Thermoelectric refrigeration offers advantages (e.g., lack of any moving parts) over other refrigeration technologies. However, because maximum performance (i.e., head load for a specified temperature drop below ambient temperature) and efficiency (i.e., coefficient of performance) are relatively low, it is important to realize them to the extent possible. Here it is shown that although the cross-sectional area of the semiconductor pellets in a thermoelectric module (TEM) does not affect performance or efficiency, it may be sized to tune TEM operating current and voltage. Then, a procedure is provided to determine the (unique) height of the semiconductor pellets and corresponding current flux through them which maximize performance. Next, it is shown that a range of pellet heights accommodates a specified performance below the maximum one and a procedure is provided to compute that corresponding to maximum efficiency. A Robin (thermal resistance) boundary condition is applied between the interface where Peltier cooling in a TEM occurs and the control point where a TEM maintains the temperature of a component or medium below ambient temperature. Robin boundary conditions are also applied between the control point and its local ambient and the interface in a TEM where Peltier heating occurs and its local ambient. The analysis is generalized by using flux based quantities where applicable and the electrical contact resistance at the interconnects in a TEM is accounted for. Flow of heat and charge are considered one-dimensional.

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