Admittedly, my understanding of thermodynamics has not progressed much beyond the 2nd grade level (aside from a class on PDEs giving me at least some enhanced intuition). My takeaway from the PDE class was that anything beyond a simple textbook problem needs to be simulated and/or observed experimentally, rather than solved for analytically.

But other things being equal, wouldn’t cold air permeate a less dense barrier (say a layer of insulation in a home) more easily than a dense barrier? Just as water (or cold air) would permeate soil more readily than rock.