Effects Of Anisotropic Thermal Conduction Research Articles

Self-similar Solution of Hot Accretion Flow with Thermal Conduction and Anisotropic Pressure

Abstract We explore the effects of anisotropic thermal conduction, anisotropic pressure, and magnetic field strength on the hot accretion flows around black holes by solving the axisymmetric, steady-state magnetohydrodynamic equations. The anisotropic pressure is known as a mechanism for transporting angular momentum in weakly collisional plasmas in hot accretion flows with extremely low mass accretion rates. However, anisotropic pressure does not extensively impact the transport of the angular momentum, it leads to shrinkage of the wind region. Our results show that the strength of the magnetic field can help the Poynting energy flux overcome the kinetic energy flux. This result may be applicable to the understanding of the hot accretion flow in the Galactic Center Sgr A* and the M87 galaxy.

Limited impact of anisotropic thermal conductivity in the mantle wedge on the slab temperature in the Tohoku subduction zone, Northeast Japan

The effects of anisotropic thermal conductivity due to the crystallographic-preferred orientation (CPO) of olivine in the mantle wedge on the steady-state thermal structure of the Tohoku subduction zone, Northeast Japan, are investigated using geodynamic modeling. Four different olivine crystal fabrics are modeled based on theoretical CPO development in the mantle wedge: random (i.e., isotropic thermal conductivity), A-type, C-type, and E-type fabrics. The thermal conductivity in the mantle wedge is highly anisotropic in the regions just above the descending slab and near the base of the overriding plate. The obtained temperature differences between the anisotropic and isotropic cases are only up to 30°C within the slab. Therefore, the impact of anisotropic thermal conductivity on the slab temperature may be limited when anisotropy is only considered in the mantle wedge.

Conjugate Heat Transfer Simulations to Evaluate the Effect of Anisotropic Thermal Conductivity on Overall Cooling Effectiveness

Abstract Ceramic matrix composites (CMCs) show promise as higher temperature capable alternatives to traditional metallic components in gas turbine engine hot gas paths. However, CMC components will still require both internal and external cooling, such as film cooling. The overall cooling effectiveness is determined not only by the design of coolant flow, but also by the conduction through the materiel itself. CMCs have anisotropic thermal conductivity, giving rise to heat flow that differs somewhat relative to what we have come to expect from experience with traditional metallic components. Conjugate heat transfer computational fluid dynamics (CFD) simulations were performed in order to isolate the effect anisotropic thermal conductivity has on a cooling architecture consisting of both internal and external cooling. Results show the specific locations and unique effects of anisotropic thermal conduction on overall effectiveness. Thermal conductivity anisotropy is shown to have a significant effect on the resulting overall effectiveness. As CMCs begin to make their way into gas turbine engines, care must be taken to ensure that anisotropy is characterized properly and considered in the thermal analysis.

Effect of Anisotropic Thermal Conductivity of Graphite Flakes and Interfacial Thermal Resistance on the Effective Thermal Conductivity of Graphite Flakes/Aluminum Composites

Effect of Anisotropic Thermal Conductivity of Graphite Flakes and Interfacial Thermal Resistance on the Effective Thermal Conductivity of Graphite Flakes/Aluminum Composites

Effects of anisotropic composite skin on electrothermal anti-icing system

To study the effects of anisotropic thermal conductivity of composite aircraft skin on the heat transfer characteristics of electrothermal anti-icing system, the differential equation of anisotropic heat conduction was established using coordinate transformation of principal anisotropy axis. In addition, it was coupled with the heat and mass transfer model of the runback water film on the anti-icing surface to perform numerical simulation of the electrothermal anti-icing system. The temperature results of the vertical and cylindrical orthotropic thermal conduction in the rectangular and semi-cylindrical composite skin were consistent with those obtained by the traditional orthotropic model, which verified the anisotropic heat conduction model. The temperature distribution of anti-icing surface agreed well with the literature data, which validated the coupled heat and mass model of the runback water flow and the anisotropic skin. The anisotropic thermal conductivity of composite skin would make temperature change more gradual, and the effect was more significant where the curvature of the temperature curve was greater. However, the anti-icing surface of the electrothermal anti-icing system was slightly affected by the anisotropic heat conduction of the multilayered composite skin.

