Optimization of a thermoelectric heat pump through cascading

A study is presented for the optimization of the coefficient of performance of a thermoelectric heat pump through the use of cascaded stages. Throughout the investigation it is assumed that the electrical and thermal conductivities of the n- and p-type elements are the same and are constant. It is further assumed that there are no electrical or thermal contact resistances and that the element is completely insulated except at the hot and cold junctions. It is shown that small variations about the optimal interstage temperatures have a negligible effect on the C.O.P. of the cascade. In addition it is shown that in many cases only limited gains are made in the C.O.P. through cascaded thermoelectric heat pumps.