heat transfer from a hot gas to a cold gas in bulk mixing

[beavertail]

Caveat: this likely sounds like someone's first year homework but isn't.

I have a reactor venting hot saturated exhaust to downstream treatment and recovery processes. The exhaust requires cooling prior to treatment for reasons of moisture removal and equipment proteciton. I've been talking to my client in terms of vent condensors or some other appropriately specified H/X unit. They are asking me, in turn, why they can't simply educt sufficient ambient air into the exhaust stream (which is under a slight vacuum) such that the blended stream is adequately cooled.

My gut tells me this doesn't work too well, that gas-gas bulk HT will be very inefficient due to low k, poor mixing etc. It seems possible to demonstrate suitability just based on a heat balance but this neglects HT _rate_ and all the variables behind it.

30 textbooks and a long websearch later and I cannot find a relation or even a qualitative discussion of the effectiveness of direct mixing of two gases or how one may estimate the resultant blended temperature.

Any thoughts? Am I just really overcomplicating matters? Conversely, can I get there from here? I'm pretty far down the rabbit hole at this point.

thanks to all.

 

[IRstuff]

Seems to me that you can certainly mix the gases better, with a mixing fan or louvers. Many airplanes mix cold outside air with exhaust air to achieve cooling.

To the first order, you should be able to consider the specific heats of the gases and the relative masses and temperatures to get an idea of how much air you need. Whether your negative pressure is enough to suck the required air is a different question.

TTFN
faq731-376

 

[macmet]

I think you might be over thinking this.

To increase mixing/turbulence you could blow the cooler air against the flow of the exhaust stream you're trying to cool. Or you could try nozzles, similar to overfire nozzles in combustion chambers, that will have high outlet velocity.

I'm sure there are many other options that would work even better.