Natural convection and anisotropic heat transfer in a ferro-nanofluid under magnetic field

In this paper, effects of anisotropic thermal conductivity and the Lorentz force in a ferro-nanofluid induced by external magnetic fields are investigated. The nanofluid is modeled as a non-linear single-phase fluid, where the viscosity is considered to depend on the nanoparticle concentration; the thermal conductivity shows anisotropy due to the existence of the magnetic field. The anisotropic thermal conductivity tensor, which depends on the magnetic field vector, is derived by considering the principle of material frame indifference of Continuum Mechanics. Numerical simulations are performed in a horizontal annulus enclosure. Effects of the nanoparticle concentration, magnetic distribution, and the dimensionless parameters, such as the Rayleigh number and the Hartmann number, are studied. The numerical results indicate that due to the anisotropic thermal conductivity, the isotherms become elliptic and deviate significantly from a circle which is a typical distribution with isotropic thermal conductivity; furthermore the elliptic shape changes as the direction of the magnetic field varies while the heat transfer is always much faster in the direction parallel to the magnetic field. For the range of the dimensionless parameters studied here, the Nusselt number increases significantly as the Rayleigh number (ranging from 2500 to 50,000) increases; depending on the situation, the magnetic field (the Hartmann number which ranges from 0 to 1) may enhance or diminish the thermal performance. In addition, the streamlines are more organized and less wavy when there exists a magnetic field; this could be attributed to the suppressive effect of the Lorentz force.

Effect of Anisotropic Thermal Conductivity on Deformation of a Thermoelastic Half-Space Subjected to Surface Loads

Effect of Anisotropic Thermal Conductivity on Deformation of a Thermoelastic Half-Space Subjected to Surface Loads

Effects of Anisotropic Thermal Conductivity and Lorentz Force on the Flow and Heat Transfer of a Ferro-Nanofluid in a Magnetic Field

In this paper, we study the effects of the Lorentz force and the induced anisotropic thermal conductivity due to a magnetic field on the flow and the heat transfer of a ferro-nanofluid. The ferro-nanofluid is modeled as a single-phase fluid, where the viscosity depends on the concentration of nanoparticles; the thermal conductivity shows anisotropy due to the presence of the nanoparticles and the external magnetic field. The anisotropic thermal conductivity tensor, which depends on the angle of the applied magnetic field, is suggested considering the principle of material frame indifference according to Continuum Mechanics. We study two benchmark problems: the heat conduction between two concentric cylinders as well as the unsteady flow and heat transfer in a rectangular channel with three heated inner cylinders. The governing equations are made dimensionless, and the flow and the heat transfer characteristics of the ferro-nanofluid with different angles of the magnetic field, Hartmann number, Reynolds number and nanoparticles concentration are investigated systematically. The results indicate that the temperature field is strongly influenced by the anisotropic behavior of the nanofluids. In addition, the magnetic field may enhance or deteriorate the heat transfer performance (i.e., the time-spatially averaged Nusselt number) in the rectangular channel depending on the situations.

Effects of anisotropic thermal conduction on wind properties in hot accretion flow

Previous works have clearly shown the existence of winds from black hole hot accretion flow and investigated their detailed properties. In extremely low accretion rate systems, the collisional mean-free path of electrons is large compared with the length-scale of the system, thus thermal conduction is dynamically important. When the magnetic field is present, the thermal conduction is anisotropic and energy transport is along magnetic field lines. In this paper, we study the effects of anisotropic thermal conduction on the wind production in hot accretion flows by performing two-dimensional magnetohydrodynamic simulations. We find that thermal conduction has only moderate effects on the mass flux of wind. But the energy flux of wind can be increased by a factor of $\sim 10$ due to the increase of wind velocity when thermal conduction is included. The increase of wind velocity is because of the increase of driving forces (e.g. gas pressure gradient force and centrifugal force) when thermal conduction is included. This result demonstrates that thermal conduction plays an important role in determining the properties of wind.

