Practical 2: 1D steady state conduction
C1 Consider heat conduction through a wall of thickness L and area A. Under what conditions will the temperature distributions in the wall be a straight line?
C2: The bottom of a pan is made of a 4mm thick aluminum layer. In order to increase the rate of heat transfer through the bottom of the pan, someone proposes a design for the bottom that consists of a 3mm thick copper layer sandwiched between two 2mm thick layers. Will the new design conduct heat better? Explain. Assume perfect contact between the layers.
1. A 6 m length of thick-walled stainless-steel pipe (k=19 Wm-1K-1) has an ID=2 cm and OD= 4 cm. The outside of the pipe is insulated with a 3 cm layer of asbestos (k=0.2 Wm-1 K-1). The inside of the pipe is maintained at 600 oC while the outside temperature is 100 oC. Calculate:
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a) The rate of heat loss from the pipe;
b) The temperature at the interface between the pipe and the insulation
2. Water at 90 oC flows through a pipe (ID=2.5 cm). The pipe wall is 0.8 mm thick, with thermal conductivity 16 Wm-1 K-1. Inside the pipe, the average heat transfer coefficient is estimated to be hi=3 500 Wm-2 K-1. Heat is lost from the outside of the pipe to the surrounding air (20oC) is due to free convection, with an average heat transfer coefficient ho=7.6 Wm-2K-1. Calculate:
a) The overall heat transfer coefficient UA, per metre length;
b) The heat loss from the pipe per metre length;
c) If the resistances due to convection from the water to the pipe and conduction through the pipe are neglected, how does this effect the calculation of the heat loss from the pipe?
d) The outside temperature of the pipe;
e) What will be the rate of heat loss from the pipe if it is insulated with a 2cm layer of calcium silicate blanket?
f) What is the outside surface temperature of the insulation?
g) For a 100m pipe network, how much energy is saving by insulating the pipe as outlined above?
h) Assuming that the heat lost from the pipe must be replaced using an electrical energy source with an greenhouse gas (GHG) emissions factor of 1.1 t CO2-equivalent per MWh, and steady, constant flow through the pipe, how much GHG emissions would be saved per year by insulating the 100 m pipe network as outline above?
3. A spherical, thin-walled metallic container stores liquid nitrogen at 77 K at a Brisbane manufacturing plant. The container has a diameter of 0.5 m, and is covered with an evacuated, reflective insulation of silica powder. The outer surface of the insulation is exposed to ambient air (300 K). Convection from the outer surface of the insulated container is characterized by a heat transfer coefficient of 20 Wm-2 K-1. Calculate:
a) If the silica powder insulation is 25 mm thick, with a thermal conductivity of 0.0017 Wm-1K-1, what is the rate of heat transfer to the liquid nitrogen?
b) If the spherical container is built in a hot, windy region where h=50 Wm-2K-1 and the air temperature regularly reaches 40oC, how much must the insulation thickness be increased to ensure that the rate of heat transferred to the liquid nitrogen is no greater than maintain the same rate of heat transfer to the sphere at the Brisbane site?
4. An electrolytic cell in an aluminium smelter operates such that its contents (molten metal and cryolite) remain at Tmolten=950 -980 oC, with occasional temperature fluctuations up to 1020oC. The walls are constructed with a 20 cm thick inner layer of silica bricks (fired diatomaceous silica) which are resistant to corrosion by crylolite, and an outer lay of fire clay bricks, which are cheaper but susceptible to corrosion. Both kinds of bricks are available in thickness of 5 cm intervals (i.e. 10 cm, 15 cm, 20 cm etc.) A plain carbon steel shell, of thickness 1 cm, encases the bricks. The coefficient for heat transfer from the molten metal & cryolite to the silica bricks is 1000 Wm-2 K-1, the coefficient for heat transfer from the outside of the steel shell to the ambient air is 20 Wm-2 K-1, and the temperature of the surrounding air is Tambient = 30 oC.
a) The cells are designed to minimize unnecessary heat loss, however some heat loss is needed to ensure that cells do not overheat during temperature fluctuations. What is the maximum thickness of fire clay brick which can be used in the outer layer, while still ensuring that the heat flux through the walls will still be at least 750 Wm-2 if Tmolten=1020 oC? What would be the thickness of bricks required if silica bricks were used instead of fire clay bricks?
Assuming that fire clay bricks are used in the design, determine the following under normal operating conditions (Tmolten=960oC):
b) What is the heat flux through the walls?
c) What is the temperature at the interface between the silica bricks and the fire clay bricks?
d) What is the outside surface temperature of the steel shell?
e) What is the heat loss due to radiation from the surface of the shell, assuming the shell has an emissivity of 0.2?
Hint: Neglect radiation in parts a-d, then consider the implication of this assumption in part e.
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