Research Topic

[Nanoscale Heat Transfer] Topic: Nanoscale Heat Transfer

Team: Amit Singh, Ellad Tadmor

Funding: AFOSR

Figure: A schematic showing heat transfer in a nanoscale bar. A temperature gradient is established by maintaining the two ends at different temperatures using numerical thermostats. As a result, heat flows from the hot end to the cold end. In nanoscale systems, heat propagates as wave with a finite velocity (called second sound) and is therefore better described by a non-Fourier heat transfer model.

Description: Fourier's law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity. In micro- and nanoscale systems, non-Fourier effects involving coupled diffusion and wavelike propagation of heat can become important. An extension of Fourier's law to account for such effects leads to a Jeffreys-type model for heat transfer with two relaxation times. We propose a new Thermal Parameter Identification (TPI) method for obtaining the Jeffreys-type thermal parameters from molecular dynamics simulations. The TPI method makes use of a nonlinear regression-based approach for obtaining the coefficients in analytical expressions for cosine and sine-weighted averages of temperature and heat flux over the length of the system. The method is applied to argon nanobeams over a range of temperature and system sizes. The results for thermal conductivity are found to be in good agreement with standard Green-Kubo and direct method calculations. The TPI method is more efficient for systems with high diffusivity and has the advantage, that unlike the direct method, it is free from the influence of thermostats. In addition, the method provides the thermal relaxation times for argon. Using the determined parameters, the Jeffreys-type model is able to reproduce the molecular dynamics results for a short-duration heat pulse where wavelike propagation of heat is observed thereby confirming the existence of second sound in argon.