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Radiation Exchange in a Nonparticipating Medium
a. Based on the analogy of electric resistance network, draw
radiation heat transfer network from surface 1 to surface 2.
b. Determine the cloth (surface 2) temperature.
13.2. A rectangular oven is 1 m wide, 0.5 m tall, and very deep into the
paper and is used to bake a carbon-fiber cloth with an electric
heater at the top. All vertical walls are reradiating (reflectory and
insulated). Take ε 1 = 0.7, ε 2 = 0.9, and ε 3 = 0.8. When 20 kW of
power is supplied, the heater temperature is 650 ◦ C. Neglecting
convection, what is the cloth temperature?
13.3. A cubic furnace (1 m × 1 m × 1 m). During the steady-state operation, the top surface is cooled at 250 ◦ C and the bottom floor is
heated at 1000 ◦ C. The side walls are insulated refractory surfaces.
The view factor between the top and bottom surfaces is 0.2.
a. Determine the net radiation transfer between the top and
bottom surfaces.
b. Determine the temperature of the insulated refractory surfaces.
c. Comment on what effect changing the values of emissivities of
top, bottom, and refractory surfaces would have on the results
of (a) and (b).
13.4. Consider two aligned, parallel, square planes (0.5 m × 0.5 m)
spaced 0.5 m apart and maintained at T 1 = 500 K and T 2 = 1000 K.
Calculate the net radiative heat transfer from surface 1 for the
following special conditions:
a. Both planes are black and the surroundings are at 0 K.
b. Both planes are black with connecting, reradiating walls.
c. Both planes are diffuse and gray with ε 1 = 0.6, ε 2 = 0.8, and
the surroundings at 0 K.
d. Both planes are diffuse and gray (ε 1 = 0.6 and ε 2 = 0.8) with
connecting, reradiating walls.
13.5. A room is 3 m square and 3 m high. The walls can be taken as
adiabatic and isothermal. The ceiling is at 35 ◦ C and has an emittance of 0.8, while the floor is at 20 ◦ C and has an emittance of 0.9.
Denote the ceiling as surface 1, the floor 2, and the walls 3.
a. Set up the radiosity equations. Determine and evaluate all
the shape factors, and tabulate as a 3 × 3 array. Solve these
equations to determine the heat flow into the floor, q 2 .
b. Draw the radiation network. Use the network to obtain an
expression for q 2 , and solve for q 2 again.
13.6. A thin plate (surface area A 1 , emissivity ε 1 , absorptivity α 1 ) is
mounted horizontally facing above a larger horizontal surface
(area A 2 , emissivity ε 2 , absorptivity α 2 ).
a. Give the corresponding thermal radiation network associated
to the problem.
b. Develop an expression without the radiosities for the radiation
heat transfer rate from 1 to 2.
c. What is the limit of this expression when the second surface is
infinite?
d. Let surface 2 be the sky which is a blackbody at a temperature 15 ◦ C cooler than ambient air, which is at 2 ◦ C. The
Radiation Exchange in a Nonparticipating Medium
a. Based on the analogy of electric resistance network, draw
radiation heat transfer network from surface 1 to surface 2.
b. Determine the cloth (surface 2) temperature.
13.2. A rectangular oven is 1 m wide, 0.5 m tall, and very deep into the
paper and is used to bake a carbon-fiber cloth with an electric
heater at the top. All vertical walls are reradiating (reflectory and
insulated). Take ε 1 = 0.7, ε 2 = 0.9, and ε 3 = 0.8. When 20 kW of
power is supplied, the heater temperature is 650 ◦ C. Neglecting
convection, what is the cloth temperature?
13.3. A cubic furnace (1 m × 1 m × 1 m). During the steady-state operation, the top surface is cooled at 250 ◦ C and the bottom floor is
heated at 1000 ◦ C. The side walls are insulated refractory surfaces.
The view factor between the top and bottom surfaces is 0.2.
a. Determine the net radiation transfer between the top and
bottom surfaces.
b. Determine the temperature of the insulated refractory surfaces.
c. Comment on what effect changing the values of emissivities of
top, bottom, and refractory surfaces would have on the results
of (a) and (b).
13.4. Consider two aligned, parallel, square planes (0.5 m × 0.5 m)
spaced 0.5 m apart and maintained at T 1 = 500 K and T 2 = 1000 K.
Calculate the net radiative heat transfer from surface 1 for the
following special conditions:
a. Both planes are black and the surroundings are at 0 K.
b. Both planes are black with connecting, reradiating walls.
c. Both planes are diffuse and gray with ε 1 = 0.6, ε 2 = 0.8, and
the surroundings at 0 K.
d. Both planes are diffuse and gray (ε 1 = 0.6 and ε 2 = 0.8) with
connecting, reradiating walls.
13.5. A room is 3 m square and 3 m high. The walls can be taken as
adiabatic and isothermal. The ceiling is at 35 ◦ C and has an emittance of 0.8, while the floor is at 20 ◦ C and has an emittance of 0.9.
Denote the ceiling as surface 1, the floor 2, and the walls 3.
a. Set up the radiosity equations. Determine and evaluate all
the shape factors, and tabulate as a 3 × 3 array. Solve these
equations to determine the heat flow into the floor, q 2 .
b. Draw the radiation network. Use the network to obtain an
expression for q 2 , and solve for q 2 again.
13.6. A thin plate (surface area A 1 , emissivity ε 1 , absorptivity α 1 ) is
mounted horizontally facing above a larger horizontal surface
(area A 2 , emissivity ε 2 , absorptivity α 2 ).
a. Give the corresponding thermal radiation network associated
to the problem.
b. Develop an expression without the radiosities for the radiation
heat transfer rate from 1 to 2.
c. What is the limit of this expression when the second surface is
infinite?
d. Let surface 2 be the sky which is a blackbody at a temperature 15 ◦ C cooler than ambient air, which is at 2 ◦ C. The