## What is/are Isotropic Thermal?

Isotropic Thermal - In this work, highly anisotropic thermally conductive polyimide/boron nitride (PI/BN) composites were successfully prepared by a simple method called “ball milling, high-pressure compression and low-temperature sintering”.^{[1]}The tool employs effective anisotropic thermalmechanical properties methodology that accurately represents non-uniformity within a die or a layer, and significantly boosts computational performance by avoiding complex geometries.

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## isotropic thermal conductivity

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.^{[1]}We first assume the laser to possess a double-ellipsoidal shape and demonstrate that a well-calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.

^{[2]}The results showed that the anisotropic thermal conductivity of the composites treated by applied magnetic field forming chain structure is obtained.

^{[3]}Shear-induced orientation of hBN platelets in the solid HDPE/hBN composites leads to significant anisotropic thermal conductivity.

^{[4]}We found the anisotropic thermal conductivity along different directions.

^{[5]}The underlying mechanisms for such large tunability of the anisotropic thermal conductivity of \Mos are explored by computing and analyzing the dispersion relations, group velocities, relaxation times and mean free paths of phonons.

^{[6]}The required anisotropic thermal conductivity tensor is deduced from the new geometric mapping.

^{[7]}The key factor for the abnormal isotropic thermal conductivity is mainly the essentially analogous group velocities along intratube and intertube directions.

^{[8]}Vickers hardness and anisotropic thermal conductivity of the composites were measured and observed that ultrasonicated fabricated composites gave better result compared with BM composite and even from pure copper.

^{[9]}In this paper, a novel design of composite metamaterial with periodic lattice structure, consisting of metal lattice layer (copper) and stretchable polymer matrix (Ecoflex), owns the ability to tune the anisotropic thermal conductivity through external strains.

^{[10]}A cubic lattice distribution is chosen, wherein the constituents exhibit isotropic thermal conductivity behavior.

^{[11]}Researchers have made great efforts to study the anisotropic thermal conductivity in ferrofluids when an external magnetic field is imposed.

^{[12]}The obtained composite shows anisotropic thermal conductivity; in the parallel direction being higher than that in the perpendicular direction.

^{[13]}The cryocooler can reach a minimum temperature of 86 K when a small value of axial thermal conductivity is applied, which is 15 K lower than that of the case with isotropic thermal conductivity.

^{[14]}Here we propose a kind of intelligent thermal metamaterials by investigating a core-shell structure, where both the core and shell have an anisotropic thermal conductivity.

^{[15]}An anisotropic thermal conductivity phase change composite was successfully prepared.

^{[16]}In this work, the 3D anisotropic thermal conductivity tensor of a (010)-oriented \b{eta}-Ga2O3 single crystal was measured by using a novel time-domain thermoreflectance (TDTR) method with a highly elliptical pump beam.

^{[17]}Our model incorporates inner geometry, material inhomogeneity, composite materials and anisotropic thermal conductivity as important thermal features.

^{[18]}The numerical model is further used to examine the proposed approach for different anisotropic thermal conductivity ratios ranging from 1.

^{[19]}Due to the deficiencies of the common method, a novel 3-D lumped-parameter thermal network (LPTN) model of HAFFSPMM is proposed and some critical issues such as anisotropic thermal conductivity, contact thermal resistance are discussed.

^{[20]}The combination of large isotropic power factor and low anisotropic thermal conductivity leads to a maximum ZT of 1.

^{[21]}Results also show that anisotropic thermal conductivity of the MR fluid under investigation is promoted by increasing the volume fraction and decreasing the size of dispersed particles.

^{[22]}The core-shell and nanogaps structure imparted an anisotropic thermal conductivity, where the out-plane electronic thermal conductivity (321±16 W m-1 K-1) was 33.

^{[23]}Our results show that CdSe has the lowest anisotropic thermal conductivity, κL, of the four materials, at 4.

^{[24]}The inherent anisotropic thermophysical properties can be used to parametrize phase field models to incorporate anisotropic thermal conductivity and thermal expansion, allowing for a more accurate description of microstructural evolution under variable temperature and irradiation conditions.

^{[25]}BNNS@PDA/ANF composite papers presented anisotropic thermal conductivity, the through-plane (λ⊥) and in-plane (λ∥) thermal conductivity coefficient values of the 50 wt% BNNS@PDA/ANF composite papers reached 0.

