Anisotropic Heat Transfer Research Articles

Humidity-Dependent Thermal Boundary Conductance Controls Heat Transport of Super-Insulating Nanofibrillar Foams

Summary Cellulose nanomaterial (CNM)-based foams and aerogels with thermal conductivities substantially below the value for air attract significant interest as super-insulating materials in energy-efficient green buildings. However, the moisture dependence of the thermal conductivity of hygroscopic CNM-based materials is poorly understood, and the importance of phonon scattering in nanofibrillar foams remains unexplored. Here, we show that the thermal conductivity perpendicular to the aligned nanofibrils in super-insulating ice-templated nanocellulose foams is lower for thinner fibrils and depends strongly on relative humidity (RH), with the lowest thermal conductivity (14 mW m−1 K−1) attained at 35% RH. Molecular simulations show that the thermal boundary conductance is reduced by the moisture-uptake-controlled increase of the fibril-fibril separation distance and increased by the replacement of air with water in the foam walls. Controlling the heat transport of hygroscopic super-insulating nanofibrillar foams by moisture uptake and release is of potential interest in packaging and building applications.

Pore-scale heat transfer of heat sink filled with stacked 2D metal fiber-PCM composite

Effective thermal management is essential for guaranteeing the working efficiency and safety of several industrial devices. Due to its excellent heat absorption characteristic, microencapsulated phase change material (MEPCM) is promising for thermal management system. However, the drawback of MEPCM's low thermal conductivity seriously hinders the heat dissipation rate from heat sink. Based on their high thermal conductivity and effective interconnected anisotropic heat transfer channels, metal fibers could be inserted into MEPCM to ameliorate its corresponding heat transfer capability. In the current work, novel stacked 2D metal fibers are designed and coupled with MEPCM in order to improve the thermal performance of heat sink. Based on the numerically reconstructed metal fibers, the thermal performance of heat sink assembly filled with MEPCM-metal fiber composite is investigated through pore-scale lattice Boltzmann modelling. When the latent heat of MEPCM is available, the heat sink assembly using anisotropic stacked 2D metal fibers has a less temperature rise compared with that using random metal fibers because of the consolidated heat transfer rate in a desired vertical direction. Furthermore, for an intermittent working heat sink, the MEPCM-stacked 2D metal fiber composite with high anisotropic degree exhibits more obvious advantage on its thermal management owing to the periodically recharged latent heat for further heat absorption.

Gradient structure polyimide/graphene composite aerogels fabricated by layer‐by‐layer assembly and unidirectional freezing

AbstractIn this work, gradient polyimide (PI)/graphene composite aerogels were prepared with poly(amic acid) ammonium salt/graphene aqueous solution through layer‐by‐layer assembly, unidirectional freezing, freezing drying, and thermal imidization process. Each layer of gradient PI aerogels was consisted of oriented channel‐like pores along the freezing direction. The gradient PI/graphene composite aerogels exhibited anisotropic conductivity and heat transfer property. The conductivity of composite aerogels in the perpendicular direction of oriented channel‐like pores was higher than that along the direction of oriented pores. The heat transfer from the high‐density end to the low‐density end of gradient density composite aerogels was faster. Compared with those of homogeneous composite aerogel with same density, the compression yield stress of gradient density composite aerogels obviously decreased, and their compression platform region also obviously shortened. Moreover, when the compressive strain exceeded 35%, the compressive strength of gradient composite aerogel with more layers was much higher.

Thermally Insulating Nanocellulose-Based Materials.

Thermally insulating materials based on renewable nanomaterials such as nanocellulose could reduce the energy consumption and the environmental impact of the building sector. Recent reports of superinsulating cellulose nanomaterial (CNM)-based aerogels and foams with significantly better heat transport properties than the commercially dominating materials, such as expanded polystyrene, polyurethane foams, and glass wool, have resulted in a rapidly increasing research activity. Herein, the fundamental basis of thermal conductivity of porous materials is described, and the anisotropic heat transfer properties of CNMs and films with aligned CNMs and the processing and structure of novel CNM-based aerogels and foams with low thermal conductivities are presented and discussed. The extraordinarily low thermal conductivity of anisotropic porous architectures and multicomponent approaches are highlighted and related to the contributions of the Knudsen effect and phonon scattering.

