Anomalous Thermal Conductivity Research Articles

Proton Collective Quantum Tunneling Induces Anomalous Thermal Conductivity of Ice under Pressure.

Proton tunneling is believed to be nonlocal in ice, but its range has been shown to be limited to only a few molecules. Here, we measured the thermal conductivity of ice under pressure up to 50GPa and found it increases with pressure until 20GPa but decreases at higher pressures. We attribute this nonmonotonic thermal conductivity to the collective tunneling of protons at high pressures, supported by large-scale quantum molecular dynamics simulations. The collective tunneling loops span several picoseconds in time and are as large as nanometers in space, which match the phonon periods and wavelengths, leading to strong phonon scattering at high pressures. Our results show direct evidence of global quantum motion existing in high-pressure ice and provide a new perspective to understanding the coupling between phonon propagation and atomic tunneling.

Full-landscape selection rules of electrons and phonons and temperature-induced effects in 2D silicon and germanium allotropes

The electron-phonon (el-ph) and phonon-phonon interactions play crucial roles in determining the electronic and thermal transport properties of materials. Using the group theory and ab-initio calculations, we have derived the full-landscape selection rules for intravalley and intervalley scattering for carriers in 2D silicon and germanium allotropes with low buckled (LB) and large honeycomb dumbbell (LHD) structures, showing dominant role of optical modes in total el-ph coupling in LHD Si/Ge due to most el-ph scattering channels via acoustic modes blocked by symmetries. Remarkably, we show that due to the relatively large optical phonon bandwidth and “bunching effect" of acoustic phonon bands, the selection rules of three-phonon interactions reveal the dominant ooo and aoo channels in LHD and LB Si/Ge, respectively, and the temprature-induced effects significantly increase the ratio between mode-resolved four-phonon interactions and three-phonon interactions in most of the phonon-frequency region, finally leading to the low thermal conductivities in both LB and LHD Si/Ge. Furthermore, we observe the anomalous temperature-dependent thermal conductivities in LHD Ge, resulted from the vanishing quasi-acoustic-optical phonon gap under the temperature-induced effects. By considering full el-ph coupling and higher-order anharmonic phonon-phonon interactions, the maximal thermoelectric figures of merits in LHD Si and LB Ge are found to reach 1.06 and 0.66 at 700 K, respectively, significantly surpassing their bulk counterparts. Our work is poised to stimulate wide-ranging exploration into phonon transport across diverse materials, and benefits both fundamental knowledge and advanced technologies of 2D Si/Ge allotropes.

Local symmetry distortion induced anomalous thermal conduction in thermoelectric layered oxyselenides

Polyhedral distortion, associated closely with the atomic arrangement and interatomic interactions, drives many unique behaviors in solids, such as phase transition and negative thermal expansion. In thermoelectric heteroanionic oxides, the anionic polyhedra are widely present, but their effect on thermal transport is rarely investigated. Here, we report an anomalous thermal conduction induced by local symmetry distortion in layered oxyselenides via solving the Boltzmann transport equation based on first-principles calculations. We found interestingly that lighter BiCuSeO exhibits lower thermal conductivity than heavier BiAgSeO. Due to the different distorted degrees of CuSe4 and AgSe4 tetrahedrons, Cu prefers the in-plane vibration, while Ag has more tendency of out-of-plane vibration. Thus, the heat-carrying phonons dominated by the rattling-like vibration of Cu are significantly suppressed, resulting in lower thermal conductivity of BiCuSeO. This study highlights the importance of polyhedral distortion in regulating thermal conduction in layered heteroanionic materials.

Anomalous thermal conductivity of alkaline-earth-metal-substituted EuTiO3 induced by resonant scattering

We have investigated thermal conductivities (κ) of polycrystalline Eu1–xAxTiO3 (A = Ca, Sr, Ba, 0 ≤ x ≤ 0.8) bulk materials in the temperature range of ∼ 2 K <T < 1173 K. The EuTiO3 demonstrates anomalous glass-like κ(T) behavior at low temperatures. Partial substitutions with Sr2+ and Ba2+ do not cause a significant change in the κ(T) behavior, while a κ(T) peak, which looks like a manifestation of a typical crystalline solid, appears only in the Ca-substituted samples with an orthorhombic structure when x ≥ 0.4. After excluding the magnetic effects on κ and discussing the possible phonon scattering mechanisms in depth, together with heat capacity Cp measurements and high-resolution X-Ray diffraction characterization, we find that the unusual low κ at low temperatures is attributed to resonant scattering induced by the intrinsic disordered local structure and lattice instability in EuTiO3. Due to the different lattice dynamics of ATiO3, the lattice structure of Eu1–xCaxTiO3 can be regarded as formed by a part-soft (from EuTiO3) part-rigid (from CaTiO3) sublattice. The anomalous κ(T) behavior of Eu1–xCaxTiO3 results from the combined effect of phonon transport between the normal phononic heat transport in the rigid sublattice and the strong damping of heat conduction in the soft sublattice.

