A $2-$mm$-$thick copper plate $($k $=387$ W$/$m$$K$)$ is sandwiched between two $5-$mm$-$thick epoxy boards $($k $=0\mathrm{.}28$ W$/$m$$K$)$ that are

$20$ cm x $30$ cm in size. If the thermal contact conductance$$on both sides of the copper plate is estimated to be $($hc$=7000$ W$/$m$2$K$),$ Calculate the total resistance if

a$.$ The thermal contact conductances are included in K$/$W

b$.$ The thermal contact conductances are ignored in K$/$W $.$

c$.$ Determine the $\%$ error involved in the total thermal resistance of the plate if the thermal contact conductances are ignored.

Hint: the total resistance including the thermal contact conductance is

Rt$=$ Rc $+$ Rc $+$REp$+$ REp $+$Rcopp