Download CHE311 HEAT TRANSFER 2016-17 Fall Semester Prof.Dr.Serpil

CHE311 HEAT TRANSFER
2016-17 Fall Semester
Prof.Dr.Serpil Takaç
PROBLEM SET-I
1. A 50-cm-diameter pipeline in the Arctic carries hot oil at 30◦C and is exposed to a surrounding
temperature of−20◦C. A special powder insulation 5 cm thick surrounds the pipe and has a
thermal conductivity of 7 mW/m◦ C. The convection heat-transfer coefficient on the outside of
the pipe is 9 W/m2 ◦C. Estimate the energy loss from the pipe per meter of length.
2. A certain insulation has a thermal conductivity of 10 W/m ◦C. What thickness is necessary to
effect a temperature drop of 500◦C for a heat flow of 400 W/m2?
3. A flat wall is exposed to an environmental temperature of 38◦C. The wall is covered with a
layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m ◦C, and the temperature
of the wall on the inside of the insulation is 315◦C. The wall loses heat to the environment by
convection. Compute the value of the convection heat-transfer coefficient that must be
maintained on the outer surface of the insulation to ensure that the outer-surface temperature
does not exceed 41◦C.
4. One side of a plane wall is maintained at 100◦C, while the other side is exposed to a
convection environment having T =10◦C and h=10 W/m2 ◦C. The wall has k =1.6W/m ◦C and
is 40 cm thick. Calculate the heat-transfer rate through the wall.
5. A copper sphere 4.0 cm in diameter is maintained at 70◦C and submerged in a large earth
region where k =1.3 W/m ◦C. The temperature at a large distance from the sphere is 12◦C.
Calculate the heat lost by the sphere.
6. Two long, eccentric cylinders having diameters of 20 and 5 cm, respectively, are maintained at
100 and 20◦C and separated by a material with k =2.5 W/m ◦C. The distance between centers
is 5.5 cm. Calculate the heat transfer per unit length between the cylinders.
7. The composite wall of an oven consists of three materials, two of which are of known thermal
conductivity, kA = 20 W/m K and kC = 50 W/m K, and known thickness, LA= 0.30 m and LC =
0.15 m. The third material, B, which is sandwiched between materials A and C, is of known
thickness, LB = 0.15 m, but unknown thermal conductivity kB.
Under steady-state operating conditions, measurements reveal an outer surface temperature
of Ts,o= 20 oC, an inner surface temperature of Ts,i = 600 oC, and an oven air temperature of
T= 800 oC. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of
B?
8. Steam pipes are sometimes carelessly buried in the earth without insulation. Consider a 10cm pipe carrying steam at 150◦C buried at a depth of 23 cm to centerline. The buried length is
100 m. Assuming that the earth thermal conductivity is 1.2 W/m ◦C and the surface
temperature is 15◦C, estimate the heat lost from the pipe.
9. Consider steady-state conditions for one-dimensional conduction in a plane wall having a
thermal conductivity k= 50 W/m K and a thickness L= 0.25 m, with no internal heat generation.
Determine the heat flux and the unknown quantity for each case and sketch the temperature
distribution, indicating the direction of the heat flux.
Case
1
2
3
4
5
T1 (oC)
50
-30
70
T2 (oC)
-20
-10
40
30
dT/dx (K/m)
160
-80
200
10. The diagram shows a conical section fabricated from pyroceram. It is of circular cross section
with the diameter D = ax, where a = 0.25. The small end is at x1 = 50 mm and the large end at
x2 = 250 mm. The end temperatures are T1= 400 K and T2 = 600 K, while the lateral surface is
well insulated. Find:
1. Temperature distribution T(x)
2. Heat transfer rate qx
Text Books:
1. Holman JP, Heat Transfer. McGraw-Hill, NY, 10th Ed., 2009.
2. Incropera FP, De Witt DP, Fundamentals of Heat and Mass Transfer. 5th Ed., J.Wiley&Sons,
NY, 2002