We have a sunroom with no chimney and have a wood burning stove in it - provides great heat!!
You can run a flue straight up and out through the ceiling and roof tiles.
You need to use twin wall flue going through the ceiling and on the outside. Can use single wall between the stove & the ceiling and I'd recommend this as the flue itself emits quite a lot of heat too - no point in wasting it!!
You'll also need some sort of fire box that sits between the ceiling and the roof tiles - it kind of keeps the flue away from direct contact with the ceiling slabs.
On the outside you'll need some sort of flashing to fit in with the tiles so that you don't have any leaks.
If you're based anywhere near the Meath area, I'd recommend you give Mi-Flues in Summerhill a shout - I've no connection with them but found them very helpful. I'd imagine they'd visit and inspect before you buy anything.
Any other questions, feel free to ask.
PS. be prepared, the twin wall flue is expensive and there are building regs to adhere to with regards to height of flue outside relative to surrounding roof.