^{[26]}In this paper, effects of anisotropic thermal conductivity and the Lorentz force in a ferro-nanofluid induced by external magnetic fields are investigated.

^{[27]}We theoretically analyze the distinct properties of different types of golden touch by delicately designing the anisotropic thermal conductivity of the shell.

^{[28]}Detailed Raman study of the axial and radial structures uncovers very strong structure anisotropy and explains the observed anisotropic thermal conductivities.

^{[29]}Copper-reduced graphene oxide composites having good anisotropic thermal conductivity and hardness values fabricated via flake powder metallurgy route.

^{[30]}By including the depth-dependent anisotropic thermal conductivity of PCD, a finite element thermal simulation is used to study the heat spreading process within a device.

^{[31]}For instance, anisotropic thermal conductivity within the graphitic flakes may be exploited to fabricate composites with bulk anisotropic thermal conductivity through preferential alignment of the flakes.

^{[32]}An experimental investigation was carried out to analyze the film cooling performance over a fiber-reinforced composite plate with anisotropic thermal conductivity (ATC).

^{[33]}We highlight the importance of the magnetic field distribution and the location of the thermal conductivity sensor in the analysis of the anisotropic thermal conductivity.

^{[34]}Here we report anisotropic thermal conductivity of suspended 2D-Te films measured by micro-Raman thermometry and the time-domain thermal reflectance (TDTR) method.

^{[35]}An empirical model that includes effects of interparticle spacing and zigzag angle to predict the anisotropic thermal conductivity of a composite containing particle chains is presented.

^{[36]}GNPs selectively distributed and oriented in the PBT phase afford the composite a low percolation threshold and anisotropic thermal conductivity.

^{[37]}A quasi one-dimensional approach was adopted to evaluate temperature dependent anisotropic thermal conductivity of a flat laminate vapor chamber called FGHP (Fine Grid Heat Pipe).

^{[38]}Knowing the exactlocal fiber orientation is critical for estimating anisotropic thermal conductivity and materials strength.

^{[39]}3 W·m–1·K–1 at room temperature), and high anisotropic thermal conductivity (k⊥/k||, ∼1.

^{[40]}Rare studies focused on the anisotropic thermal conductivity, while anisotropic thermal conductivity and hardness of reduced graphene oxide/metal are still far behind the expected values.

^{[41]}Phase change material (PCM) with anisotropic thermal conductivity can induce heat directional transmission in thermal control of the electronic devices, which improves the thermal control performance.

^{[42]}In this paper, a semi-analytical solution of the time-dependent heat conduction equation is presented for laterally infinite, multi-layered media with anisotropic thermal conductivities, convective outer boundaries and perfect thermal contact between the layers.

^{[43]}In addition, the magnesia nanofiber composite sheet showed anisotropic thermal conductivity derived from the fiber direction and had electrical insulation (7.

^{[44]}In addition, the magnesia nanofiber composite sheet showed anisotropic thermal conductivity derived from the fiber direction and had electrical insulation (7.

^{[45]}This work reports the first experimental evidence of in-plane anisotropic thermal conductivities in suspended Td-WTe2 samples of different thicknesses, and is also the first demonstration of such anisotropy in 2D transition metal dichalcogenides.

^{[46]}As the content of h-BN content further increased, the thermal conductivity decrease, which can be explained by the anisotropic thermal conductivity of h-BN and its distribution in the composites.

^{[47]}Owing to external magnetic fields and the anisotropic properties of RGO@Fe3O4 NPs, the nanocomposite with aligned RGO@Fe3O4 NPs exhibited an anisotropic thermal conductivity(λ).

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## isotropic thermal expansion

Polycrystalline solids composed of crystals with anisotropic thermal expansion coefficients exhibit ratchet growth (RG), a phenomenon characterized by a cumulative and irreversible volume expansion that develops upon exposing the material to cyclic excursions in temperature.^{[1]}Calcite has a highly anisotropic thermal expansion coefficient, and repeated heating and cooling cycles can potentially destabilize chalks by breaking cement bonds between neighboring particles.

^{[2]}5 and shows highly anisotropic thermal expansion properties.

