Question

Consider a round, flat plate in space with a diameter of ( 1 mathrm{~m} ). Half of which is covered by a dome (really half a dome; the half-dome has the same diameter as the plate); the other half of the plate is open to space. Radiation is lost to space, but radiation from space is negligible, so all the radiation absorbed by the plate comes from the dome. The plate is a graybody (emissivity ( = ) absorbtivity) with ( varepsilon=0.6 ). The dome is a blackbody with ( varepsilon=1 ) and has a surface temperature of ( 1000 mathrm{~K} ). a. What is the view factor from the dome to the plate? b. How much heat ( (q) ) is emitted from the half dome in W? Note: this is just the heat emitted (think blackbody radiation). c. How much heat from the half-dome is absorbed by the plate? d. For the plate to be steady state (i.e., at a constant temperature, with q_in = q_out), what is the surface temperature of the plate in ( K ) ? e. Suppose that both surfaces are at the same temperatures ( 1000 for the half dome, your answer to part ( d ) for the plate), but both are blackbodies ( (varepsilon=1) ). In this scenario, what is the net rate of heat transfer from the half dome to the plate?

          Consider a round, flat plate in space with a diameter of ( 1 mathrm{~m} ). Half of which is covered by a dome (really half a dome; the half-dome has the same diameter as the plate); the other half of the plate is open to space. Radiation is lost to space, but radiation from space is negligible, so all the radiation absorbed by the plate comes from the dome. The plate is a graybody (emissivity ( = ) absorbtivity) with ( varepsilon=0.6 ). The dome is a blackbody with ( varepsilon=1 ) and has a surface temperature of ( 1000 mathrm{~K} ).
a. What is the view factor from the dome to the plate?
b. How much heat ( (q) ) is emitted from the half dome in W? Note: this is just the heat emitted (think blackbody radiation).
c. How much heat from the half-dome is absorbed by the plate?
d. For the plate to be steady state (i.e., at a constant temperature, with q_in = q_out), what is the surface temperature of the plate in ( K ) ?
e. Suppose that both surfaces are at the same temperatures ( 1000 for the half dome, your answer to part ( d ) for the plate), but both are blackbodies ( (varepsilon=1) ). In this scenario, what is the net rate of heat transfer from the half dome to the plate?

Consider a round, flat plate in space with a diameter of ( 1 mathrm m ). Half of which is covered by a dome (really half a dome; the half-dome has the same diameter as the plate); the other half of the plate is open to space. Radiation is lost to space, but radiation from space is negligible, so all the radiation absorbed by the plate comes from the dome. The plate is a graybody (emissivity ( = ) absorbtivity) with ( varepsilon=0.6 ). The dome is a blackbody with ( varepsilon=1 ) and has a surface temperature of ( 1000 mathrm K ).
a. What is the view factor from the dome to the plate?
b. How much heat ( (q) ) is emitted from the half dome in W? Note: this is just the heat emitted (think blackbody radiation).
c. How much heat from the half-dome is absorbed by the plate?
d. For the plate to be steady state (i.e., at a constant temperature, with qin = qout), what is the surface temperature of the plate in ( K ) ?
e. Suppose that both surfaces are at the same temperatures ( 1000 for the half dome, your answer to part ( d ) for the plate), but both are blackbodies ( (varepsilon=1) ). In this scenario, what is the net rate of heat transfer from the half dome to the plate?

Added by Hannah G.

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