1. A small radiant heater has metal strips 6 mm with a total length of 3 m. The surface emissivity of the strips is 0.85. To what temperature must the strips be heated if they are to dissipate 2000 W of heat to a room at 25 ºC?

2. One side of a plane wall is maintained at 100 ºC, while the other side is exposed to a convection environment having T = 10 ºC and h = 10 W/m2 -ºC. The wall has k = 1.6 W/m-ºC and is 40 cm thick. Calculate the heat-transfer rate through the wall.

3. A black 20-by-20 cm plate has air forced over it at a velocity of 2 m/s and a temperature of 0 ºC. The plate is placed in a large room whose walls are at 30 ºC. The back side of the plate is perfectly insulated. Calculate the temperature of the plate resulting from the convection-radiation balance.

4. A plate having a thickness of 4.0 mm has an internal heat generation of 200 MW/m3 and a thermal conductivity of 25 W/m-ºC. One side of the plate is insulated and the other side is maintained at 100 ºC. Calculate the maximum temperature in the plate.

5. A very long copper rod (k = 372 W/m-ºC) 2.5 cm in diameter has one end maintained at 90 ºC. The rod is exposed to a fluid whose temperature is 40 ºC. The heattransfer coefficient is 3.5 W/m2 -ºC. How much heat is lost by the rod?

6. A 4.0-cm cube of aluminum is initially at 450 ºC and is suddenly exposed to a convection environment at 100 ºC with h = 120 W/m2 -ºC. How long does it take the cube to cool to 250 º?

7. Oxygen at a pressure of 2 atm and 27 ºC blows across a 50-cm-square plate at a velocity of 30 m/s. The plate temperature is maintained constant at 127 ºC. Calculate the total heat lost by the plate.

8. Calculate the heat transfer from a 20-cm-square plate over which air flows at 35 ºC and 14 kPa. The plate temperature is 250 ºC, and the free-stream velocity is 6 m/s.

9. Water at the rate of 0.8 kg/s is heated from 35 to 40 ºC in a 2.5-cm-diameter tube whose surface is at 90 ºC. How long must the tube be to accomplish this heating?

10. Air at 70 kPa and 20 ºC flows across a 5-cm-diameter cylinder at a velocity of 15 m/s. Compute the drag force exerted on the cylinder.

11. Ethylene glycol at 0 ºC flows at the rate of 23 m/s parallel to a 0.6 m square, thin flat plate at 40 ºC, which is suspended from a balance. Assume the fluid flows over both sides of the plate and that the critical Reynolds number is 500000. (a) What drag should be indicated by the balance? (b) What is the heat transfer rate from the plate to the fluid?

12. A 3 in o.d. steam pipe without insulation is exposed to a 30 mph wind blowing normal to it. The surface temperature of the pipe is 200 ºF and the air is at 40 ºF. Find the heat loss per foot of pipe.

13. A heat exchanger wall consists of a copper plate 3/8 inch thick. The surface coefficients on the two sides of the plate are 480 and 1250 Btu/h-ft2 -ºF, corresponding to fluid temperatures of 200 and 90 ºF, respectively. Assuming that the thermal conductivity of the wall is 220 Btu/h-ft-ºF, (a) draw the thermal circuit, (b) compute the surface temperatures in ºF, and (c) calculate the heat flux in Btu/h-ft2 .

14. A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3 . One side of the wall is insulated, and the other side is exposed to an environment at 93 ºF. The convection coefficient between the wall and the environment is 567 W/m2 -K. If the thermal conductivity of the wall is 0.12 W/m-K, calculate the maximum temperature in the wall.

15. Determine the rate of heat loss in Btu/hr from the wall of a building in a 10-mph wind blowing parallel to its surface. The wall is 80 ft long, 20 ft high, its surface temperature is 80 ºF, and the temperature of the ambient air is 40 ºF.

16. Compare the rate of heat loss from a human body with the typical energy intake from consumption of food (1300 kcal/day). Model the body as a vertical cylinder 30 cm in diameter and 1.8 m high in still air. Assume the skin temperature is 2 ºC below normal body temperature. Neglect radiation, transpiration cooling (sweating), and the effects of clothing.

17. Estimate the rate of heat transfer across a 1-m tall double-pane window assembly in which the outside pane is at 0 ºC and the inside pane is at 20 ºC. The panes are spaced 1 cm apart. What is the thermal resistance ("R" value) of the window?

18. Water at 82.2 ºC is flowing through a thin copper tube (15.2 cm ID) at a velocity of 7.6 m/s. The duct is located in a room at 15.6 ºC and the unit-surface-conductance at the outer surface of the duct is 14.1 W/m2 -K. (a) Determine the heat transfer coefficient at the inner surface. (b) Estimate the length of duct in which the water temperature drops (5/9) ºC.

19. Determine the average unit-surface conductance for air at 60 ºC flowing at a velocity of 1 m/s over a bank of 6-cm-OD tubes arranged as shown in the accompanying sketch (shows a staggered tube bank). The tube-wall temperature is 117 ºC.

20. A light oil flows through a copper tube of 2.6 cm ID and 3.2 cm OD. Air is flowing over the exterior of the tube. The convective heat transfer coefficient for the oil is 120 W/m2 -K and for the air is 35 W/m2 -K. Calculate the overall heat transfer coefficient based on the outside area of the tube (a) considering the thermal resistance of the tube, (b) neglecting the resistance of the tube.

21. A shell-and-tube heat exchanger has one shell pass and four tube passes. The fluid in the tubes enters at 200 ºC and leaves at 100 ºC. The temperature of the fluid entering the shell is 20 ºC and is 90 ºC as it leaves the shell. The overall heat transfer coefficient based on a surface area of 12 m2 is 300 W/m2 -K. Calculate the heat transfer rate between fluids.

22. Water entering a shell-and-tube heat exchanger is at 35 ºC is to be heated to 75 ºC by an oil. The oil enters at 110 ºC and leaves at 75 ºC. The heat exchanger is arranged for counterflow with water making one shell pass and the oil two tube passes. If the water flow rate is 68 kg/min and the overall heat transfer coefficient is estimated from Table 8.1 to be 320 W/m2 -K, calculate the required heat exchanger area.

23. Determine the total average hemispherical emittance and the emissive power of a surface which has a spectral hemispherical emittance of 0.8 at wavelengths less than 1.5 μm, 0.6 from 1.5 to 2.5 μm, and 0.4 at wavelengths longer than 2.5 μm. The surface temperature is 1111 K.

24. A black sphere (1 inch diameter) is placed in a large infrared heating oven whose walls are maintained at 700 ºF. The temperature of the air in the oven is 200 ºF and the heat-transfer coefficient for convection between the surface of the sphere and air is 5 Btu/h-ft2 -ºF. Estimate the net rate of heat flow to the sphere when its surface temperature is 100 ºF.