Cooled walls

sparrow

in a conserved scalar combustion model of a flame in a chamber, how can i deal with cooled walls?

as the mixture fraction is conserved i dont think i can just set this to a particular value at the boundary as this will not be consistent. i think i have to use a zero gradient assuption at the wall.

also anything i do to the scalar at the wall must also surely implicate the other species that are related to the mixture fraction?

is the answer to make the temperature no longer a function of mixture fraction? if this is the case can the other speicies still be a function of the mixture fraction, as surely the temperature change will effect the burning, so how does the temperature changes feed back to the species?

any help would be great.