(a) Explain why the apparatus of Problem 2.17 cannot be used to obtain an accurate measurement of the aerogel's thermal conductivity.
(b) The engineer designs a new apparatus for which an electric heater of diameter D=150 mm i d ihdbt is sandwiched between two thin plates of aluminum. The steady-state temperatures of the 5-mm thick aluminum plates, T1 and T2, are measured with thermocouples. Aerogel sheets of thickness t=5 mm are placed outside the aluminum plates, while a coolant with an inlet temperature of Tc,i=25°C maintains the exterior surfaces of the aerogel at a low temperature. The circular aerogel sheets are formed so that they encase the heater and aluminum sheets, providing insulation to minimize radial heat losses. At steady state, T1=T2=55C, and the heater draws 125 mA at 10V. Determine the value of the aerogel thermal conductivity ka.
(c) Calculate the temperature difference across the thickness of the 5-mm-thick aluminum plates. Comment on whether it is important to know the axial locations at which the temperatures of the aluminum plates are measured.
(d) If liquid water is used as the coolant with a total flow rate of 1 kg/min (0.5 kg/min for each of the two streams), calculate the outlet temperature of the water, Tc,o.