Three-dimensional heat transfer effects in external layers of a magnetized neutron star

ABSTRACT Determination of a magnetic field structure on a neutron star (NS) surface is an important problem of a modern astrophysics. In a presence of strong magnetic fields, a thermal conductivity of a degenerate matter is anisotropic. In this paper, we present 3D anisotropic heat transfer simulations in outer layers of magnetized NSs, and construct synthetic thermal light curves. We have used a different from previous works tensorial thermal conductivity coefficient of electrons, derived from the analytical solution of the Boltzmann equation by the Chapman–Enskog method. We have obtained an NS surface temperature distribution in presence of dipole-plus-quadrupole magnetic fields. We consider a case, in which magnetic axes of a dipole and quadrupole components of the magnetic field are not aligned. To examine observational manifestations of such fields, we have generated thermal light curves for the obtained temperature distributions using a composite blackbody model. It is shown that the simplest (only zero-order spherical function in quadrupole component) non-coaxial dipole-plus-quadrupole magnetic field distribution can significantly affect the thermal light curves, making pulse profiles non-symmetric and amplifying pulsations in comparison to the pure-dipolar field.

Properties of gradient polyimide aerogels prepared through layer‐by‐layer assembly

AbstractA series of density gradient polyimide (PI) aerogels were prepared using layer‐by‐layer assembly and radial freezing method. Briefly, a layer of poly(amic acid) (PAA) ammonium salt aqueous solution was first radially frozen. Then, the second layer of PAA ammonium salt (PAS) aqueous solution of different concentration was added on the top of the first PAS layer and radially frozen. A multilayer gradient PAS solid sample could therefore be fabricated by repeating this similar procedure. The density gradient PI aerogels were obtained after freezing drying and final thermal imidization treatment. Each layer of gradient PI aerogels had anisotropic pore structure, which consisted of tube‐like pores along the radial direction and toward the center axis of the cylindrical samples. The compressive strength of five‐layer gradient PI aerogel was higher than that of three‐layer gradient and single‐layer PI aerogels with the same density. The gradient PI aerogels exhibited anisotropic heat transfer behavior in the direction of density gradient, and heat transfer from the higher density side to the lower density side was faster.

Anisotropic convective heat transfer in open-cell metal foams: Assessment and correlations

Open-cell metal foams are promising materials for heat transfer augmentation, due to their tortuosity and high specific surface area. The volume-averaging technique under the assumption of local thermal non-equilibrium between the solid and fluid phases is often used to model devices equipped with open-cell foams; it requires an accurate knowledge of the interfacial convective heat transfer coefficient. Its dependence on the anisotropy of elongated foam cells is investigated numerically in the present work. Four aluminum foam samples with different porosities and equal PPIs are considered; their geometry is reconstructed by means of x-ray computed tomography. Mass, momentum and energy equations for the fluid phase (air) are solved, while the solid phase is accounted for with a uniform heat flux boundary condition. Interfacial convective heat transfer coefficients and Nusselt numbers are predicted. The dependence of the interfacial heat transfer coefficient in the elongation direction on the effective porosity and fluid inlet velocity is pointed out. The comparison of predicted values with those given by correlations from the open literature shows a good agreement. Finally, correlations for the prediction of Nusselt numbers, accounting for the foam anisotropy, are proposed, which can be useful in the study of metal foams.

3D Simulation of Anisotropic Heat Transfer in Outer Layers of Magnetized Neutron Stars

The results of three-dimensional numerical simulation of heat transfer in the outer layers of magnetized neutron stars are presented. Determining the structure of the magnetic field on a neutron star surface is an important task of modern astrophysics. In the presence of strong magnetic fields, the medium becomes anisotropic, and the laws of heat conduction change. The tensor coefficient of thermal conductivity for magnetized degenerate plasma was obtained by Bisnovatyi-Kogan and Glushikhina by solving the Boltzmann equation with the Chapman–Enskog method. In this paper, the temperature distribution on the surface of a magnetized neutron star is obtained for magnetic fields of the dipolar and quadrupolar type, as well as for their superposition. To numerically solve the stationary temperature distribution problem in the outer layers of a magnetized neutron star, the basic (support) operator numerical method was extended to a three-dimensional case. The problem was solved on the grid which consists of tetrahedra.

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion. With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces, the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime. Several one- and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS, and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.

Numerical simulation of an anisotropic heat transfer in magnetized neutron stars with 3D basic operators method

We have solved numerically a three dimensional boundary-value problem for a heat transfer equation in a magnetized neutron star crust with an updated tensorial heat conductivity coefficient. The temperature distribution in a neutron star crust in presence of a magnetic field was simulated. To calculate the surface temperature distribution, we have constructed a local one-dimensional plane-parallel model of a magnetized outer envelope of the neutron star and used it as an outer boundary condition for 3D problem to find a self-consistent solution.This problem was solved with our extension of a basic (support) operators numerical method on a tetrahedral mesh. The idea of operator approach consists of inclusion the boundary conditions into difference form of the solving problem and its formulation as one operator equation. The finite difference operators are constructed in the way to fulfill corresponding relations between continuous operators (for example, div(curl)=0, div is conjugated to -grad so div(grad) is self-conjugated etc.). Such approach allows to obtain completely conservative implicit finite difference schemes. Efficient iterative methods can be used to find the solution because constructed matrixes have good properties, such as symmetry and positive definiteness.

