A testing lab is contracted to measure the thermal conductivity of various liquids as a function of
Question:
A testing lab is contracted to measure the thermal conductivity of various liquids as a function of the liquid temperature. Typically, the lab would measure the thermal conductivity and its temperature dependence by performing many time-consuming experiments at various operating temperatures. A new experimental design is proposed whereby the temperature dependence may be determined in one experiment. The proposed apparatus consists of multiple layers, with each layer consisting of a t1cm-thick square sheet of low thermal conductivity material sandwiched between two tss = 1-mm-thick stainless steel plates with kss = 15 W/m ∙ K. The resulting stainless steel-low thermal conductivity-stainless steel sandwiches then separate N = 5, t1, = 2-mm-thick layers of the liquid. The entire structure is heated from above to eliminate natural convection within the liquid, and cooled from below with a flowing liquid. The temperature of each stainless steel sheet is measured with a thermocouple, and the device is encased in insulation. The temperature range over which the thermal conductivity of a particular liquid is to be measured is 300 K < T < 400 K. To resolve the temperature dependence of the liquid's thermal conductivity, the temperature difference across each liquid layer is to be held to within L1 T = 2°C. The nominal thermal conductivity of the liquid is k, = 0.8 W/m ∙ K.
(a) Consider the low thermal conductivity material to be Bakelite. Determine the overall height, H, of the experimental apparatus.
(b) Consider replacing the Bakelite with an aero-gel characterized by ka = 0.0065 W/m ∙ K. What is the overall height of the apparatus?
(c) To minimize heat losses through the sides of the device, the area of the heater (Ah) is made 10 times larger than the area of the sides (As) of the device. Compare the required heater area and required electrical power for devices constructed using Bakelite and aero-gel low thermal conductivity materials.
Step by Step Answer:
Fundamentals of Heat and Mass Transfer
ISBN: 978-0471457282
6th Edition
Authors: Incropera, Dewitt, Bergman, Lavine