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I wonder if using radiating surface on the inside of a ducted fan to dispel the waste heat of an engine would provide an economic advantage by increasing thrust? Since a typical engine “wastes” some 40% of its energy as heat could it not be used to expand the air going through the duct a little like a jet?

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That's basically what happens with the radiator on the P-51. It uses the Meredith effect to use the heat from the radiator to provide a small amount of thrust.

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