Basal-plane heat transport in graphite thin films

While the phonon hydrodynamic regime has recently been highlighted experimentally in graphite films, the understanding and modeling of heat transport along their basal plane remain elusive. From first-principles-based modeling, we predict a significant influence of the surface roughness on basal-plane thermal conductivity due to the collective phonon drift. The occurrence condition of the phonon Knudsen minimum is also shown to strongly depend on the surface roughness. We summarize the basal-plane heat transport along graphite thin films into coherent and incoherent regimes and also present a speculation for the recently observed anomalous thickness-dependent thermal conductivity. Our work provides guidance for the experimental explorations of phonon hydrodynamics in graphitic micro- and nanostructures in the future.

Anomalous lattice thermal conductivity driven by all-scale electron-phonon scattering in bulk semiconductors

Electron-phonon coupling (EPC) has been broadly considered to govern the charge transport in solids, whereas its effect on thermal conductivity, especially for semiconductors at ambient temperatures, is a widely debated issue in condensed-matter physics. Employing state-of-the-art first-principles calculations to quantify all the possible scattering factors, we show the dominant role of EPC in phonon transport of $n$-doped GaSb, which yields an unprecedented reduction of lattice thermal conductivity and triggers anomalous temperature-independent behavior. The significant EPC impact hinges on the joint effect of multiple conduction pockets, large EPC strength, and bunched heat-carrying acoustic branches, provoking strong electron-phonon scattering to surpass the intrinsic phonon-phonon scattering for all-scale phonons, in contrast to the case in silicon that only long-wave phonons can be scattered by carriers even at high doping level. This work advances the understating of phonon transport in doped semiconductors and stimulates potential heat management application of anomalous thermal conductivity.

Spin-phonon interactions induced anomalous thermal conductivity in nickel (II) oxide

Nickel (II) oxide is a prominent candidate for spintronic and spin-caloritronic applications operating at room temperature. Although there are extensive studies on nickel oxide, the roles of magnon- and spin-phonon interactions on thermal transport are not well understood. In the present work, the relationship between spin-phonon interactions and thermal transport is investigated by performing inelastic neutron scattering, time-domain thermoreflectance thermal conductivity measurements, and atomistic thermal transport calculations. Inelastic neutron scattering measurements of the magnon lifetime imply that magnon thermal conductivity is trivial, and so heat is conducted only by phonons. Time-domain thermoreflectance measurements of the thermal conductivity vs. temperature follow T−1.5 in the antiferromagnetic phase. This temperature dependence cannot be explained by phonon-isotope and phonon-defect scattering or phonon softening. Instead, we attribute this to magnon-phonon scattering and spin-induced dynamic symmetry breaking. The spin-phonon interactions are saturated in the paramagnetic phase and lead to a weaker temperature dependence of T−1.0 at 550–700 K. These results reveal the importance of spin-phonon interactions on lattice thermal transport, shedding light on the engineering of functional antiferromagnetic spintronic and spin-caloritronic materials through these interactions.

A molecular dynamics study of thermal conductivity and viscosity in colloidal suspensions: From well-dispersed nanoparticles to nanoparticle aggregates

