A $10-$cm$-$thick wall is to be constructed with $9-$m$-$long wood studs $($k $=0\mathrm{.}11$ W$/$m$$K$)$ that have a cross section of $10$ cm $10$ cm$.$ At some point the builder ran out of those studs and started using pairs of $2\mathrm{.}5-$m$-$long wood studs that have a cross section of $5$ cm $10$ cm nailed to each other. The manganese steel nails $($k $=50$ W$/$m$$K$)$ 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 to the wall such that the nails cross the wall. The temperature difference between the inner and outer surfaces of the wall is $8$C$.$ Assume the thermal contact resistance between the two layers to be negligible. Use $=22/7.$

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NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Determine the rate of heat transfer through the solid stud $($in W$).$