Chapter 3, Problem 3.120P

A carbon nanotube is suspended across a trench of width $s=5\text{μm}$ that separates two islands, each at $T_{\infty }=300\text{K}\text{.}$ A focused laser beam irradiates the nanotube at a distance $\xi$ from the left island, delivering $q=10\text{μW}$ of energy to the nanotube. The nanotube temperature is measured at the midpoint of the trench using a point probe. The measured nanotube temperature is $T_1=324.5\text{K}$ for ${\xi }_1=1.5\text{μm}$ and $T_2=326.4\text{K}$ for ${\xi }_2=3.5\text{μm}\text{.}$

Determine the two contact resistances, $R_{t,c,L}$ and $R_{t,c,R}$ at the left and right ends of the nanotube, respectively. The experiment is performed in a vacuum with $T_{\text{sur}}=300\text{K}\text{.}$ The nanotube thermal conductivity and diameter are ken $k_{\text{cn}}=3100\text{W/m}\cdot \text{K}$ and $D=14\text{nm,}$ respectively.