Optimized performance of a thermoelectric heat pump with surface heat transfer and finite fins

Equations are presented for the steady-state temperature distribution, optimum heat pumping capacity, optimum coefficient of performance, and maximum no-load temperature difference for a single element thermoelectric heat pump with constant properties. Part of the longitudinal surface of the thermoelement is convectively cooled; fins of varying size exist at the hot and cold junctions and three different surface heat transfer coefficients can be arbitrarily selected, one for the hot junction fins, one for the fins at the cold junction, and one for the surface of the thermoelement. It is shown that surface heat transfer can be used to substantially increase the heat pumping capacity and, in some cases, the coefficient of performance is improved. The effect of fin size at the junctions of the thermoelement on performance is shown. An example is presented in which optimized performance curves are compared for devices using fins with infinite and finite conductance and where the thermoelements have varying amounts of surface heat transfer. The results given are presented in dimensionless form so that they apply for many different conditions. The results show that gains in heat pumping capacity of the order of 300–400 per cent are possible.