If you take a Cold wet face cloth and hold under a hot tap, why does cold water first flow out before the hot water. why doesnt hot water warm the cold water?
It takes time for the two layers of water, hot and cold, to mix and reach thermal equilibrium. Each molecule has to exchange thermal energy upon contact with adjacent molecules and then those molecules have to move to come into contact with other molecules. This is a process of convection.
In the time required for the water to reach thermal equilibrium the cold water has already been pushed through by the hot water behind it.
The transition from hot to cold is gradual and depends on the flow of the water. As the face cloth is already wet with cold water, any additional water running into the facecloth will supersaturate it resulting in a runoff of mainly cold water as that is what's in the cloth. The hotter water indeed mixes with the cold and for a few seconds it is at an intermediate temperature between cold and hot. After that the hot water has saturated the cloth so much that there is no cold left in the cloth and the runoff becomes hot.