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Default Calculating radiator size for awkward room

I posted a while ago with requests for help about insulating the sloping
roof of my daughter's bedroom - thanks for all the help: plasterer
finished yesterday and all looks hunky dory (hopefully so will my gas
bill next spring).

Anyway - now I need to install a new, appropriately-sized radiator.
Trouble is I've tried a few "calculators", however they don't cover the
complex shape structure of the room; cross-section looks like this
(except the slopey bits are shallower than this):

________
/ \
/ \
/ \
| |
|____________|

Also there's a dormer window built into one side of the room.

For example:

- The slopey ceiling is made up of 2mm plaster/9mm plasterboard/50mm
polystyrene/50mm Kingspan/0 sarking/clay tiles.

- Flat ceiling is 20mm lath-and-plaster/200mm Rockwool

- Vertical external walls are 2mm plaster/9mm plasterboard/50mm
polystyrene/50mm Kingspan/200mm solid brick

I'm sure your average heating engineer would just eyeball the room and
fit any old rad he knew would be at least OK, however I'd like to get it
reasonably right! How do I go about this?

Thanks
David
 
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