A $10-$cm$-$thick wall is to be constructed with $2\mathrm{.}5-$m long wood studs $($k $=0\mathrm{.}11$ W$/$m C$)$ that have a cross section of $10$ cm x $10$ cm$.$ At some point the builder ran out of those studs and started using pairs of $2\mathrm{.}5-$m$-$long wood studs that have a cross section of $5$ cm x $10$ cm nailed to each other instead. The manganese steel nails $($k $=50$ W$/$m C$)$ are $10$ cm long and have a diameter of $0\mathrm{.}4$ cm$.$ A total of $50$ nails are used to connect the two studs, which are mounted tothe wall such that the nails cross the wall. The temperature difference between the inner andouter surfaces of the wall is $8$ C$.$ Assuming the thermal contact resistance between the twolayers to be negligible, determine the rate of heat transfer $($a$)$ through a solid stud and $($b$)$ through a stud pair of equal length and width nailed to each other. $($c$)$ Also determine theeffective conductivity of the nailed stud pair.

Answers: $($a$)2\mathrm{.}2$ W; $($b$)4\mathrm{.}7$ W; $($c$)0\mathrm{.}235$ W$/$m C