Thermal parameter identification for non-Fourier heat transfer from molecular dynamics

Abstract

Please cite this article in press as: A. Singh, E.B. Tadmor, Thermal parameter identification for non-Fourier heat transfer from molecular dynamics, J. Comput. Phys. (2015), http://dx. AbstractFourier'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 nano-scale 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. An implementation of the TPI method in MATLAB is available as part of the online supplementary material.

Removing artificial Kapitza effects from bulk thermal conductivity calculations in direct molecular dynamics

“…The thermodynamic temperature and heat flux are obtained as time averages over the instantaneous values (see details in Ref. 14).…”

“…(1) The thermal conductivity k is calculated for different beam lengths (L m ) and thermostat damping times () using the NEMD direct method (see, for example, Singh and Tadmor 14 ). (2) The data for different k, L m , and are fit to Eq.…”

“…[12][13][14] In the direct method, a temperature gradient is established either by adding a heat flux to the system 15,16 or by maintaining different regions of the system at different temperatures using thermostats. 14,17 The latter approach leads to the discontinuous jumps in temperature described above. Tenenbaum et al 17 observed these phenomena in their early NEMD simulations in dense fluids and proposed pressure and density-based models to quantify the jumps.…”

Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

“…However, one limitation of the Fourier theory is its accuracy, which is deficient for extreme low-temperature or ultra-short-pulse thermal heating in temporal-spatial scale [3][4][5][6]. As a result, non-Fourier heat conduction schemes have been proposed, the simplest of which is Cattaneo-Vernotte (C-V) approach [7,8].…”

Nonequilibrium ab initio molecular-dynamics simulations of lattice thermal conductivity in irradiated glassy Ge2Sb2Te5

“…In practice, the temperature of the boundary region will oscillate significantly and there will be an artificial thermal boundary resistance at the interface with the core region due to the thermostat that is employed in the outer shell. 21,27,28 The Cartesian coordinates of atoms in the core region, x, y and z, reside in the real interval [0, L], where L = a − 2r, a is the size of the periodic cubic simulation box and r is the thickness of the boundary region. Under these assumptions, the resulting heat equation can be written as:…”