Parameter identification for non-Fourier heat transfer in atomistic systems
Amit Singh (University of Minnesota), Ellad Tadmor (University of Minnesota)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Wed 9:00 - 10:30
CIT 165
The question whether non-stationary heat conduction is adequately modeled by Fourier's model or whether non-Fourier models, such as the Cattaneo-Vernotte or Jeffreys type (dual-phase-lag) models, are necessary has been a matter of discussion. Fourier’s equation only predicts diffusion phenomenon whereas non-Fourier models predict a coupled diffusion-wave response. In this work, using classical Non-Equilibrium Molecular Dynamics (NEMD) experiments, we investigate the process of heat conduction in a three-dimensional atomic beam of finite length, and propose a novel thermal parameter identification (TPI) approach to calculate thermal conductivity of materials. In this approach, Langevin and Nose-Hoover thermostats were used to maintain a temperature gradient so that a heat flux vector would develop within the system. Results of the simulations in the form of spatio-temporal temperature profiles were obtained and a curve fitting procedure based on the Iteratively Re-weighted Least Squares regression method was used to estimate the parameters appearing in the Jeffreys-type model. This helps us calculate not only the thermal conductivity but relaxation times as well which cannot be obtained from the Fourier model alone. The results were compared with and found to be in agreement with two other procedures, Green-Kubo and direct NEMD, and other computational experiments. Of these three approaches, the TPI method described above has the advantage of taking the least amount of simulation time to calculate thermal parameters. This is because the procedure is based on unsteady heat conduction and only a few spatio-temporal profiles are necessary; in contrast for the other approaches the system needs to be brought to steady state which can take a very long time. Finally, the speed of heat waves were measured for the argon beam, and they were found to be in agreement with the prediction of a Jeffreys-type model with parameters obtained using the curve fitting approach.