This study investigates the microscopic transport behavior of nanofluids addressing some debatable points including the anomalous thermal conductivity (κ), against the predictions of classical effective medium theories. International Nanofluid Property Benchmark Exercise (INPBE) [J. Buongiorno et al., J. Appl. Phys. 106 (2009) 094312] has shown that no such anomaly found in well-dispersed nanofluids after conducting experiments for range of different types of nanofluids. However, a number of molecular dynamics based studies reported otherwise making inconsistent conclusion with INPBE. In this work, it is argued that the over predicted κ values reported in previous computational studies can be attributed to the ill-defined partial enthalpy formulation of the Green-Kubo method for multicomponent systems. Present study begins by addressing this issue via non-equilibrium molecular dynamics and shows that the results are in agreement with the conclusions of INPBE. Further, it is shown that the contribution of potential micro-mechanisms such as micro-convection due to Brownian motion, and the solid-like liquid layering are either absent or suppressed by the interface thermal resistance. The observed decreasing trend of viscosity enhancement to thermal conductivity enhancement ratio (Cη/Cκ) with increasing particle size indicates the improved heat transfer performance in nanofluids with larger nanoparticles. The effect of nanoparticle aggregation, the proposed originative mechanism of anomalous κ, is evaluated arranging nanoparticles as chain-like structures. A 67% improvement in κ is achieved with negligible viscosity variation. This rapidly reduces Cη/Cκ indicating better heat transfer performance with the presence of conductive paths due to the aggregation or in general extended nanostructures.

Anomalous and non-monotonic strain dependent thermal conductivity of typical negative thermal expansion material ScF3

It is well known that the lattice thermal conductivity of the vast majority of bulk materials increases under compressive strain and decreases under tensile strain. In this paper, taking the typical negative thermal expansion material ScF3 as an example, we systematically investigate the effect of strain on the phonon transport properties by means of first-principles calculation combined with the Boltzmann transport equation. The results show that the thermal conductivity of ScF3 exhibits an anomalous strain dependence, where the thermal conductivity decreases under compressive strain while increasing as the tensile strain is smaller than −4.2 GPa. When the tensile strain increases further (larger than −4.2 GPa), however, the thermal conductivity of ScF3 decreases with tensile strain, presenting a non-monotonic behavior. Through analyzing the phonon mode information, we demonstrate that such anomalous and non-monotonic strain dependent thermal transport in ScF3 mainly originated from the intrinsic character of the negative Grüneisen parameter (negative thermal expansion). Moreover, the root mean square displacement is also utilized to further demonstrate the variation of phonon anharmonicity and thermal conductivity of ScF3 with strain. The findings shed light on the underlying association between thermal expansion and thermal conductivity and provide a feasible strategy for searching for materials with anomalous strain dependent thermal conductivity.

A renovated Jaffrey-Hamel flow problem and new scaling statistics for heat, mass fluxes with Cattaneo–Christov heat flux model

In dire situations, such as the restricted spatial scale in nanoparticle systems and the analogous analysis of non-Fourier heat conduction and conventional heat conduction, the transmission of heat and momentum will exhibit non-linear and nonlocal behavior. The mechanisms of heat and mass transfer for non-Newtonian fluid flow between two inclined planes (convergent channel) with porous walled are taken into consideration. The Jaffrey-Hamel flow equation is renovated with the contribution of Carreau rheological model. The Cattaneo heat flux is presented to designate the anomalous heat, mass transport of Carreau nanofluid considering the influences of radiation flux, Brownian diffusion, and thermophoresis. Assumption, theories, and conservation law's leads to governing PDEs, which are solved numerically by invoking the Keller-Box scheme. It was concluded that for both conduit, flow reversal occurs only in the divergent domain of the channel but not in the converging where rapid acceleration of flow occurs, and inertial forces dominate the transport process. The flow instability in a porous media incorporate fluid inertia. The renovated model, which incorporates non-Fourier's law of heat conduction, can explain the anomalous thermal conductivity enhancement. The thermal relaxation effects the heat flux significantly, the conduction mechanism switches to oscillatory conduction with narrower temperature.

Enhanced Anharmonicity by Forming Low-Symmetry Off-Center Phase: The Case of Two-Dimensional Group-IB Chalcogenides.

Enhanced anharmonicity is required to achieve many interesting phenomena in thermoelectricity, superconductivity, ferroelectricity, etc. Here, we propose a novel mechanism for enhancing anharmonicity by forming the low-symmetry off-center ground state, such as the s(II) phase, in two-dimensional AIB2X chalcogenides (AIB = Cu, Ag and Au; X = S, Se, and Te). In this system, the in-plane rotational phonon mode introduces a much stronger anharmonicity in the distorted s(II) phase than in the nondistorted s(I) phase. We show that the stabilities of the s(I) and s(II) phases arise from the ionicity and the ionic size; for example, the low ionicity and the small ionic size favor the s(II) phase. We further demonstrate that the anharmonicity can be tuned by controlling the strain-induced s(II)-to-s(I) phase transition, which explains the anomalous lattice thermal conductivity. Our work relates anharmonicity to symmetry-breaking structural distortion and widens the ways to design excellent thermoelectric materials.

