Circular cooling fins of diameter D = 1 mm andlength L = 25.4 mm, made of copper (k = 400 W/m·K), areused to enhance heat transfer from a surface that is maintainedat temperature Ts1 = 132°C. Each rod has one end attached tothis surface (x = 0), while the opposite end (x = L) is joinedto a second surface, which is maintained at Ts2 = 0°C. Theair flowing between the surfaces and the rods is also at T` =0°C, and the convection coefficient is h = 100 W/m2·K.(a) Express the function u(x) = T(x) - T` along a fin, andcalculate the temperature at x = L/2. (b) Determine the rate of heat transferred from the hot surface through each fin and the fin effectiveness. Is the use of fins justified? Why? (c) What is the total rate of heat transfer from a 10-cm by 10-cm section of the wall, which has 625 uniformly distributed fins? Assume the same convection coefficient for the fin and for the unfinned wall surface.
Circular cooling fins of diameter D = 1 mm and
length L = 25.4 mm, made of copper (k = 400 W/m·K), are
used to enhance heat transfer from a surface that is maintained
at temperature Ts1 = 132°C. Each rod has one end attached to
this surface (x = 0), while the opposite end (x = L) is joined
to a second surface, which is maintained at Ts2 = 0°C. The
air flowing between the surfaces and the rods is also at T` =0°C, and the convection coefficient is h = 100 W/m2·K.
(a) Express the function u(x) = T(x) - T` along a fin, and
calculate the temperature at x = L/2. (b) Determine the rate of heat transferred from the hot surface
through each fin and the fin effectiveness. Is the
use of fins justified? Why?
(c) What is the total rate of heat transfer from a 10-cm by
10-cm section of the wall, which has 625 uniformly distributed
fins? Assume the same convection coefficient
for the fin and for the unfinned wall surface.
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