Why are extended surfaces or fins are the best method to increase the heat transfer from hot surfaces to the surroundings?
Ans: The rate of heat transfer from a surface at a temperature Ts to the surrounding medium is given by Newton's law of cooling as
it can be seen that both temperature of the surface of the body and the surrounding medium temperature are fixed by design. That is we don't have much control over these two quantities because the surrounding temperature can not be changed easily (usually it is atmospheric temperature) and the surface temperature of the body is dependent on the application area for example the electronic circuit temperature is dependent on the heat generated inside the body.
The second option is to increase the heat transfer coefficient h by using an external machine like a pump or fan but it increases the overall cost of the system and hence sometimes it becomes impractical.
Now, the third and cheaper option is to increase the surface area which is nothing but extended surfaces called fins. These fins are made up of highly conductive material. Due to higher surface areas, the convection heat transfer increases significantly.
Hence, According to Newton's law of cooling above, if we attach more and more fins to the plane surface the heat transfer area increases and in turn the heat transfer also increases.(upto certain economical limit)