Hi Mehran- You're asking about various aspects of how temperature differences drive electrical currents. I'll try to answer your specific questions but also give some other background.
1. The picture is of a rod with one hot end and one cold end. It's very unlikely for ordinary rod sizes, etc. that many electrons actually travel from the hot end to the cold end to dump there extra energy. The electrons typically travel less than 1/100000 cm before exchanging energy with their surroundings. So the energy creeps, step-by-step, down from the hot end to the cold end. The electrons make a random walk, not going much of anywhere, rather than flowing systematically. In metals, lattice vibrations also account for a small fraction of the thermal conductivity.
2. If you just have an ordinary metal ring, the answer is no. How would the electrons know whether to go clockwise or counterclockwise?
However, if the ring is made of two different metals then a net current can be generated. One junction between the two metals is hot, the other one cold. If the tendency of each metal to give up electrons depends differently on temperature, electrons will flow from one metal to the other at the hot end and back at the cold end, making a net circuit. This is a pretty ineffective way to generate electrical power, but it is a very good way to generate small signals for use in thermometers. For example, many gas heaters use this system to generate signals to control valves, so the valves only open when the hot end is very hot, which means when the pilot light is burning. This temperature sensing system is called a thermocouple.
Incidentally, if you drive a current around a loop (say, using a battery) where two dissimilar metals make a junction as in a thermocouple, you can convert some of the electrical energy to heat, or, if the current is going the other way, even use the device to cool down one of the junctions of dissimilar metals. This is called the Peltier effect, and is used to cool some electronic components.
3. The current around the loop can't avoid either side. (see 2) There really isn't any significant current loop generated in either arm separately (see 1)
3. (again) So no, in this set-up we don't need a diode. Now you can use diodes between hot and cold resistors to set up a net flow of current around a circuit, but it's very hard to make that an efficient way to convert thermal energy to electrical energy.
5. The electron migration does indeed rapidly come to an end in a rod, after a very very slight shift of electrons down toward the cold end. The heat flow continues. You can think of the electrons as shuttling around on a very small scale. On the average, an electron shuttling between a hot region and a cold region tends to dump more energy in the cold region than it picks up, and pick up more energy in the hot region than it dumps. That's true even when the electrons are shuttling short distances so the temperature differences are small.
Mike W. (and a little bit from Tom)
(published on 10/22/2007)