Be careful the fresh air entry is not in a low or negative pressure zone on the roof as you could end up with a double whammy if it starts sucking!
Sorry thought you meant a duct beside your 'exhaust' duct
Quote - "Now that you mention it, an intake duct alongside the exhaust duct would be the best solution"
Here is the link to an earlier discussion on here about cowboy installers with a few useful hints about chimneys etc
Your duct should extend downward from the ceiling to close to the bottom of your woodburner so that you are keeping the hot air inside the room. Your total vent size should also take into account any VMC or other extractor fan(s) you use in the kitchen and W.C/bathroom.
It might be a leaky old house ATM but almost everyone wants to draft proof in the winter!
Back to first principals.
You need a supply of air to burn logs.
Air comes from outside.
Air from the outside is cold
Air indoors is warm
You want to burn cold air and logs to produce heat
Therefore you want the source of the cold air to be as close to the wood burner as possible so that there are no cold drafts.
A vent under the Wood-burner and connected to it would be perfect, so that all the combustion air is supplied from the outside and the heat from the stove warms the room.
The most modern stoves, designed for BBC (Eco) homes, do just that.
Me? I've got a classic Godin (output c 13Kw) with a 180mm chimney and a 160mm air vent from the vide sanitaire immediately beside it. Connected to 230mm twin wall conduit for the hot exhaust where it passes through ceiling and the loft. not all artisans are qualified for the installation and commissioning of log burners. There have been issues with some Anglais experts who quite frankly should be charged with attempted murder for their total disregard of any Standards.