Cylindrical heat conduction and structural acoustic models for enclosed fiber array thermophones

Calculation of the heat loss for thermophone heating elements is a function of their geometry and the thermodynamics of their surroundings. Steady-state behavior is difficult to establish or evaluate as heat is only flowing in one direction in the device. However, for a heating element made from an array of carbon fibers in a planar enclosure, several assumptions can be made, leading to simple solutions of the heat equation. These solutions can be used to more carefully determine the efficiency of thermophones of this geometry. Acoustic response is predicted with the application of a Helmholtz resonator and thin plate structural acoustics models. A laboratory thermophone utilizing a sparse horizontal array of fine (6.7 μm diameter) carbon fibers is designed and tested. Experimental results are compared with the model. The model is also used to examine the optimal array density for maximal efficiency.