8.11 Equation of transfer or radiative transfer equation (RTE) 293

FIGURE 8.37

Two-dimensional, gray-diffuse evacuated enclosure considered in exercise problem 8.10.

respectively. The inner and outer tube surfaces are maintained at 260 K and 300 K, respectively.

aDetermine all the view factors for this two surface enclosure.

bDetermine the net radiation heat transfer between the two surfaces.

8.10A two-dimensional, gray-diffuse evacuated enclosure (with no heat transfer to outside), as shown in Fig. 8.37, has all the surfaces maintained at uniform tem-

perature. Relevant details are given below.

Surface 1: T1 = 1400 K, L1 = 3.0 m, ε1 = 0.50. Surface 2: T2 = 300 K, L2 = 2.4 m, ε2 = 0.95. Surface 3: T3 = 800 K, L3 = 3.8 m, ε3 = 0.15.

a Calculate all the view factors for this three-surface enclosure. b Determine the net radiation heat transfer from all the surfaces. c Verify energy balance.

8.11Consider two spheres with diameters 0.5 and 0.25 m that are placed concentrically as shown in Fig. 8.38. The surface emissivities of the outer and inner spheres are 0.4 and 0.7, respectively. The temperatures of the outer and inner spheres are maintained at 303 and 404 K, respectively. Answer the following questions:

a.Net heat transfer from the inner to the outer sphere.

b.Will there be any change in the heat transfer rate by altering the position of the inner sphere?

FIGURE 8.38

Radiation involving concentric spheres under consideration in problem 8.11.

294CHAPTER 8  Thermal radiation

8.12A mixture of 40% of H2O and 50% of CO2 and 10% of NO2(by volume) at a temperature of 2000 K and a total pressure of 1 atm is contained in a furnace in the shape of a cuboid of dimensions 1 m × 2 m × 1.5 m. The inside walls of the furnace are black, with the wall temperature being 1200 K.

a.Determine the emissivity of the gas mixture.

b.Determine the absorptivity of the gas mixture.

c.Determine the radiation heat transfer to the walls of the furnace.

8.13Repeat problem 8.12 for the case of a total pressure of 2 atm.

References

Balaji, C., 2014. Essentials of Radiation Heat Transfer. John Wiley and Sons, NJ, USA. Hottel, Hoyt C., 1954. Radiant heat transmission. Heat Transmission. WH McAdams,

New York.

Leckner, B., 1972. Spectral and total emissivity of water vapor and carbon dioxide. Combust, Flame 19 (1), 33–48.