Solve the below problem:
Q: To measure thermal conductivity, two similar 1-cm-thick specimens are placed in an apparatus shown in the accompanying sketch. Electric current is supplied to the 6-cm by 6-cm guarded heater, and a wattmeter shows that the power dissipation is 10 watts (W). Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in Btu/(h ft°F) and W/(m K).
GIVEN
Thermal conductivity measurement apparatus with two samples as shown
Sample thickness (L) = 1 cm = 0.01 cm
Area = 6 cm A=6 cm = 36 cm2 = 0.0036 m2
Power dissipation rate of the heater (qh) = 10W
Surface temperatures
Thot = 322 K and Tcold = 300 K
ASSUMPTIONS
One dimensional, steady state conduction
No heat loss from the edges of theapparatus
