A 0.61 m radius hemisphere (811 K surface temperature) is filled with a gas mixture containing 6.67 % CO2 and water vapor at 0.5 % relative humidity at 533 K and 2-atm pressure. Determine the emissivity and absorptivity of the gas, and the net rate of radiant heat flow to the gas.
GIVEN
A hemisphere filled with a gas mixture
Hemisphere radius (r) = 0.61 m
Hemisphere surface temperature (T1) = 811 K
Gas temperature (Tm) = 533 K
Gas pressure (pT) = 2 atm
Gas mixture: 6.67% of CO2 and water vapor at R.H. = 0.5%
FIND
(a) The emissivity (?m) and absorptivity (?m) of the gas
(b) The net rate of radiant heat flow to the gas (q1–m)
ASSUMPTIONS
The hemisphere surface is black (?1 = 1)
SKETCH
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant
the saturation pressure of water at 533
(a) The path length for the hemisphere is
For a relative humidity of 0.5% , the partial pressure of the water vapor is
for 1 atm pressure (?H2O)pT=1 = 0.18
This must be corrected for the total pressure
Repeating this procedure for the CO2
Partial pressure
The emissivity of the mixture (? m) is
where is determined by interpolating between values
Therefore
(b) To evaluate the rate of heat transfer, the emissivity and absorptivity must be evaluated at the surface temperature
The total absorptivity is the sum of the H2O and CO2 absorptivities
The rate of heat transfer is
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