Transport Processes: Assignment

Transport Processes (SKKK 2313)
ASSIGNMENT # 1

1. Consider a steam pipe of length L=20 m, inner radius r1=6 cm, outside radius r2=8 cm, and thermal conductivity k=20 W/m.k. The inner and outer surfaces of the pipe are maintained at average temperatures of T1=150oC and T2=60oC, respectively. Obtain a general relation for the temperature distribution inside the pipe under steady conditions, and determine the rate of heat loss from the steam through the pipe.
Assume that heat transfer is one-dimensional and there is no heat generation.
The general equation can be expressed as:
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2. Consider a 0.8m high and 1.5 m wide double-pane window consisting of two 4mm thick layers of glass (k = 0.78 W/m.oC) separated by a 10 mm wide stagnant air (k = 0.026 W/m.oC).
Determine the steady rate of transfer through this double-pane window and the temperatures of its inner surface for a day during which the room is maintained at 20oC while the temperature of the outdoors is -10oC. Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be h1 = 10 W/m2.oC and h2 = 40 W/m2.oC, which includes the effects of radiation.

3.A steam at T∞1=320oC flows in a cast iron pipe (k=80 W/m.K) whose inner and outer diameters are D1=5 cm and D2=5.5 cm, respectively. The pipe is covered with 3-cm thick glass wool insulation with k=0.05 W/m.K. Heat is lost to the surroundings at T∞2=5oC by natural convection and radiation, with a combined heat transfer coefficient inside the pipe to be h2=18 W/m2.K. Taking the heat transfer coefficient inside the pipe to be h1=60 W/m2.K, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation.

4. A spherical, thin-walled metallic container is used to store liquid nitrogen at 77 K. The container has a diameter of 0.5 m and is covered with an evacuated, reflective insulation composed of silica powder. The insulation is 25 mm thick, and its outer surface is exposed to ambient air at 300 K. The convection coefficient is known to be 20 W/m2.K. The latent heat of vaporisation and the density of liquid nitrogen are 2x105 J/Kg and 804 Kg/m3, respectively.
What is the rate of heat transfer to the liquid nitrogen?

5. An electric wire having a diameter of 1.5mm and covered with a plastic insulation
(thickness = 2.5mm) is exposed to air at 300K and h0 = 20 W/m2K. The insulation has a k of
0.4 W/m.K. It is assumed that the wire surface temperature is constant at 400K and is not affected by the covering.
a) Calculate the value of critical radius.
b)

Calculate the heat loss per m of wire length with no insulation.

c) Repeat (b) for insulation present

6. An electric wire having a diameter of 1.5mm and covered with a plastic insulation (thickness
= 2.5mm) is exposed to air at 300K and h0 = 20 W/m2K. The insulation has a k of 0.4 W/m.K. It is assumed that the wire surface temperature is constant at 400K and is not affected by the covering. a) Calculate the value of critical radius.
b)

Calculate the heat loss per m of wire length with no insulation.

c) Repeat (b) for insulation present