A procedure for measuring the thermal conductivity of

Chapter 12, Problem 12.95

(choose chapter or problem)

A procedure for measuring the thermal conductivity of solids at elevated temperatures involves placement ofa sample at the bottom of a large furnace. The sampleis of thickness Land is placed in a square container ofwidth Won a side. The sides are well insulated. Thewalls of the cavity are maintained at Tw, while the bot-tom surface of the sample is maintained at a muchlower temperature Tcby circulating coolant throughthe sample container. The sample surface is diffuseand gray with an emissivity ?s. Its temperature Tsismeasured optically.(a) Neglecting convection effects, obtain an expres-sion from which the sample thermal conductivitymay be evaluated in terms of measured andknown quantities (Tw, Ts, Tc, ?s, L). The measure-ments are made under steady-state conditions. If Tw?1400 K, Ts?1000 K, ?s?0.85, L?0.015 m, andTc?300 K, what is the samplethermal conductivity? (b) If W?0.10 m and the coolant is water with a flowrate of , is it reasonable to assume auniform bottom surface temperature Tc?