Liquid cooled engines have channels that go through them that allow liquid to travel via something called a water pump. As the liquid goes through the channels, it picks up heat generated from the engine and then it is deposited at the top of the radiator. The liquid then drains to the bottom while the fins in the radiator spread the heat to a large area and is blown on by the radiator fan and air coming in from driving. The cooler liquid is then shot through the engine again with the water pump and the whole process starts again.
A common problem with engines is sludgy oil / coolant, there is a failure somewhere (all the moving parts in an engine sit in what is essentially a bath of oil except for the combustion chambers) which is allowing the coolant that moves through the engine to mix with the oil.
Not all engines are liquid cooled, Lycoming and Continental produce 4 and 6 cylinder horizontally opposed engines that are entirely air cooled. They can do that because there is a huge prop that acts as a fan *and* as the airplane goes up in altitude the air cools significantly, making liquid cooling mostly unnecessary.
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