Page 528 - Bird R.B. Transport phenomena

508 Chapter 16 Energy Transport by Radiation

QUESTIONS FOR DISCUSSION

1. The "named laws" in this chapter are important. What is the physical content of the laws as-
sociated with the following scientists' names: Stefan and Boltzmann, Planck, Kirchhoff, Lam-
bert, Wien?
2. How are the Stefan-Boltzmann law and the Wien displacement law related to the Planck
black-body distribution law?
3. Do black bodies exist? Why is the concept of a black body useful?
4. In specular (mirrorlike) reflection, the angle of incidence equals the angle of reflection. How
are these angles related for diffuse reflection?
5. What is the physical significance of the view factor, and how can it be calculated?
{c
{
6. What are the units of q \ q^\ and q f?
7c Under what conditions is the effect of geometry on radiant heat interchange completely ex-
pressible in terms of view factors?
8. Which of the equations in this chapter show that the apparent brightness of a black body with
a uniform surface temperature is independent of the position (distance and direction) from
which it is viewed through a transparent medium?
9. What relation is analogous to Eq. 16.3-2 for an ideal monatomic gas?
10. Check the dimensional consistency of Eq. 16.3-9.

PROBLEMS

16A.1. Approximation of a black body by a hole in a other than the sun may be neglected, and a convection heat
2
sphere. A thin sphere of copper, with its internal surface transfer coefficient of 2.0 Btu/hr • ft • F may be assumed. A
highly oxidized, has a diameter of 6 in. How small a hole maximum temperature of 100°F may be assumed for the
must be made in the sphere to make an opening that will surrounding air. The solar constant of Example 16.4-1 may
have an absorptivity of 0.99? be used, and the absorption and scattering of the sun's rays
Answer: Radius = 0.70 in. by the atmosphere may be neglected.
(a) Solve for a perfectly black roof.
16A.2. Efficiency of a solar engine. A device for utilizing (b) Solve for an aluminum-coated roof, with an absorptiv-
solar energy, developed by Abbot, 1 consists of a parabolic ity of 0.3 for solar radiation and an emissivity of 0.07 at the
mirror that focuses the impinging sunlight onto a Pyrex tube
containing a high-boiling, nearly black liquid. This liquid is temperature of the roof.
circulated to a heat exchanger in which the heat energy is 16A.5. Radiation errors in temperature measurements.
transferred to superheated water at 25 atm pressure. Steam The temperature of an air stream in a duct is being mea-
may be withdrawn and used to run an engine. The most effi- sured by means of a thermocouple. The thermocouple
cient design requires a mirror 10 ft in diameter to generate wires and junction are cylindrical, 0.05 in. in diameter, and
2 hp, when the axis of the mirror is pointed directly toward extend across the duct perpendicular to the flow with the
the sun. What is the overall efficiency of the device? junction in the center of the duct. Assuming a junction emis-
Answer: 15% sivity e = 0.8, estimate the temperature of the gas stream
from the following data obtained under steady conditions:
16A.3, Radiant heating requirement A shed is rectangu-
lar in shape, with the floor 15 ft by 30 ft and the roof 75 ft Thermocouple junction temperature = 500°F
above the floor. The floor is heated by hot water running Duct wall temperature = 300°F
through coils. On cold winter days the exterior walls and Convection heat transfer coefficient
roof are about -10°F. At what rate must heat be supplied from wire to air = 50 Btu/hr • ft -F
2
through the floor in order to maintain the floor temperature The wall temperature is constant at the value given for 20
at 75°F? (Assume that all surfaces of the system are black.)
duct diameters upstream and downstream of the thermo-
16A.4. Steady-state temperature of a roof. Estimate the couple installation. The thermocouple leads are positioned
maximum temperature attained by a level roof at 45° north so that the effect of heat conduction along them on the
latitude on June 21 in clear weather. Radiation from sources junction temperature may be neglected.
16A.6. Surface temperatures on the Earth's moon.
1 (a) Estimate the surface temperature of our moon at the
C. G. Abbot, in Solar Energy Research (F. Daniels and
J. A. Duffie, eds.), University of Wisconsin Press, Madison (1955), point nearest the sun by a quasi-steady-state radiant en-
pp. 91-95; see also U.S. Patent No. 2,460,482 (Feb. 1,1945). ergy balance, regarding the lunar surface as gray. Neglect