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Analytical Heat Transfer
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.
14.6. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 2 × 10 −7 × T ◦ K (KW/(m −
◦ C))
Volumetric radiation extinction coefficient: = 10 −6 m 2 3
β
( /m )
a. Determine the rate of heat loss if one wall is at 500 ◦ K and the
other wall is at 100 ◦ K. Take ε 1 = ε 2 = 0.1, L = 0.2 m.
b. If β = 100 (m 2 /m 3 ), what would be the result in (a)?
14.7. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 1 × 10 −7 × T ◦ K(KW/(m − ◦ C))
Volumetric radiation extinction coefficient: β = 10 −6 2 3
(m /m )
The walls are made of a polished metal, with an emissivity of 0.2.
The gap between the walls is 0.5 m.
a. Determine the rate of heat loss if one wall is at 300 ◦ K and the
other wall is at 100 ◦ K.
b. If β = 100 (m 2 /m 3 ), what would be the result in (a)?
14.8. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 3 × 10 −7 × T ◦ K(KW/(m − ◦ C))
Volumetric radiation extinction coefficient: β = 10 −6 (m 2 /m 3 )
The walls are made of a polished metal, with an emissivity of 0.1.
The gap between the walls is 0.3 m.
a. Determine the rate of heat loss if one wall is at 400 ◦ K and the
other wall is at 100 ◦ K.
b. If β = 100 (m 2 3
/m ), what would be the result in (a)?
14.9. Agas turbine combustion chamber may be approximated as a long
tube of 0.4 m diameter. The combustion gas is at a pressure and
temperature of 1 atm and 1000 ◦ C, respectively, while the chamber
surface temperature is 500 ◦ C. If the combustion gas contains CO 2
and water vapor, each with a mole fraction of 0.15, what is the
net radiative heat flux between the gas and the chamber surface,
which may be approximated as a blackbody?
14.10. Consider a hemispherical furnace, with a reradiating floor and a
water-cooled ceiling, contains 2CO 2 + 8N 2 gases at 1 atm pressure
and 1200 ◦ C. Take ε 1 = 0.9, ε 2 = 0.6, D = 1.5 m, and T 2 = 350 ◦ C.
Determine the radiant heat transfer to the ceiling of the furnace.
14.11. Consider a hemispherical furnace radiation heat transfer problem.
The furnace floor (surface 1) has area A 1 and emissivity ε 1 at temperature T 1 , whereas the furnace enclosure (surface 2) has area
A 2 and emissivity ε 2 at temperature T 2 . If the furnace contains
CO 2 + N 2 gases at 1 atm pressure and temperature T g , determine
Analytical Heat Transfer
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.
14.6. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 2 × 10 −7 × T ◦ K (KW/(m −
◦ C))
Volumetric radiation extinction coefficient: = 10 −6 m 2 3
β
( /m )
a. Determine the rate of heat loss if one wall is at 500 ◦ K and the
other wall is at 100 ◦ K. Take ε 1 = ε 2 = 0.1, L = 0.2 m.
b. If β = 100 (m 2 /m 3 ), what would be the result in (a)?
14.7. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 1 × 10 −7 × T ◦ K(KW/(m − ◦ C))
Volumetric radiation extinction coefficient: β = 10 −6 2 3
(m /m )
The walls are made of a polished metal, with an emissivity of 0.2.
The gap between the walls is 0.5 m.
a. Determine the rate of heat loss if one wall is at 300 ◦ K and the
other wall is at 100 ◦ K.
b. If β = 100 (m 2 /m 3 ), what would be the result in (a)?
14.8. A cryogenic storage chamber has double walls for the purpose of
insulation against heat loss. The gap between the walls is filled
with a gas whose properties are
Thermal conductivity: K(T) = 3 × 10 −7 × T ◦ K(KW/(m − ◦ C))
Volumetric radiation extinction coefficient: β = 10 −6 (m 2 /m 3 )
The walls are made of a polished metal, with an emissivity of 0.1.
The gap between the walls is 0.3 m.
a. Determine the rate of heat loss if one wall is at 400 ◦ K and the
other wall is at 100 ◦ K.
b. If β = 100 (m 2 3
/m ), what would be the result in (a)?
14.9. Agas turbine combustion chamber may be approximated as a long
tube of 0.4 m diameter. The combustion gas is at a pressure and
temperature of 1 atm and 1000 ◦ C, respectively, while the chamber
surface temperature is 500 ◦ C. If the combustion gas contains CO 2
and water vapor, each with a mole fraction of 0.15, what is the
net radiative heat flux between the gas and the chamber surface,
which may be approximated as a blackbody?
14.10. Consider a hemispherical furnace, with a reradiating floor and a
water-cooled ceiling, contains 2CO 2 + 8N 2 gases at 1 atm pressure
and 1200 ◦ C. Take ε 1 = 0.9, ε 2 = 0.6, D = 1.5 m, and T 2 = 350 ◦ C.
Determine the radiant heat transfer to the ceiling of the furnace.
14.11. Consider a hemispherical furnace radiation heat transfer problem.
The furnace floor (surface 1) has area A 1 and emissivity ε 1 at temperature T 1 , whereas the furnace enclosure (surface 2) has area
A 2 and emissivity ε 2 at temperature T 2 . If the furnace contains
CO 2 + N 2 gases at 1 atm pressure and temperature T g , determine