An Exact Solution for Transient Anisotropic Heat Conduction in Composite Cylindrical Shells

Abstract In this study, an analytical solution is proposed for the problem of transient anisotropic conductive heat transfer in composite cylindrical shells. The composite shells are considered to have directional heat transfer properties, which is due to the existence of fibers which can be winded in any direction. The composite shells usually show high conductivity in the direction parallel to fiber direction and low conductivity in other two orthogonal directions. To solve the heat transfer partial differential equation, finite Fourier transform and separation of variables method are used. The present solution is used to find the temperature distribution in a composite cylindrical vessel for which the composite material is graphite/epoxy and the vessel is prone to an external heat flux and also ambient flow. The analytical solution is verified perfectly by the data obtained from a second-order finite difference solution. The solution is used to investigate the effects of values of fiber angle and material conductivity coefficients on temperature distribution of the composite cylindrical vessel. The results show the important role of fiber angle values on the temperature distribution of vessel.

Heterogeneous anisotropic conductive heat transfer in composite conical shells: An exact analysis

In present paper, problem of anisotropic heat conduction in heterogeneous composite conical shells is solved analytically. Arbitrary values for fiber angle (ranging from zero to 90 degrees) cause anisotropy for the heat conduction problem in composite conical shells. In our analysis, heat convection between conical shell and ambient flow is taken into account. In addition, an external source of radiative heat transfer is modeled. Herein, the heat conduction problem is assumed to be heterogeneous which is due to dependence of the conductivity coefficient on temperature. Kirchhoff transformation followed by an integral transform method are used to solve present heterogeneous heat conduction problem. Green’s functions are applied to find the solution of final ordinary differential equations. Verification of the present analytical solution is obtained through comparing the analytical results with those of a second order finite difference method. Good agreement between the analytical and numerical results has been found. In order to evaluate the capability of our analytical solution in solving real industrial problems, the temperature distributions in a typical pressure vessel and a pin fin are calculated.

Metasurface-mediated anisotropic radiative heat transfer between nanoparticles

Metasurfaces, the two-dimensional (2D) counterpart of metamaterials, have recently attracted a great attention due to their amazing properties such as negative refraction, hyperbolic dispersion, manipulation of the evanescent spectrum. In this work, we propose a theory model for the near field radiative heat transfer (NFRHT) between two nanoparticles in the presence of an anisotropic metasurface. Specifically, we set the metasurface as an array of graphene strips (GS) since it is an ideal platform to implement any metasurface topology, ranging from isotropic to hyperbolic propagation. We show that the NFRHT between two nanoparticles can not only be significantly amplified when they are placed in proximity of the GS, but also be regulated over several orders of magnitude. In this configuration, the anisotropic surface plasmon polaritons (SPPs) supported by the GS are excited and provide a new channel for the near-field energy transport. We analyze how the conductance between two nanoparticles depends on the orientation, the structure parameters and the chemical potential of the GS, on the particle-surface or the particle-surface distances by clearly identifying the characteristics of the anisotropic SPPs such as dispersion relations, propagation length and decay length. Our findings provide a powerful way to regulate the energy transport in the particle systems, meanwhile in turn, open up a way to explore the anisotropic optical properties of the metasurface based on the measured heat transfer properties.

A New Exact Analysis for Anisotropic Conductive Heat Transfer in Truncated Composite Spherical Shells

ABSTRACTIn the present paper, a general analytical solution is proposed for anisotropic heat conduction through truncated composite spherical shells. The solution is so important in designing the spherical vessels which are usually used to store the CNG, LNG, LPG and other petroleum condensates. Herein, it is supposed that the fiber angle of composite laminate is in range of zero to 90 degrees. Heat convection with ambient flow, an external heat radiation, and a possible internal heat generation are modeled within the heat transfer equation. The exact solution is derived using the complex finite Fourier transform method. The particular solution of transferred equation is found based on the Green’s function and Sturm-Liouville theories. Finally, an inverse integral transformation is applied to form the final analytical solution in physical space. Defining four materials differing in the value of conductivity coefficient in fiber direction, the effects of used composite material and fiber angle on temperature distribution of the spherical shell are investigated in detail.

Comparison of cooling plate configurations for automotive battery pack thermal management

A numerical simulation was developed combining micro and macro scale models, to determine the thermal state of battery packs in electric vehicles. A spatially resolved Ohm’s law model was integrated with the single particle model to resolve the electrochemistry in prismatic cells, and then coupled with a thermal transport simulation. The objective was to compare the effectiveness of two types of liquid channel cooling plate configurations. The first, known as ice plates are placed between every second cell in the battery pack. The second, known as cold plates, are placed underneath a block of cells, and absorb heat only through the small lower face of the cell, exploiting anisotropic heat transfer properties. In general, the ice plate performs better. The cold plate is less complicated and expensive to integrate into the battery pack, and has more scope for higher coolant circulation rates. This paper compares the performance of the two cooling systems, highlighting the conditions where each system works best, along with quantitative assessments obtained through numerical simulation.

