Roger wrote:

I may be venturing into the unknown (or at least somewhere I haven't
been for the best part of 40 years) but the difference between say 290 K
and 287.6 K is just about significant at the 4th power but it pales into
insignificance when the temperature difference is say 15 K.

For small temperature differences (relative to the absolute temperature)
you can forget the fourth-power law and assume that the net heat flow is
proportional to the difference in temperature between the bodies. So a
~2.5 K change in 15 K difference makes about 15% difference in the heat
loss from the warmer body.

No. The warm body in question is the human body that dIMM maintains
loses heat very much faster when the ambient temperature is raised to
compensate for the discomfort caused by having a poorly insulated house.

OK (penny drops) - I see what you were saying now. Yes that does work
in the opposite direction to the radiation argument. I need to go away
and think about this some more...

Well for a start a poorly heated room needs much more heat to keep it up
to temperature than a well insulated room and if that heat is supplied
by a radiator some 40% is probably radient heat. If supplied by a fire
it will of course be a much higher percentage.

Yes, but the source will, in those cases, have a much smaller surface
area than the walls. To work out the net heat flow to any point you'd
need to integrate the radiant flux from all the surfaces 'visible' over
the whole 4*pi of solid angle. This (AIUI) is what leads to the concept
of mean radiant temperature.

Secondly the radiator (if that is the heat source) being considerably
hotter is a much better radiator than the cool walls. If the walls are
say at 16 C, the warm body at 39 C and the radiator at say 60 C I will
leave you to work out what those proportions would mean in degrees K at
the 4th power.

That's easy for plane facing surfaces, otherwise far more tricky:

* 60 C -- 39 C is a net flux of 160 W/m^2 (assuming emissivities of 1)
* 16 C -- 39 C is a net flux of -142 W/m^2.


--
Andy