Innovative Approaches to the Thermal Conductivity Tensor in Ionospheric Plasma of the Northern Hemisphere’s F-region

Dispersion relations and sum rules for the transport coefficients of dilute ionized gases in a magnetic field

Investigations on thermal transport in cross-linked elastomers subjected to elongational deformations are reviewed and discussed. The focus is on experimental research, in which the deformation-induced anisotropy of the thermal conductivity tensor in several common elastomeric materials is measured using novel optical techniques developed in our laboratory. These sensitive and noninvasive techniques allow for the reliable measurement of thermal conductivity (diffusivity) tensor components on samples in a deformed state. When combined with measurements of the stress in deformed samples, we are able to examine the validity of the stress–thermal rule, which predicts a linear relationship between the thermal conductivity and stress tensor in deformed polymeric materials. These results are used to shed light on possible underlying mechanisms for anisotropic thermal transport in elastomers. We also present results from a novel experimental technique that show evidence of a deformation dependence of the heat capacity, which implies that, in addition to the usual entropic contribution, there is an energetic contribution to the stress in deformed elastomers.

We compared the conductivity tensor becoming important parameter of ionospheric plasma using the real geometry of Earth’s magnetic field in the Northern hemisphere for both cold and warm ionospheric plasma for equinox days. It could be that the conductivity tensor certainly depends on the vector of wave propagation (k) and the adiabatic sound speed (Ue) in warm ionospheric plasma and it is possible to say that the adiabatic sound speed for electron generally decreases the magnitudes of conductivity tensor components with respect to the cold ionosphere plasma except for $$\sigma_{{ 2 3 {\text{R}}}}^{\prime }$$ (Ue ≠ 0) = $$\sigma_{{ 2 3 {\text{R}}}}$$ (Ue = 0), $$\sigma_{{ 3 3 {\text{R}}}}^{\prime }$$ (Ue ≠ 0) = $$\sigma_{{ 3 3 {\text{R}}}}$$ (Ue = 0), $$\sigma_{{ 1 3 {\text{S}}}}^{\prime }$$ (Ue ≠ 0) = $$\sigma_{{ 1 3 {\text{S}}}}$$ (Ue = 0) and $$\sigma_{{ 3 3 {\text{S}}}}^{\prime }$$ (Ue ≠ 0) = $$\sigma_{{ 3 3 {\text{S}}}}$$ (Ue = 0). In this sense, the resistivity and reactance increase in ionospheric plasma. In this context, according to the accepted conditions, the change of conductivity with local time is similar to change of electron density with local time for both (cold and warm) conditions in ionospheric plasma as trend.

Comprehensive measurement of three-dimensional thermal conductivity tensor using a beam-offset square-pulsed source (BO-SPS) approach

The lattice thermal conductivity for bulk β-Ga2O3 is computed from the phonon Boltzmann transport equation using first-principles methods to obtain scattering rates. Force constants for both the second and third order potential interactions are computed with a real-space finite-displacement approach. Phonon band structures as well as anharmonic properties are then computed and used to calculate the bulk thermal conductivity tensor κ, for temperatures ranging from 25 K to 1050 K. The calculated conductivity tensor components and analytic fits to their temperature dependences are elaborated. We compare our results with available data and show good agreement with experimentally observed values. Decomposing κ into mode contributions reveals that optical phonon modes contribute significantly to the overall thermal conductivity, as much as 44% at 300 K in the [010] direction, which differs from previous interpretations of experimentally observed thermal conductivity tensor anisotropy.

We have calculated the thermoelectric conductivity tensor εij and the thermal conductivity tensor λij of a unidirectional lateral superlattice (ULSL) (\(i,j = x,y\), with the x-axis aligned to the principal axis of the ULSL), based on the asymptotic analytic formulas of the electrical conductivity tensor σij in the literature valid at low magnetic fields where large numbers of Landau levels are occupied. With the resulting analytic expressions, we clarify the conditions for the Mott formula (Wiedemann–Franz law) to be applicable with high precision to εij (λij). We further present plots of the commensurability oscillations δεij, δλij, δκij, and δSij in εij, λij, (an alternative, more standard definition of) the thermal conductivity tensor κij, and the thermopower tensor Sij, calculated using typical parameters for a ULSL fabricated from a GaAs/AlGaAs two-dimensional electron gas (2DEG). Notable features of the δSij are (i) anisotropic behavior (δSxx ≠ δSyy) and (ii) the dominance of the xy component over the other components (\(|\delta S_{xy}| \gg |\delta S_{yx}|,|\delta S_{xx}|,|\delta S_{yy}|\)). The latter clearly indicates that the two Nernst coefficients, Sxy and Syx, can be totally different from each other in an anisotropic system. Both (i) and (ii) are at variance with the previous theory and are attributable to the inclusion of a damping factor due to the small-angle scattering characteristic of GaAs/AlGaAs 2DEGs, which have not been taken into consideration in δSij thus far.