^{[3]}The extracted unit cell parameters of the kinetically favorable crystal structures as a function of temperature were used to quantify the anisotropic thermal expansion coefficients along the three principal crystallographic directions.

^{[4]}Firstly, the anisotropic thermal expansion coefficient of KY(WO4)2 makes it challenging to integrate the crystal on glass substrates.

^{[5]}On warming, the dmpnH2 2+ cation experiences an ordered state with gradual increase of the local vibration motions of the central CH2 and terminal CH3 groups, a partially disordered state with gradually enhanced flipping motion between the major and minor orientations, and finally a twisting or rotating motion after the phase transition, accompanied by prominent anisotropic thermal expansions and dielectric anomalies/relaxations.

^{[6]}Due to the anisotropic chemical bonding, Mo2AlB2 has anisotropic thermal expansion coefficients αa = 6.

^{[7]}The thermal behavior of mixed sulfate–selenate and pure selenate compounds is anisotropic, with the highest thermal expansion in the direction perpendicular to the sheets of Np-bearing polyhedra, while the structure of the pure sulfate compound experiences almost isotropic thermal expansion with slightly higher expansion within the layer, which is explained by the influence of stronger Cs–O bonding.

^{[8]}The MG compacts made by UP had graphite grains aligned in the transverse direction and severe anisotropic thermal expansion and conductivity according to direction of orientation (axial and transverse).

^{[9]}The results show that the feldspars have a low and isotropic thermal expansion that do not affect the molecular structure as much in red and white granite, while on the other hand, thermal stresses are confined in quartz crystal, resulting in intense intragranular cracking for golden and black granite.

^{[10]}The system crystallises in Cccm and harbours three coexisting distortions relative to the parent Fm3[combining macron]m structure, which leads to anisotropic thermal expansion with a near-zero component in one direction.

^{[11]}The ab initio calculated anisotropic Gruneisen parameters of the different phonon modes in all the chalcogenides along with the elastic constants are used to compute anisotropic thermal expansion behavior, which is found in good agreement with experiments.

^{[12]}A uniaxial compressive stress is applied on the thin film through changing the temperature due to the anisotropic thermal expansion of the polyvinylidene fluoride (PVDF) substrate.

^{[13]}TOC for ne is higher than no, which has been explained on the basis of anisotropic thermal expansion.

^{[14]}The grains, formed at the stage of plastic deformation by twinning, prove to be unstable even at the stage of polygonization, due to the mobility of highly disoriented boundaries under conditions of the anisotropic thermal expansion of neighboring regions.

^{[15]}Raman spectra and density functional theory (DFT) calculations demonstrate that spring-like geometric deformation results in the anisotropic thermal expansion behaviour.

^{[16]}The precise determination of the cell parameters by Rietveld refinement enabled the determination of the anisotropic thermal expansion behavior of the crystalline Nb2O5 phase.

^{[17]}5 GW/cm2 @1064 nm, 10 ns), favorable anisotropic thermal expansion (αa/αb = 5.

^{[18]}(100) or (010) crystal cuts should be chosen for applications of a R EScO 3 as a substrate material, when mostly isotropic thermal expansion or longitudinal stiffness in-plane is desired, respectively.

^{[19]}Anisotropic thermal expansion coefficients of tetragonal γ-TiAl and hexagonal α2-Ti3Al phases were calculated using first principles methods.

^{[20]}This study presents a microscopic description of connection between anisotropic thermal expansion and a cooperative J-T effect, which inspired exploration of thermal-mechanical coupled functional materials based on LaPbMSbO6 double perovskites.

^{[21]}Li4Na2CsB7O14 with unique edge-sharing [BO4]5- tetrahedra, an unprecedented [B14O28]14- cluster, and high anisotropic thermal expansion has been obtained under atmospheric pressure conditions, indicating that high pressure is not essential for obtaining edge-sharing [BO4]5- tetrahedra-containing borates.

^{[22]}A multiplicative split of the deformation gradient into a thermal, an elastic and a plastic part is introduced, where isotropic thermal expansion and isochoric plastic deformation are assumed.

^{[23]}Bistable panels are obtained by exploiting the anisotropic thermal expansion of anti-symmetric composite laminates, which directly influences the post-cured shape.

^{[24]}The phosphor exhibited good luminescence characteristics but possessed poor mechanical strength, which was probably caused by anisotropic thermal expansion due to the orthorhombic crystal structure of Ba2SiO4.

