Measuring thermal conductivity of a wide range of materials accurately is a difficult task. One example of an instrument to measure thermal conductivity is the hot disk analyzer, which is simply a flat, circular hot wire heater that is calibrated to measure surface temperature and surface heat flux. Consider the version of the hot disk analyze, where a cylinder of material is placed onto the disk of the same diameter, and the sides are well insulated. The temperature of the top of the cylinder is measured optically to avoid thermal contact resistance errors, and so the top must be open to the air. The primary challenge of any thermal conductivity measurement is to minimize error due to unintentional heat loss. You wish to measure the thermal conductivity of pure silver (k = 429 W/m-K) to calibrate the machine and estimate its error. The cylinder and disk both have a diameter D = 0.01, and the cylinder has a height of L = 0.02. You apply 5.2 W to the heater and measure a temperature difference between the top and bottom surface of the cylinder of 2.7 C. What is the measured thermal conductivity of the cylinder?