From the dimension you give, the vertical height of the back of the hood is about 12". Deducting about 2" (more or less ?) from the bottom for the grease rail & to clear inside edge of the filters leaves 10" to install a fan. The fan opening needs to be framed with an angle to match as required for the fan. .... I don't see a fan larger than 8" can fit into the plenum, may be smaller. The fan you linked to is 14" diameter. The only way for that fan can work is to mount to the side of the hood with a larger plenum box connected by a duct (8" diam) to the end of the hood. ... Assuming wall mounted fan & shutter since that is the type linked to.
From the length of the hood, I think you only need 400 to 800 CFM of exhaust air. ... You stated the 45,000 BTU/per hr for the propane; then 45000/10000 X100 CFM = 450 CFM ???
post edited by edwmax - 2011/12/08 16:59:22