Determine the thermal conductivity of the carbon nanotube of Example 3.4 when the heating island temperature is measured to be T_h = 332.6 K, without evaluating the thermal resistances of the supports. The conditions are the same as in the example.

Example 3.4

The thermal conductivity of a D = 14-nm-diameter carbon nanotube is measured with an  instrument that is fabricated of a wafer of silicon nitride at a temperature of T_∞ = 300K. The 20-m-long nanotube rests on two 0.5-μm-thick, 10 μm X 10 μm square islands that are  separated by a distance s = 5 μm. A thin layer of platinum is used as an electrical resistor on  the heated island (at temperature T_h) to dissipate q = 11.3 μW of electrical power. On the  sensing island, a similar layer of platinum is used to determine its temperature, T_s. The platinum’s  electrical resistance, R(T_s) = E/I, is found by measuring the voltage drop and electrical  current across the platinum layer. The temperature of the sensing island, T_s, is then determined from the relationship of the platinum electrical resistance to its temperature.