An analysis of electrothermodynamic heating and cooling

Abstract

Current advances in semiconductor manufacturing have brought about an increasing use of thermoelectricity in a variety of applications. Most of these applications, however, have involved the steady state application of this phenomenon. As a result, few have considered the transient aspect of this field (Gray 1960). In recent years there has been an increasing demand to heat and cool objects very quickly. One particular proposal to use the transient nature of thermoelectricity was made by Lagoudas and Kinra (I 993) in regard to shape memory alloy (SMA) actuators. In general, SMA actuators have been largely limited by the rate that heat may be extracted from the SMA. In their investigation, they proposed the concept of using the SMA directly as the cold junction of a thermocouple. By way of the Peltier effect, then, heat could be added or removed at the interfaces at a rate proportional to the current density and local temperature; by increasing the current, the rate of cooling would be increased, albeit at the expense of the Joule heating within the conductor. This investigation explores the dynamic nature of thermoelectrically cooled/heated regions in effort to gain a greater understanding of the transient application of thermoelectricity, including the role of the surrounding material properties. To this end, we consider a pair of semi-infinite rods of equal cross-sectional area in perfect thermoelectric contact. At time t = 0, a DC current begins to flow in the axial direction. The electrothermodynamic response of the composite rod at the interface is calculated. The transient interface temperature is completely described by a single dimensionless parameter called the MOET number (Modulus Of ElectroThermodynamics). Perhaps the most interesting result is that the minimum temperature at the interface is independent of the current density. Of course, the time required to reach this minimum temperature does depend on the current density; it varies as 1/J2.