^{[25]}The induced magnetic anisotropy is attributed to the anisotropic thermal expansion in the substrate.

^{[26]}Nevertheless, most such materials exhibit anisotropic thermal expansion in the crystal lattice.

^{[27]}In contrast to cubic ZrW2O8 and ZrMo2O8, which have isotropic negative thermal expansion, the compounds Sc2(WO4)3 and Sc2(MoO4)3 with the orthorhombic structure show anisotropic thermal expansion that is negative along the b and c axes.

^{[28]}2·2MeOH exhibits anisotropic thermal expansion in which the flat layers shift sideways as the temperature is increased, with colossal interlayer expansion occurring (αc = +200 MK-1 over 140-180 K, αc = +165 MK-1 over 200-280 K).

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## isotropic thermal property

This paper opens an avenue for developing thermal metamaterials with programmable anisotropic thermal properties.^{[1]}A method is presented to characterize the anisotropic thermal properties of materials based on nanosecond transient thermoreflectance (TTR).

^{[2]}The proposed approach uses a thermal simulation of a 3D-printed part, accounting for the anisotropic thermal properties, and the orientation of the local material properties are assigned based on the deposition path in multiple print orientations.

^{[3]}The composites exhibit anisotropic thermal properties owing to their laminated architecture and two-dimensional character of graphene.

^{[4]}Accurate determination of anisotropic thermal properties is important for the assessment of the structural integrity of composite members.

^{[5]}Graphene's highly anisotropic thermal properties result in high thermal conductivity in the planar direction, while it is low in the normal direction.

^{[6]}Layered two-dimensional (2D) materials have highly anisotropic thermal properties between the in-plane and cross-plane directions.

^{[7]}Assembly of such vdW solids has enabled novel electronic devices and could lead to control over anisotropic thermal properties through tuning of inter-layer coupling and phonon scattering.

^{[8]}Lithium-ion cells show highly anisotropic thermal properties due to the different layers of the electrodes.

^{[9]}The effect of the doping concentration on the anisotropic thermal properties of Yb:YCOB crystals was systematically evaluated for the first time to our knowledge.

^{[10]}Self-assembly and orientation of thermally conductive fillers into ordered scaffold often lead to composites with anisotropic thermal properties.

^{[11]}Great care has been taken to model the anisotropic thermal properties of the coils, enabling the CFD simulations to present an accurate model validated in wind tunnel experiments.

^{[12]}Recently, metals with graphene and graphene oxide have been extensively used to enhance the mechanical and anisotropic thermal properties of composites.

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## isotropic thermal conduction

The modeling includes anisotropic thermal conduction within an evolving magnetic topology, and parameters separate the Alfvénic, resistive-wall, and plasma-resistive timescales.^{[1]}In this paper, we propose an approach using a Cartesian reference system to treat the anisotropic thermal conduction of problems for which the solid medium is characterized by a set of tensors of thermal conductivity of different natures (Cartesian and/or cylindrical and/or spherical), with or without phase change.

^{[2]}The anisotropic functionality of the ACPCs enabled them to be used in electrical and thermal management applications, such as subminiature integrated circuits, highly reliable electrical interconnects and anisotropic thermal conduction.

^{[3]}However, most models of structure formation neglect potentially important physical processes, like anisotropic thermal conduction (ATC).

^{[4]}We include non-equilibrium cooling and chemistry, a homogenous interstellar radiation field, and shielding with a modern pressure-energy smoothed particle hydrodynamics (SPH) method including isotropic thermal conduction and a meshless-finite-mass (MFM) solver.

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## isotropic thermal pressure

An investigation of the ion acoustic nonlinear periodic (cnoidal) waves in a magnetized plasma with positive ions having anisotropic thermal pressure and Maxwellian electrons is carried out.^{[1]}We show how the QHA is violated by materials exhibiting anisotropic thermal pressure.

^{[2]}The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors.

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## isotropic thermal transport

5 Wm-1K-1, about 50% larger than that of kc, showing the clear anisotropic thermal transport property of the -W films.^{[1]}Herein, a biomimetic design enabled by radially aligned, bimodal graphene frameworks (RG-Fin) is proposed to achieve highly efficient and isotropic thermal transport.

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