Chapter 3, Problem 65P

A 10-cm-thick vall is to be constructed with 2.5-rn-long wood studs $(k=0.11\text{ W/m}\text{.K}$ and that have a cross section of $\text{10 cm }\times \text{ 1 0 cm}\text{.}$ and At some point the builder ran out of those studs and started using pairs of 2.5-rn-long wood studs that have a cross section of $\text{5 cm }\times \text{ 1 0 cm}$ nailed to each other instead. The manganese steel nails $(k=50\text{ W/m}\text{.K)}$ and are 10 cm long and have a diameter of 0.4 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. Assuming the thennal contact resistance between the two layers 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 the effective conductivity of the nailed stud pair.