Heat flow in low pressure, knudsen number

[Flanders3]

Hi! Been lurking around here for a while but joined today :)

My question is about heat transfer in low pressures. I have an object in a vacuum chamber that is much smaller than the mean free path of the air in the chamber. However, the general dimensions of the chamber are much larger than the air mean free path. Heat radiation from the object is easy to calculate but how about conduction/convection to the surrounding air? I'm pretty sure it is low, but how low?

 

[Flanders3]

I thought i couldn't use molecular flow because the air in the chamber is viscous, but I can't use viscous flow either because the air molecules are so likely to 'miss' the heated object.