Thermoelectric devices are in our everyday lives although many of us are not aware of their existence or how they actually function. All thermoelectric devices are powered through what is known as the thermoelectric effect.
This refers to the reaction caused when a difference in temperature creates an electric potential or vice versa. This specifically may be known as the Seebeck effect, the Peltier effect, or the Thomson effect, although each three laws have different specifics. For many materials, this effect is not productive or useful, but in certain materials that have a strong thermoelectric effect they can be used for things such as power generation and refrigeration.
Thermoelectrics generate the electricity from the movement of electrons within a metal. Metals are good conductors because electrons can move freely within them, similar to a fluid in a pipe. Heating one end of a thermoelectric material causes the electrons to move away from the hot end toward the cold end. When the electrons shift from one end to the other they cause an electrical current.
Below shows one generator prototype that uses thermoelectric energy
Although when many people think of thermoelectric devices the word heat comes to mind, thermoelectrics are also key in refrigeration and cooling devices. The Peltier effect was named after the man who discovered that when the electrons of a material are flowing from end to end, heat is absorbed at one end of the junction and released at the other. This process forms the basis for thermoelectric cooling and temperature control, these are currently the widest applications of thermoelectric devices. The device has two sides, and when DC electricity flows through the device, it brings heat from one side to the other, so that one side gets cooler while the other gets hotter. The “hot” side is attached to a heat sink so that it remains at ambient temperature, while the cool side goes below room temperature. In some applications, multiple coolers can be cascaded together for lower temperature.
Resources:
https://powerpractical.com/pages/how-do-thermoelectrics-work
http://thermoelectrics.matsci.northwestern.edu/thermoelectrics/index.html