293
Radiation Transfer through Gases
gas temperature; cylindrical or spherical furnace geometry; nongray gases;
nongray nondiffuse surfaces; gases with scattering particulates and soot formation; and sphere fillet or fiber porous medium. These topics belong to
advanced radiation transfer.
PROBLEMS
14.1. A hemispherical furnace is shown in Figure 14.7. If the furnace
contains CO 2 + N 2 gases at 1 atm pressure and temperature T g ,
determine the total radiation heat transfer from gases to surfaces 1 and 2 (assume T g > T 1 > T 2 , and make other necessary
assumptions).
a. Based on the analogy of electric resistance network, draw a
radiation heat transfer network from gases to surfaces 1 and 2.
b. Determine the total radiation from gases to surfaces 1 and 2.
The final solutions should be the function of given temperatures, surface area, and radiation properties.
14.2. A hemispherical furnace is shown in Figure 14.7.
a. If the furnace contains N 2 gas at 5 atm pressure, determine the
net radiation heat transfer from surface 1 to surface 2 (assume
T 1 > T 2 , and make other necessary assumptions).
b. If the furnace contains CO 2 + N 2 gases at 5 atm pressure and
temperature T g , determine total radiation heat transfer from
gases to surfaces 1 and 2 (assume T g > T 1 > T 2 , and make
other necessary assumptions).
c. Reconsider (b), if surface 1 now is a reradiating surface, determine the total radiation heat transfer to the surface 2 of the
furnace. In this new condition, comment on whether the radiation transfer to surface 2 will be higher, the same, or lower
than that of (b) (make necessary assumptions).
14.3. A long hemicylindrical furnace is shown.
a. Determine the net radiation heat transfer from surface 1 to
surface 2, q 12 .
b. If T 2 = T 2 (θ), describe how to determine q 12 .
c. Consider combustion gray gas with a uniform temperature T g
and emissivity ε g inside the furnace, and determine the total
radiation heat transfer from gas to surfaces 1 and 2, q g . Assume
T 1 , T 2 constant.
14.4. A hemispherical furnace, with a reradiating floor and a watercooled ceiling, contains CO 2 and N 2 gases at 1 atm pressure
and 1000 ◦ C. Take ε 1 = 0.8, ε 2 = 0.7, D = 1 m, and T 2 = 500 ◦ C.
Determine the radiant heat transfer to the ceiling of the furnace.
Assume gray gases.
Given: σ = 5.67 × 10 −8 (w/m 2 K 4 ).
Volume of a sphere = (4/3)π((1/2)D 2
)
Surface of a sphere = 4π((1/2)D 2
)
14.5. A hemispherical furnace, with a reradiating floor and a watercooled ceiling, contains 2CO 2 and 8N 2 gases at 1 atm pressure
Radiation Transfer through Gases
gas temperature; cylindrical or spherical furnace geometry; nongray gases;
nongray nondiffuse surfaces; gases with scattering particulates and soot formation; and sphere fillet or fiber porous medium. These topics belong to
advanced radiation transfer.
PROBLEMS
14.1. A hemispherical furnace is shown in Figure 14.7. If the furnace
contains CO 2 + N 2 gases at 1 atm pressure and temperature T g ,
determine the total radiation heat transfer from gases to surfaces 1 and 2 (assume T g > T 1 > T 2 , and make other necessary
assumptions).
a. Based on the analogy of electric resistance network, draw a
radiation heat transfer network from gases to surfaces 1 and 2.
b. Determine the total radiation from gases to surfaces 1 and 2.
The final solutions should be the function of given temperatures, surface area, and radiation properties.
14.2. A hemispherical furnace is shown in Figure 14.7.
a. If the furnace contains N 2 gas at 5 atm pressure, determine the
net radiation heat transfer from surface 1 to surface 2 (assume
T 1 > T 2 , and make other necessary assumptions).
b. If the furnace contains CO 2 + N 2 gases at 5 atm pressure and
temperature T g , determine total radiation heat transfer from
gases to surfaces 1 and 2 (assume T g > T 1 > T 2 , and make
other necessary assumptions).
c. Reconsider (b), if surface 1 now is a reradiating surface, determine the total radiation heat transfer to the surface 2 of the
furnace. In this new condition, comment on whether the radiation transfer to surface 2 will be higher, the same, or lower
than that of (b) (make necessary assumptions).
14.3. A long hemicylindrical furnace is shown.
a. Determine the net radiation heat transfer from surface 1 to
surface 2, q 12 .
b. If T 2 = T 2 (θ), describe how to determine q 12 .
c. Consider combustion gray gas with a uniform temperature T g
and emissivity ε g inside the furnace, and determine the total
radiation heat transfer from gas to surfaces 1 and 2, q g . Assume
T 1 , T 2 constant.
14.4. A hemispherical furnace, with a reradiating floor and a watercooled ceiling, contains CO 2 and N 2 gases at 1 atm pressure
and 1000 ◦ C. Take ε 1 = 0.8, ε 2 = 0.7, D = 1 m, and T 2 = 500 ◦ C.
Determine the radiant heat transfer to the ceiling of the furnace.
Assume gray gases.
Given: σ = 5.67 × 10 −8 (w/m 2 K 4 ).
Volume of a sphere = (4/3)π((1/2)D 2
)
Surface of a sphere = 4π((1/2)D 2
)
14.5. A hemispherical furnace, with a reradiating floor and a watercooled ceiling, contains 2CO 2 and 8N 2 gases at 1 atm pressure