Thermoacoustic modeling and uncertainty analysis of two-dimensional conductive membranes

Abstract

A model for two-dimensional graphene-based thermoacoustic membranes is investigated analytically and numerically validated using Bayesian statistics in this study. The temperature and the pressure variables are first analytically determined in one-dimension by noticing that the magnitude of the pressure time derivative is small in the heat transfer equations and by taking advantage of the large disparity between the length scales. The one-dimensional findings are then extended to three-dimensions, where pressure fluctuation produced by the surface temperature variation is determined using an acoustic piston model. Through the one and three-dimensional model analysis, the dependence of acoustic pressure as a function of frequency is studied. The acoustic response with respect to the frequency shows different characteristics when assuming Dirichlet (temperature) or Neumann (heat flux) boundary conditions. The thermoacoustic model is validated with a graphene-on-paper loudspeaker using Bayesian statistical methods and a Delayed Rejection Adaptive Metropolis algorithm to identify model parameters and their uncertainty. The findings provide insights into the heat transport mechanisms associated with sound generation from thermally cycling thin conductive membranes at high frequencies. V

Free-Standing Graphene Thermophone on a Polymer-Mesh Substrate

“…This dramatic increase of the SPL can be mathematically expressed in terms of the thermoacoustic model, which predicts the change of the sound pressure using the heat transferred from a graphene conductor. Although there are several models based on partial differential equations, the various assumptions and constraints introduced to solve the differential equations cause discrepancies between the calculation and actual measurement data . To tackle this problem, Dascheski et al recently proposed a model based on the fact that sound pressure from the thermoacoustic loudspeaker is proportional to the amount of transferred heat energy to fluid, and inversely proportional to the transferred volume of the heat in the fluid .…”

SonoTweezer: An Acoustically Powered End-Effector for Underwater Micromanipulation

“…A derivation of (2) from the original form of Gor'kov potential is described in supplementary information (SI) Appendix A. Next, we approximate the acoustic pressure generated by our immersible transducers with a flat piston source model [31]. Given the number of transducers (N t ) in a hemispherical array, assigned with a normalized pressure constant ( p 0 ), the overall pressure field can be computed based on the superposition principle [11].…”

Graphene‐Based Devices for Thermal Energy Conversion and Utilization

“…Different from the traditional speaker, the sound‐emitting device with thermoacoustic effect can realize the vibration‐free sound of the conductive film itself, and it is expected to realize the acoustic output of the wide‐band. The thermoacoustic effect physical process can be described as that when alternating current signals pass through a thin conductor film, Joule heat is generated and rapidly transmitted to the surrounding air medium, and the temperature of the metal surface periodically rises and falls, heating a thin layer of air molecules on the conductor surface . Expansion and contraction occur, which in turn produces sound waves.…”