A Irradition to base of cylindric gray gas volume

[M_1]

TL;DR Summary

What is the irradiation [W/m2] to the base of a cylinder with gray gas?

Anyone who has an idea for how to calculate the irradition [W/m2] to the base of a cylinder with radius R, height H, absorption coefficient k, and temperature T? I've looked at the approach with mean beam length by Hottel but cannot figure out what to do when it is the base of the cylinder that is the area of interest. Any help would be very much appreciated.

 

[berkeman]

Summary:: What is the irradiation [W/m2] to the base of a cylinder with gray gas?

Anyone who has an idea for how to calculate the irradition [W/m2] to the base of a cylinder with radius R, height H, absorption coefficient k, and temperature T? I've looked at the approach with mean beam length by Hottel but cannot figure out what to do when it is the base of the cylinder that is the area of interest. Any help would be very much appreciated.

Sorry, what is "irradition"? Do you mean irradiation? If so, what sort of radiation? Light, particles, other?

And if light, is the issue the multiple path lengths that are taken from the illumination point at the top of the cone down to the flat base area? But you seem to be asking about a cylinder instead of a cone -- is the light collimated when entering the top surface of the cylinder?

Can you attach a sketch or figure of the problem?

 

[M_1]

Thanks for answer and sorry for not being clear. I mean a gray gas that emits thermal radiation. So the thermal radiation is created inside the cylinder and I need to figure out the irradiation hitting the base of the cylinder. So there is no collimated light and no light entering the cylinder.

 

[berkeman]

What exactly is "gray gas"? How transparent it it to IR? What is the mechanism for this gas emitting IR radiation?

 

[M_1]

The gray gas is a fire. So the emitting parts are mainly CO2, H2O and graybody radiation from soot.