How to clean the heat exchanger in a tankless water heater

I have a tankless / instant / demand gas water heater. The manual says to clean carbon and oxidation build up from the heat exchanger every 6 to 12 months. My unit has copper pipes which are coated white, but this may be put there to stop heat loss, I'm not sure. The fins in the heat exchanger are coated black and white with oxidation and carbon. How do I clean them. I don't want to use a wire brush, it's not practical. Basically I want to dip it in a solution of something.
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