Modeling of cryo-adsorption of hydrogen on MOF-5 pellets: Effect of pellet properties on moderate pressure refueling

Refueling of a single MOF-5 pellet with cryogenic hydrogen at moderate pressures is modeled in this work. A MOF-5 pellet in a discharged state is placed in a hydrogen atmosphere at refueling conditions of 80 K temperature and 30 bar pressure. The absolute adsorption isotherm for hydrogen on MOF-5 is described by the Unilan model, hydrogen is modeled as a real gas, and properties of the compressed MOF-5 pellet are obtained from polynomial fits to low temperature experimental data. Pellet properties change due to the addition of expanded natural graphite (ENG) and various levels of compaction. A parametric study is performed using COMSOL® Multiphysics 4.2 to understand the effect of ENG and pellet compaction on refueling behavior of a single pellet. Specifically, the role of permeability and thermal conductivity, and the effect of anisotropic thermal conductivity are investigated using a two-dimensional axisymmetric model. The variation in pellet refueling time with varying pellet sizes is studied in order to determine the “optimal” pellet size for fast refueling. Results show that both stick-like geometry (h/d≫1) and flat hockey-puck geometry (h/d≪1) provide fast refueling. Conversely, pellets with h/d≈0.5 show the longest refueling times and are therefore not recommended for use in a packed bed design.

Spatial Variation of Temperature on Printed Circuit Boards: Effects of Anisotropic Thermal Conductivity and Joule Heating

A printed circuit board (PCB) consists of multiple layers of dielectric material and current-carrying metal traces and vias. Performing system-level simulations of PCBs with detailed trace and via geometries is very costly, the present approach considers the effects of the trace and via geometry in the physical model by importing Electronic Computer Aided Design (ECAD) data comprising the trace and via layout of the board and determines spatially varying orthotropic conductivity (kx, ky, and kz) on the PCB based on the ECAD data. In addition, the present approach considers the effects of joule heating in the current-carrying traces by utilizing multiple 2-D sources where the powermap is determined by solving the governing dc electric field equations on the trace. In this paper, the effects of both the trace layer orthotropic thermal conductivity and joule heating are studied on a sample PCB. Comparisons are made with earlier studies and conventional models when possible. It is shown that the location of the hot spots and temperature values differ substantially if different methods are used.

IMPACT OF TEMPERATURE-DEPENDENT RESISTIVITY AND THERMAL CONDUCTION ON PLASMOID INSTABILITIES IN CURRENT SHEETS IN THE SOLAR CORONA

In this paper we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection $X$-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting $X-$points and transfer the heat into the $O-$points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, $\eta \sim T^{-3/2}$, the decrease in plasma temperature at the $X-$points leads to: (i) increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction; (ii) increase in the reconnection rate; and, (iii) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.

Effect of the anisotropic thermal conductivity of GDL on the performance of PEM fuel cells

Gas diffusion layers (GDLs) are one of the main components in proton exchange membrane (PEM) fuel cells. In this paper, the effect of anisotropic thermal conductivity of the GDL is numerically investigated under different operating temperatures. Furthermore, the sensitivity of the PEM fuel cell performance to the thermal conductivity of the GDL is investigated for both in-plane and through-plane directions and the temperature distributions between the different GDL thermal conductivities are compared. The results show that increasing the in-plane and through-plane thermal conductivity of the GDL increases the power density of PEM fuel cells significantly. Moreover, the temperature gradients show a greater sensitivity to the in-plane thermal conductivity of the GDL as opposed to the through-plane thermal conductivity.

