Step 1 - Understanding the types of heat transfer
There are three types of heat transfer: conduction, convection and irradiation. Let's see how each one works:
a) Conduction: is when a very hot substance enters in contact with a cooler substance. The atoms in the hotter substance are moving with a greater velocity and will therefore collide with the atoms of the cooler substance.
b) Convection: it happens especially in liquids and air (fluids). The liquid is warmed up at the bottom first, via conduction. The heated bottom thus changes its density: it becomes less dense, and go up. This process repeats itself several times, warming the whole liquid.
c) Irradiation: when something is put near a heat source, but do not touch it directly. In this case, there's no direct atom collision, but indirect: the rapid atoms of the heat source collide with atoms in the air which then collide with the atoms in the object that is being heated.
Step 2 - Discovering the type of heat transfer in each scenario
In the first scenario, the water at the bottom is in direct contact with the pan. Therefore, water molecules will directly collide with "pan" molecules (probably aluminum atoms or other materials). But there's also convection. The water is not heated only by conduction.
In the second scenario, the hands are near the Bunsen burner, but not directly touching it. What is happening here is then heat irradiation, not conduction.
In the third scenario, the hand is touching the object (the handle of the pan). Even though handles are made of material that poorly conduct heat, it will increase its temperature, at least a little bit. When we touch it, we can feel it is hotter than before. In this case, only conduction is involved (from the handle to our hand). In this case atoms are directly colliding and this is the only source of heat.
Finally, in the last scenario, we also have a case of irradiation: the pan with water is near the heat source, but not directly touching it.
Step 3 - How to set an experiment
In science in general, anytime we want to investigate some effect it is good manners to investigate a system controling all other effects. We want to investigate a variable at a time.
Therefore, while both scenario 1 and 3 involve conduction, scenario 1 also involves convection, which could be a problem to a experiment intending to study conduction only.
The best experiment would be then scenario 3, hands touchind the handle of pan siting in a Bunsen burner.
