Re: flight report
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The standard installation for a carburated engine is to have two heat exchangers. There is a reason for this, and it has worked pretty successfully for thousands of aircraft.
The carb heat should come from a muff clamped around the exhaust pipe, and it open to the lower cowling area. This has an additional advantage because it is taking air that has already received some heat from the engine. The carb heat system does not need the overflow system that cabin heat uses.
Cabin heat should take fresh air from the upper plenum area of the cowling, deliver it through a heat muff, then flow to a diverter valve. It uses fresh air to ensure that any exhaust gases, say from a leaky exhaust gasket, is delivered to the cockpit. As I recall, the carb heat system needs the diverter to prevent hot spots on the exhaust pipe under the cabin heat exchanger which could cause distortion and cracking.
I really think you ought to go to the standard two muff system. Do a Google image search for Exhaust Carb Heat Cabin Heat for lots of examples.
I eliminated my carb heat system when I went to fuel injection.