A model for two-dimensional graphene-based thermoacoutic membranes is investigated analytically and validated numerically in this study. In one-dimension, the temperature and the pressure variables are analytically determined by decoupling the two variables in the governing equations due to the large disparity between length scales. We further extend the one-dimensional findings to three dimensions. The three-dimensional pressure fluctuation produced by the surface temperature variation is determined with the aid of the acoustic piston model. Through the one and three-dimensional model analysis, the dependence of acoustic pressure as a function of frequency is studied and the acoustic response with respect to the frequency shows different characteristics when assuming Dirichlet (temperature) or Neumann (heat flux) boundary conditions. The general thermoacoustic model is then applied to a graphene-on-paper sound device. Probabilistic Bayesian method coupled with Monte Carlo Markov Chain (MCMC) algorithms is used to optimize model parameters and to analyze model parameter uncertainty. Excellent correlations of thermoacoustic behavior is predicted by the model which provides insight into heat transport mechanisms associated with generating sound from thermally cycling graphene at high frequencies.

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