Page 82 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 63

3.5 In the system shown below, the rate of heat generation is 800 W/ m3 in Region
A which is perfectly insulated on the left-hand side. Given the conditions indicated
in the figure, calculate the heat flux and temperature at the right-hand side, i.e.,
at x = 100 cm, under steady-state conditions.
Rate of heat generation = 800 W / m3

(Answer: 320 W, 41.3"C)

3.6 Uniform energy generation rate per unit volume at R = 2.4 x lo6 W/ m3 is
occurring within a spherical nuclear fuel element of 20 cm diameter. Under steady
conditions the temperature distribution is given by

T = 900 - 10,000 r2
where T is in degrees Celsius and T is in meters.

a) Determine the thermal conductivity of the nuclear fuel element.
b) What is the average heat transfer coefficient at the surface of the sphere if the
ambient temperature is 35 "C?
(Answer: a) 40 W/ m. K b) 104.6 W/ m2. K)

3.7 A plane wall, with a surface area of 30 m2 and a thickness of 20 cm, separates
a hot fluid at a temperature of 170 "C from a cold fluid at 15 "C. Under steady-state
conditions, the temperature distribution across a wall is given by

T = 150 - 6002 - 502'

where x is the distance measured from the hot wall in meters and T is the temper-
ature in degrees Celsius. If the thermal conductivity of the wall is 10 W/ m. K :
a) Calculate the average heat transfer coefficients at the hot and cold surfaces.
b) Determine the rate of energy generation within the wall.
(Answer: a) @)hot = 300 W/ m2. K, = 477 W/ m2. K b) 6000 W)

3.8 Derive Eq. (3.214).
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(Hint:Ekpress 2 and TZ in terms of (T).)

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