Can a furnace/water heater single wall flue be routed into a round clay tile flue that is inside a cement block chimney? Does there have to be an aluminum liner inside the clay tile all the way to the top?
Also the furnace is in the clothes closet of a bedroom.
Can anyone tell me the rules about that?
Yes it should be taken all the way.
Reason is the B vent is sized properly according to the appliance mainly .
Why do you want to route a single wall vent inside a round clay tile flue in a chimney for a furnance. Confused. 
only the newer furnaces require a liner…the flue is not your problem…the closet may be
And the cracked chimney blocks show another problem.
picky deal killer…:mrgreen:
There is a crack in that block chimney and I would be concerned about the failure. As for the sizing it is based on the BTU output and charts are available in the B149 or In your case I would say IFGC International Fuel Gas code. As for the clothes closet it is a not go here for that installation.
Good catch as I assumed B vent on a furnace .
It is B vent double wall and along with a clay tile it is fine as long it does not condense. I believe the Heil SP 80 is not.
Single wall vent into a wall chimney flue mortared in and done.
Now address the problem with the chimney itself.
Kevin, do you know what caused the cracks?:)
Vertical cracking,very interesting.
I would say expansion of the clay tile long before high efficiency was put in place. This is based on what I see and the cap does not have a drip so this may have helped with the expansion forces against the walls of the chimney block.
I still say it is double wall on the SP 80 by looking at the flue connection.
Kevin ,do you consider that furnace to be high efficiency?
I hope that was a typo.
Yes. It would be no different than a rectangular liner provided it is sized properly.
No, it has a clay liner that runs all the way. Correct?
Yes…
Tempstare Furnace? Bought out by Carrier.
Yes to liner, but why.?
Opps!That’s right Bob this one is a SP 80.
The furnace flue & the water heater flue are single wall but the vertical flue that then turns 90 into the masonry is B vent
If it is single wall then it is wrong for the SP 80. How did you determine it was single wall?