Application of 3D basic operators method extension to astrophysical problems

Basic (support) operators method (Samarskii’s method, operator-difference method) has proven itself well in 2D numerical simulations of the astrophysical problems. An idea of the operator approach consists of the inclusion of boundary conditions in a finite difference form into the grid analogue of solving problem and formulation of the finite difference problem as an operator equation. The finite difference operators are constructed in the way to fulfill corresponding relations between continuous operators (for instance, div(rot)=0, div is conjugated to -grad; -div(grad) is self-conjugated etc.). The approach allows obtaining completely conservative finite difference schemes. The matrix which corresponds to the self-conjugated operator is symmetrical and can be inversed efficiently by modern iteration methods. In the paper a 3D generalization of 2D grid analogues for continuous differential operators using a cell-node approximation on triangular grid was realized for tetrahedral mesh. For testing we calculated a 3D Newtonian gravitational potential, and a stationary heat transfer equation in spherical layer with the first type boundary condition on the inner surface and the third type boundary condition on the outer one was calculated. The method was applied to simulation of anisotropic heat transfer in magnetized neutron star crust.

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.

Temperature-responsive thermal metamaterials enabled by modular design of thermally tunable unit cells

Integrated circuits or miniaturized portable electronics require adaptive thermal control under certain temperatures. Thermal metamaterials (TMs), which artificially manipulate the heat passing through mediums have shown innovative thermal functions at a continuum scale. However, they cannot implement tunable thermal functions at local spots depending on the operating temperatures. Herein, we introduce temperature-responsive TMs enabled by modular design of thermally tunable unit cells. As ambient temperature changes, tunable thermal shifters can dynamically turn on/off their intrinsic functions to guide anisotropic heat transfer through the transition of thermal conductivities from the inner phase change nanocomposites (PCNCs), and their modular design realizes temperature-responsive thermal shields having switchable functions. The layered structures of stainless steel and the PCNC of n-octadecane embedding carbon nanotubes and copper powder are fabricated as tunable thermal shifters. Their 4 × 4 modular structure confirms the feasibility of temperature-responsive TMs, verified by the disappearance and appearance of thermally shielded regimes at low- and high-temperature ranges. The potential use of the developed concept was demonstrated as tunable interfaces between thermal dissipation and insulation for protecting temperature-sensitive components. This work can offer new capabilities for conventional passive TMs, such as local thermal adaptation, active thermal control interface, and thermal disturbance mitigation.

Effect of thermal anisotropy on binary alloy dendrite growth

A numerical model to study the effect of thermal anisotropy on binary alloy dendrite growth is presented. The model is based on the volume averaged enthalpy method with explicit surface tension anisotropy for crystal orientation. Thermal anisotropy is incorporated using anisotropic thermal conductivity in the energy equation. This is done by splitting the anisotropic conductivity into two parts, equivalent isotropic conductivity and anisotropic departure source term, enabling the use of a conventional isotropic solver to model anisotropic heat transfer. The proposed model is applied to study the effect of thermal anisotropy ratio on tip velocity, aspect ratio and equivalent radius of an equiaxed grain growing in an undercooled binary alloy melt. It is found that the thermal energy stored in the grain during solidification plays an important role in interface evolution, and thus anisotropic conductivity in the solid affects the grain morphology. There is a consistent increase in the aspect ratio of grains with increase in thermal anisotropy ratio, although the grain volume remains almost invariant. Due to unequal growth rates of the perpendicular arms, severe distortion of the solid crystal is seen at higher thermal anisotropy ratios. The model is further extended to study the growth of multiple dendrites in order to simulate microstructure evolution with thermal anisotropy. It is observed that thermal anisotropy significantly affects the grain morphology at low grain density but has a smaller influence at high grain density as compared to other governing factors such as solute transport.

Inverse Thermal Modeling to Determine Power Losses in Induction Motor

An electrical motor's inverse thermal model formulates the precision with which its power losses can be predicted from noisy local temperature measurements. This paper proposes constrained linear least square optimization followed by noise smoothing as a method to accurately predict a 37 kW induction motor's power loss components. The anisotropic heat transfer and complex geometry of the motor are represented well by the motor's lumped thermal network and 3-D finite element models, which characterize its intrinsic heat-transfer processes. With the inverse solution method, satisfactory temperature to power inverse mapping was achieved for different sets of noisy temperature inputs simulated from analytical and numerical forward solutions. This paper demonstrates that even with measurement noise in input data, if reliable information about the expected response of the system is available, an accurate reconstruction of power losses can be achieved.