Candidates must attempt THREE out of FOUR questions
Q1. A large plane wall shown in Figure Q1a has a thickness L= 0.5 m and thermal conductivity k=25 W/mK. On one of the wall surfaces, on the left (x=0), is subjected to a uniform heat flux 𝑞 " and its temperature is kept constant. Another, right surface (x=L) experiences convection and radiation heat transfer. This surface temperature is TL=180℃ and the temperature of the surrounding air is 20℃. The emissivity and the convective heat transfer coefficient on the right surface are 0.8 and 16 W/m2K, respectively.
i) Show that the variation of temperature over the wall thickness can be expressed as
ii) Determine the value of heat flux 𝑞 " .
iii) Determine the temperature of the left wall surface.
iv) Determine the temperature of the left surface of the wall for the case when the wall has two layers of different materials of equal thickness and the material of the right layer has thermal conductivity k2=5 W/mK (see Figure Q1b).
Q2. a) 10 aluminium fins (k = 200 W/mK) are placed on the outside of flat surface of an electronic device. Each fin is a plate of 100 mm wide, 20 mm high and 4 mm thick.
The surface of the electronic device is a square with side length of 100 mm. The fins are located parallel to each other at distance of 8 mm between fin middle surfaces. The temperature of the electronic device surface is 50 C and the temperature of surrounding air is 20 ℃. The convection heat transfer coefficient is 80 W/m2K.
You can assume that the fin tips are in adiabatic condition.
Determine:
i) The rate of heat loss from the electronic device to the surrounding air.
ii) The fin effectiveness. [10 marks] [5 marks]
b) A metal plate 0.01 m thick, 1 m long and 0.5 m wide is heated in an oven for 120 seconds. The initial temperature of the plate is 20 ℃, air in the oven is maintained at 600 ℃ and the convection heat transfer coefficient is 180 W/m2K. The material properties of the metal plate are:
• Thermal conductivity, 180 W/mK
• Density, 2600 kg/m3
• Specific heat, 800 J/kgK
Determine the temperature of the plate when it is removed from the oven.
Q3. Hot air at 50 ℃ and 1 bar pressure is cooled by a flat plate of 1.5 m long. The air flows at a velocity of 3 m/s in parallel over the upper surface of the flat plate. If the flat plate surface temperature is maintained at 0 ℃, determine:
i) The local convection heat transfer coefficient at 1 m from the leading edge.
ii) The average convection heat transfer coefficient over the entire plate.
iii) The average heat flux transfer to the plate. iv) Suggest at least three methods to increase the heat flux transfer to the plate.
Q4. A 2 m 2 m 3 m furnace is shown in Figure Q4. The base, top and side surfaces of the furnace are maintained at uniform temperature of 400 K, 600 K and 500 K respectively. All surfaces are grey body with emissivity of 0.8.
i) Determine view factors for the surfaces of the furnace.
ii) Calculate the net radiation heat transfer of the base surface.
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