Joule heating provides a straightforward and controllable method to convert electricity to heat at a resistive load, and it is used in a wide range of industrial and household systems. While the dissipation of electricity to heat is known to be highly efficient, heat losses at the electrical connection between the heating element and power supply can be significant, especially when considering that effective electrical conductors generally exhibit high thermal conductivities. Here, we present a straightforward derivation, using the Wiedemann–Franz law, to specify optimal designs for contacts in a manner that minimizes heat loss. We quantify the performance of these contacts for systems operating at different temperatures and scales and find that resistively heated microscale systems yield significant heat losses at contacts, and these losses dramatically decrease with increases in system scale. These results offer general guidelines to proper electrical contact design and present a more comprehensive picture of total energy efficiency in resistively heated systems.
Cremers et al. (Mon,) studied this question.