We devise a finite volume scheme for nonlinear heat transfer in materials with anisotropic thermal conductivity. We focus on the difficulties arising from the discretization of complex domains which are typical in the simulation of industrially relevant processes. For polyhedral domains in two dimensions, we consider Cartesian as well as cylindrical coordinates. Our finite volume scheme is base...

A mathematical model of average nonuniform flow in heterogeneous tratified media is developed. The averaged Darcy's law is obtained by deriving the analytical expression of the effective conductivity tensor for media with small heterogeneities. The fundamental solution of the average flow equation (mean Green function) corresponding to the flow toward a single point source of deterministic disc...

We consider one-dimensional two-phase Stefan problems for a finite substance with different boundary conditions at the fixed faces. The goal of this paper is to determine the behavior of the free boundary and the temperature when the thermal coefficients of the material change. We obtain properties of monotony with respect to the latent heat, the common mass density, the specific heat of each p...

We present simulations using finite-temperature density-functional-theory molecular dynamics to calculate the dynamic electrical conductivity in warm dense aluminum. The comparison between exchange-correlation functionals in the Perdew-Burke-Enzerhof and Heyd-Scuseria-Enzerhof (HSE) approximation indicates evident differences in the density of states and the dc conductivity. The HSE calculation...

We discuss several post-processing issues in molecular dynamics (MD) calculation of lattice thermal conductivity using the Green–Kubo formula. For crystals with high thermal conductivity such as SiC, converting the MD raw data on heat current fluctuations into thermal conductivity result is non-trivial. One can accelerate the process using Fast Fourier Transform and the spectral method. A few m...

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is 3 times as large as that without trigonal warping and 6 times larger than that in single layer graphene. Although the trigonal warping of t...

The effects of exponentially varying viscosity and linearly varying thermal conductivity on unsteady MHD natural convective flow past a semi infinite vertical plate in a thermally stratified medium is studied. The variables of both viscosity and thermal conductivity are considered only a function of temperature. The governing boundary layer equations of continuity, momentum and energy have been...

The inverse problem in 3D eddy current imaging is ill-posed and non-linear. The most commonly used image reconstruction algorithms for electrical imaging are based on a linear approximation (the Jacobian Matrix). We start with an initial conductivity distribution. The forward problem is solved and the predicted voltages compared with the calculated voltages from the Finite Element model. The co...

this research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. heat conduction equation in cylindrical coordinate system is solved. thermal conductivity coefficient is graded along the radial direction. by considering a symmetric distribution of temperature, loading and boundary conditions, strain-displacement and stress-strain relations can b...

work was supported by NIH NCRR Grant No. 5P41RR012553. Abstract— The influence of brain tissue conductivity magnetoencephalography (MEG) has been largely nown. We compared the normal component of the netic field calculated at 61 detectors and the localization racy of 9 different realistic head finite element method ) models containing various gray and white matter uctivities to the results obta...