Physicists have determined the theoretical value of the thermal conductivity of a carbon nanotubes to be k_∞.r = 5000W/m ∙ K.

(a) Assuming the actual thermal conductivity of the carbon nanotubes is the same as its theoretical value, find the thermal contact resistance, R,.", that exists between the carbon nanotubes and the top surface of the heated and sensing islands in Example 3.3.

(b) Using the value of the thermal contact resistance calculated in part (a). plot the fraction of the total resistance between the heated and sensing islands that is due to the thermal contact resistances for is- land separation distances of 5 μm < s < 20 μm.