To determine the thermal conductivity of a long, solid 2.5 cm diameter rod, one half of the

Question:

To determine the thermal conductivity of a long, solid 2.5 cm diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at 27?C. After steady state had been reached, the temperatures at two points 7.6 cm apart were measured and found to be 126?C and 91?C, respectively. The heat transfer coefficient over the surface of the rod exposed to the air was estimated to be 22.7 W/(m2 K). What is the thermal conductivity of the rod?GIVENA solid rod, one half inserted into a furnaceDiameter of rod (D) = 2.5 cm = 0.25 mAir temperature (T??) = 27?CSteady state has been reachedTemperatures at two points 7.6 cm apartT1 = 126?CT2 = 91?CThe heat transfer coefficient ( hc ) = 22.7 W/(m2 K)ASSUMPTIONSUniform thermal conductivityOne dimensional conduction along the rodThe rod approximates a fin of infinite length protruding out of thefurnace