The dynamics of Rayleigh-Taylor stable and unstable contact discontinuities with anisotropic thermal conduction

We study the effects of anisotropic thermal conduction along magnetic field lines on an accelerated contact discontinuity in a weakly collisional plasma. We first perform a linear stability analysis similar to that used to derive the Rayleigh-Taylor instability (RTI) dispersion relation. We find that anisotropic conduction is only important for compressible modes, as incompressible modes are isothermal. Modes grow faster in the presence of anisotropic conduction, but growth rates do not change by more than a factor of order unity. We next run fully non-linear numerical simulations of a contact discontinuity with anisotropic conduction. The non-linear evolution can be thought of as a superposition of three physical effects: temperature diffusion due to vertical conduction, the RTI, and the heat flux driven buoyancy instability (HBI). In simulations with RTI-stable contact discontinuities, the temperature discontinuity spreads due to vertical heat conduction. This occurs even for initially horizontal magnetic fields due to the initial vertical velocity perturbation and numerical mixing across the interface. The HBI slows this temperature diffusion by reorienting initially vertical magnetic field lines to a more horizontal geometry. In simulations with RTI-unstable contact discontinuities, the dynamics are initially governed by temperature diffusion, but the RTI becomes increasingly important at late times. We discuss the possible application of these results to supernova remnants, solar prominences, and cold fronts in galaxy clusters.

THE EFFECT OF ANISOTROPIC CONDUCTION ON THE THERMAL INSTABILITY IN THE INTERSTELLAR MEDIUM

Thermal instability (TI) can strongly affect the structure and dynamics of the interstellar medium (ISM) in the Milky Way and other disk galaxies. Thermal conduction plays an important role in the TI by stabilizing small scales and limiting the size of the smallest condensates. In the magnetized ISM, however, heat is conducted anisotropically (primarily along magnetic field lines). We investigate the effects of anisotropic thermal conduction on the nonlinear regime of the TI by performing two-dimensional magnetohydrodynamic simulations. We present models with magnetic fields of different initial geometries and strengths, and compare them to hydrodynamic models with isotropic conduction. We find anisotropic conduction does not significantly alter the overall density and temperature statistics in the saturated state of the TI. However, it can strongly affect the shapes and sizes of cold clouds formed by the TI. For example, for uniform initial fields long filaments of cold gas are produced that are reminiscent of some observed HI clouds. For initially tangled fields, such filaments are not produced. We also show that anisotropic conduction suppresses turbulence generated by evaporative flows from the surfaces of cold blobs, which may have implications for mechanisms for driving turbulence in the ISM.

Can conduction induce convection? On the non-linear saturation of buoyancy instabilities in dilute plasmas

We study the effects of anisotropic thermal conduction on low-collisionality, astrophysical plasmas using two and three-dimensional magnetohydrodynamic simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable for either sign of the temperature gradient: the heat-flux-driven buoyancy instability (HBI) operates when the temperature increases with radius while the magnetothermal instability (MTI) operates in the opposite limit. In contrast to previous results, we show that, in the presence of a sustained temperature gradient, the MTI drives strong turbulence and operates as an efficient magnetic dynamo (akin to standard, adiabatic convection). Together, the turbulent and magnetic energies contribute up to ~10% of the pressure support in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5% of rho c_s^3. These findings are robust even in the presence of an external source of strong turbulence. Our results on the nonlinear saturation of the HBI are consistent with previous studies but we explain physically why the HBI saturates quiescently by re-orienting the magnetic field (suppressing the conductive heat flux through the plasma), while the MTI saturates by generating sustained turbulence. We also systematically study how an external source of turbulence affects the saturation of the HBI: such turbulence can disrupt the HBI only on scales where the shearing rate of the turbulence is faster than the growth rate of the HBI. In particular, our results provide a simple mapping between the level of turbulence in a plasma and the effective isotropic thermal conductivity. We discuss the astrophysical implications of these findings, with a particular focus on the intracluster medium of galaxy clusters.

