A 2.2-mm-diameter and 10-m-long electric wire istightly wrapped with a 1-mm-thick plastic cover whose thermalconductivity is K = 0.15 W/m·K. Electrical measurementsindicate that a current of 13 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulatedwire is exposed to a medium at T` = 30°C with a heat transfercoefficient of h = 24 W/m2·K, determine the temperature at theinterface of the wire and the plastic cover in steady operation.Also determine if doubling the thickness of the plastic coverwill increase or decrease this interface temperature.

The thermal conductivity of a solid material can be determined using asetup similar to the one shown in the accompanying figure. The thermocouples are placed at 2.5 cm intervals in the known material (copper alloy, k - 52 w/m.k) and the unknown sample, as shown. The known material is heated on the top by a heating element, and the bottom surface of the sample is cooled by running water through the heat sink shown. Determine the thermal conductivity of the unknown sample for the set of data given in the accompanying table. Assume no heat loss to the surroundings and perfect thermal contact at the common interface of the sample and the copper.