/$m$?$ K$.$ The resistor is $1\mathrm{.}2$ cm long and has a diameter of $0\mathrm{.}3$

cm$.$ Assume heat to be transferred uniformly from the length of the resistor $($neglecting loss from the

ends$).$

a $)$ Determine the surface temperature of the resistor.

b $)$ It is prposed that a thin plastic coating $($with thermal conductivity k $=0\mathrm{.}15$ W$/$m$-$K$)$ be applied to

the resistor to reduce its temperature. What coating thickenss will minimize the temperature, and

what temperature will be achieved?