Spherical accretion with anisotropic thermal conduction

We study the effects of anisotropic thermal conduction on magnetized spherical accretion flows using global axisymmetric MHD simulations. In low collisionality plasmas, the Bondi spherical accretion solution is unstable to the magnetothermal instability (MTI). The MTI grows rapidly at large radii where the inflow is subsonic. For a weak initial field, the MTI saturates by creating a primarily radial magnetic field, i.e., by aligning the field lines with the background temperature gradient. The saturation is quasilinear in the sense that the magnetic field is amplified by a factor of $\sim 10-30$ independent of the initial field strength (for weak fields). In the saturated state, the conductive heat flux is much larger than the convective heat flux, and is comparable to the field-free (Spitzer) value (since the field lines are largely radial). The MTI by itself does not appreciably change the accretion rate $\dot M$ relative to the Bondi rate $\dot M_B$. However, the radial field lines created by the MTI are amplified by flux freezing as the plasma flows in to small radii. Oppositely directed field lines are brought together by the converging inflow, leading to significant resistive heating. When the magnetic energy density is comparable to the gravitational potential energy density, the plasma is heated to roughly the virial temperature; the mean inflow is highly subsonic; most of the energy released by accretion is transported to large radii by thermal conduction; and the accretion rate $\dot M \ll \dot M_B$. The predominantly radial magnetic field created by the MTI at large radii in spherical accretion flows may account for the stable Faraday rotation measure towards Sgr A* in the Galactic Center.

Effect of anisotropic thermal conductivity of the GDL and current collector rib width on two-phase transport in a PEM fuel cell

A two-dimensional two-phase model based on the classical two-fluid model is used to analyze electrochemical and thermal transport in a PEMFC. The model is extended to account for the dependence of interfacial area density on liquid volume fraction. At a given fixed voltage, the fuel cell generates maximum current density for low through-plane and high in-plane thermal conductivities at high humidity operating conditions. It is also predicted that for low humidity operating conditions, the fuel cell generates maximum current density if the GDL is tailored to have high through-plane thermal conductivity near the inlet and progressively decreasing through-plane thermal conductivity at distances away from the inlet. At fully humidified cathode inlet conditions, narrower current collector ribs generate higher current densities at all voltages by reducing the resistance to diffusion of reactants and products through the GDL. In order to maximize the current density at low humidities, ribs must be wider near the inlet and narrower away from the inlet. The proposed methodology for tailoring GDL through-plane thermal conductivities and rib widths reduces the risk of membrane dehydration near inlet and also reduces the possibility of excessive liquid accumulation in the region away form the inlet.

Simulations of the Field-Reversed Configuration with the NIMROD Code

The recently formed Plasma Science and Innovation Center (PSI-Center) is refining the NIMROD code to simulate field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity. This, combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Some initial simulations are focused on 2D (n = 0 only) non-linear two-fluid simulations. We present initial validations of a translating FRC and note good conservation of density and magnetic flux. As a validation of the effects of anisotropic thermal conduction, we present a comparison of an FRC with standard thermal transport to one with anisotropic conduction. Two-fluid simulations are shown which produce significant spin-up due to the end-shorting boundary condition. Finally, simulations of the tilt instability are presented, which show that Hall physics significantly retards, but does not eliminate the growth rate.

Anisotropic Heat Conduction Effects in Proton-Exchange Membrane Fuel Cells

The focus of this work is to study the effects of anisotropic thermal conductivity and thermal contact conductance on the overall temperature distribution inside a fuel cell. The gas-diffusion layers and membrane are expected to possess an anisotropic thermal conductivity, whereas a contact resistance is present between the current collectors and gas-diffusion layers. A two-dimensional single phase model is used to capture transport phenomena inside the cell. From the use of this model, it is predicted that the maximum temperatures inside the cell can be appreciably higher than the operating temperature of the cell. A high value of the in-plane thermal conductivity for the gas-diffusion layers was seen to be essential for achieving smaller temperature gradients. However, the maximum improvement in the heat transfer characteristics of the fuel cell brought about by increasing the in-plane thermal conductivity is limited by the presence of a finite thermal contact conductance at the diffusion layer/current collector interface. This was determined to be even more important for thin gas-diffusion layers. Anisotropic thermal conductivity of the membrane, however, did not have a significant impact on the temperature distribution. The thermal contact conductance at the diffusion layer/current collector interface strongly affected the temperature distribution inside the cell.