Two test tubes full of water are heated -one from below and the other from near the top. In which case will the water heat up faster and why?

The test tube heated from below will heat up faster.

We know that hot water rises up. So, as the hot water will rise up, cold water from top will take it's place. 

We know that that if the temperature difference is more, heat conduction is faster. So, in case of the test tube heater from below, the heat transferred will be higher as the water will move away after being heated up constantly and cooler water will keep coming down.