Once the thermostat has opened, the hot coolant flows from the thermostat housing on the engine into the top of radiator and out the bottom of the radiator back into the water pump.
Open the radiator drain and let drain into a catch basin. Run water through the radiator by filling through the radiator cap with a hose till the water coming out is clear. Fill through the overflow bottle if there is not a radiator cap present.
The radiator fan may be smoking on your Mustang if there is a radiator leak. You will need to check the radiator to make sure there is enough water and fluid inside.
from the top to the bottom
Coolant is sucked in from the lower radiator hose, pumped into both sides of the block, through the block, up into both heads, through the heads, out the front of both heads into the intake manifold, out through the thermostat housing, into the upper radiator hose and back into the radiator. All coolant connections on the exterior of the water pump are return/suction.
The water does not flow through the radiator until the engine is at operating temperature. At that time the thermostat will open and allow it to flow.Sometimes you are unable to see it, depending on the direction of flow. Increase the engine rpm and you should notice a change.
Are you sure it's pumping in the wrong direction? It should be pulling water from the radiator through it's lower hose. Water will be returning to the radiator through the upper hose past the thermostat after it warms up. If your water is flowing the wrong direction and you have a mechanical pump ( one with a belt on it ) you will have to replace it. If you have a uni-belt setup (serpentine belt), it may be on incorrectly. If you have an electrical water pump ( probably aftermarket ) reverse the polarity on the power connection.
The water pump humps cool water from the radiator through the engine. Hot water. Leaves the engine and enters the top of the radiator. The hot water works its way through the radiator cooling itself.
Your radiator fan. It may have a thermostat on it that lets it turn on and off to cool the water in the radiator when needed. They can be quite noisy.
Remove the bottom radiator hose. Stick a hose in the top of the radiator. Turn the water on. Allow the water to run through the radiator and out the bottom of the radiator.
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When the thermostat is open the coolant will flow through the top radiator hose in to the radiator and out to the water pump through the bottom radiator hose
Water jackets are the hollowed out spaces in the engine block and head through which the coolant flows. In water jackets, waste heat generated by the engine is picked up by the coolant. After flowing through the water jackets, water flows through the radiator. The radiator is basically a heat exchanger which, through a system of tubes and fins, transfers this waste heat from the coolant to the atmosphere. After the water is cooled in the radiator, it flows back into the water jackets of the engine to pick up more waste heat.