Two infinitely large black plane surfaces are 0.3 m apart and the space between them is filled by an isothermal gas mixture at 811 K and atmospheric pressure consisting of 25% CO2, 25% H2O, and 50% N2 by volume. If one of the surfaces is maintained at 278 K and the other at 1390 K respectively, calculate

Question

(a) the effective emissivity of the gas at its temperature

(b) the effective absorptivity of the gas to radiation from the 1390 K surface

(c) the effective absorptivity of the gas to radiation from the 278 K surface

(d) the net rate of heat transfer to the gas per square meter of surface area

GIVEN

Two infinitely large black plane surfaces with an isothermal gas mixture between them

Distance between surfaces (s) = 0.3 m

Gas mixture temperature (Tm) = 811 K

Gas mixture pressure = 1 atm

Gas contents: 25% CO2, 25% H2O, 50 % N2 by volume

Surface temperatures

T1 = 278 K

T2 = 1390 K

FIND

(a) The effective emissivity of the gas at its temperature (? mix)

(b) The effective absorptivity of the gas to radiation from A1

(c) The effective absorptivity of the gas to radiation from A2

(d) The net rate of heat transfer to the gas per square meter of surface are (qm/A)

ASSUMPTIONS

Steady state

Convection is negligible

SKETCH

Answer 1

(a) The partial pressures of the CO2 and H2O are both 0.25 atm. The equivalent mean hemi- spherical beam length, L, is













(b) To find the absorptivity to radiation from A1, the emittances of the H2O and CO2 must first be evaluated at T1 = 278 K.

Using the procedure shown above with:









Applying



(c) Repeating this procedure for T2 = 1390 K and pH2O L (Ts/TH2O) = 0.257



(d) The rate of heat flow from the gas to A1 is



The rate of heat flow from the gas to A2 is



The net rate of heat transfer from the gas is