In this article, we propose a numerical analysis of the effect of the orthotropic tensor of thermal conductivity during microwave heating of a heterogeneous core–shell morphology. The core is made of a material with high thermal conductivity, whose dielectric loss coefficient guarantees high microwave energy to heat conversion. This type of morphology has a high potential for use in the ablation of tumors, chemotherapy, drug release, and enhancing nano-catalysis, among other applications. Nonetheless, the effect of orthotropic thermal conductivity has not been extensively studied. The system under analysis is a core surrounded by two shells, which are made of materials whose thermal conductivities vary orthogonally. The thermal model consists of a system of three time-dependent coupled parabolic partial differential equations. Such a model is numerically solved using finite elements, and assuming a thermal conductivity tensor for each layer. A strong effect of this type of anisotropy was observed on temperature profiles compared to traditional isotropic materials. Besides, the symmetric release of its internally generated energy was seriously affected. Selected simulated experimental scenarios are presented.

3D hybrid finite element enthalpy for anisotropic thermal conduction analysis

Metal frame structures with controlled anisotropic thermal conductivity

Thermal conductivity tensor of NbO2

The anisotropic overall thermal conductivity induced by preferentially oriented pores

The in-plane and through-the-thickness thermal conductivities are fundamental input parameters for cure simulations of composite manufacturing processes such as vacuum assisted transfer molding (VARTM). The modeling of these conductivities is challenging due to the inherent anisotropy of composite materials, difficulty of the measurements during the cure process, and availability of the equipment. In general, cure simulations consider the homogenized thermal conductivities at lamina level and hence, micromechanics is often used to connect the individual matrix and fiber properties with the homogenized lamina properties based on microstructure, fiber volume fraction, and void content. This work presents the experimental determination and multiscale modeling of the thermal conductivity tensor of a textile VARTM composite as a function of the thermoset cure. Mechanics of structure genome (MSG) is used to compute the equivalent thermal conductivity tensor of the lamina as a function of the thermoset degree of cure. Two-step homogenization is iteratively performed coupling the evolution of the resin thermal conductivity with SwiftCompTM, a general-purpose multiscale constitutive modeling code based on the MSG. The dynamic response of the thermoset resin is measured by means of differential scanning calorimetry to characterize the cure kinetics and thermal conductivity. In addition, an in-house measuring apparatus is used to determine the through-the-thickness thermal conductivities of the dry fabric and cured composite part. The predicted through-the-thickness thermal conductivities of the cured composite are compared against experimental data. The MSG proved to be an efficient method to predict the evolution of thermal conductivity during curing process, and hence, helped bridge the gap by providing data that could not be measured directly with the present experiment.

Anisotropic thermal conductivity tensor of β-Y2Si2O7 for orientational control of heat flow on micrometer scales

Purpose – The purpose of this paper is to study the statistics of thermal conductivity and resistivity tensors in two-phase random checkerboard microstructures at finite mesoscales. Design/methodology/approach – Microstructures at finite scales are generated by randomly sampling an infinite checkerboard at 50 percent nominal fraction. Boundary conditions that stem from the Hill-Mandel homogenization condition are then applied as thermal loadings on these microstructures. Findings – It is observed that the thermal response of the sampled microstructures is in general anisotropic at finite mesoscales. Based on 1,728 boundary value problems, the statistics of the tensor invariants (trace and determinant) are obtained as a function of material contrast, mesoscale and applied boundary conditions. The histograms as well as the moments (mean, variance, skewness and kurtosis) of the invariants are computed and discussed. A simple analytical form for the variance of the trace of mesoscale conductivity tensor is proposed as a function of individual phase conductivities and the mesoscale. Originality/value – A rigorous methodology to determine the evolution of the invariants of thermal conductivity (and resistivity) tensors across a variety of length scales (microscale to macroscale) is presented. The objective is to enable setting up of constitutive equations applicable to heat conduction that are valid across all length scales.

Thermal transport in the axial direction of polymers has been extensively studied, while the strain effect on the thermal conductivity, especially in the radial direction, remains unknown. In this work, we calculated the thermal conductivity in the radial direction of a crystalline polyethylene model and simulated the uniaxial strain effect on the thermal conductivity tensor by molecular dynamics simulations. We found a strong size effect of the thermal transport in the radial direction and estimated that the phonon mean free path can be much larger than the prediction from the classic kinetic theory. We also found that the thermal conductivity in the axial direction increases dramatically with strain, while the thermal conductivity in the radial direction decreases with uniaxial strain. We attribute the reduction of thermal conductivity in the radial direction to the decreases in inter-chain van der Waals forces with strains. The facts that the chains in the crystalline polyethylene became stiffer and more ordered along the chain direction could be the reasons for the increasing thermal conductivity in the axial direction during stretching. Besides, we observed longer phonon lifetime in acoustic branches and higher group velocity in optical branches after uniaxial stretching. Our work provides fundamental understandings on the phonon transport in crystalline polymers, the structure-property relationship in crystalline polymers, and the strain effect in highly anisotropic materials.