A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in three-omega method—one of most precise and sensitive techniques for measuring thermal conductivity thin films interfaces—must include bends curves to avoid obstructions on surface a sample. Although analysis assumes that heating wire is infinitely long straight, recent experimental work has demonstrated that, some cases, curved-wire geometries can be without introducing detectable systematic error. We describe general numerical method calculate temperature with arbitrary geometries. This provides experimentalists simple quantitative procedure calculating how large error caused by particular asymmetry will be. show calculations two useful cases: straight single bend angle forms circle. find amplitude in-phase oscillations near circle differs from prediction using analytic straight-line source solution <12%, provided penetration depth less than ten times radius curvature path. The 1.5 widths away 90° within 11% all depths greater width. Our indicate breaks down significantly when 45°.