Visible light modulation and anomalous thermal transport in two-dimensional &lt;i&gt;X&lt;/i&gt;-AlN (&lt;i&gt;X&lt;/i&gt; = C, Si, TC) semiconductor

Aluminum nitride (AlN) is of paramount importance in developing electronic devices because of excellent stability and thermal transport performance. However, lack of novel materials which can provide colorful physical and chemical properties seriously hinders further digging out application potential. In this work, we perform an evolutionary structural search based on first-principles calculation and verify the dynamic and thermal dynamic stability of porous buckled AlN and &lt;i&gt;X&lt;/i&gt;-AlN (&lt;i&gt;X&lt;/i&gt; = C, Si, TC) structural system, which constructs by introducing C, Si atoms and triangular carbon (TC) into the porous vacancy of AlN, by calculating phonon spectra and first-principles molecular dynamic simulations. Structural deformation becomes gradually serious with the increase of structural unit size and significantly influences structural, electronic, and thermal transport properties. Firstly, we point out that a flat energy band appears around the Fermi level in C-AlN and Si-AlN because of weak interatomic interaction between C/Si and the neighbor Al atoms. Unoccupied C-/Si-p&lt;sub&gt;&lt;i&gt;z&lt;/i&gt;&lt;/sub&gt; and Al-p&lt;sub&gt;&lt;i&gt;z&lt;/i&gt;&lt;/sub&gt; do not form &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ {\rm{\pi }} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20230116_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20230116_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; bond and only a localized flat band near Fermi level arises, and thus the absorption peaks of structures are enhanced and the red shift occurs. Bonding state of &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ {\rm{\pi }} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20230116_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20230116_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; bond from hybridized C-p&lt;sub&gt;&lt;i&gt;z&lt;/i&gt;&lt;/sub&gt; orbitals in triangular carbon of TC-AlN lowers the energy of conduction band at &lt;i&gt;K&lt;/i&gt; point in the first Brillouin zone and the corresponding antibonding state raises the band at &lt;i&gt;Γ&lt;/i&gt;, therefore transition from indirect bandgap of AlN to direct bandgap of TC-AlN appears. Secondly, porous buckled AlN shows the lowest thermal conductivity due to asymmetric Al—N bonds around the porous vacancy and vertically stacked N—N bonds. Introduced C and Si atoms both reduce structural anharmonicity, while the former has a relatively small distortion, and so it has a higher thermal conductivity. Triangular carbon in TC-AlN hinders phonon scattering between FA mode and other phonon modes and has the weakest anharmonicity because of the strongest bond strength, and obtains the highest thermal transport performance. Finally, we unveil the physical mechanism of anomalous thermal conductivity in &lt;i&gt;X&lt;/i&gt;-AlN system by modulating the biaxial tensile strain. Enhanced vertical N—N bonds dominate thermal transport due to its weaker anharmonicity with a slightly strain, and when tensile strain is above the 4%, soften phonon modes reduce phonon velocity and thus hinders the thermal transport process. Therefore, occurs the anomalous thermal transport behavior, i.e. thermal conductivity first rises and then drops with applied biaxial strain increasing. Our work paves the way for modulating two-dimensional AlN performance and provides a new insight for designing promising novel two-dimensional semiconductors.

Anharmonic Interaction in Negative Thermal Expansion Material CaTiF6.

Although the quasi-harmonic approximation (QHA) method applies to many materials, it is necessary to study the anharmonic interaction for extremely anharmonic materials. In this work, the unusual negative thermal expansion (NTE) property of CaTiF6 is studied by combing QHA and anharmonic interaction. The improved self-consistent phonon approximation (ISCPA), which treats anharmonic effects in solids nonperturbatively, is employed. The agreement of NTE behavior between the calculation and the experiment can be further promoted from qualitative consistency by QHA to quantitative consistency by the ISCPA. From mode Grüneisen parameters, it is found that the low-frequency phonons, especially acoustic phonons, contribute greatly to the NTE behavior of CaTiF6. The rigid unit modes (RUMs) of low-frequency optical phonons can be identified. The phonon lifetime of CaTiF6 is calculated from three-phonon interactions; thereby, the NTE mechanism can be further explored by phonon lifetimes of phonons with different frequencies on heating. The anomalous lattice thermal conductivity (LTC) is predicted using the Boltzmann transport equation within the relaxation time approximation. The glasslike LTC can occur in crystal CaTiF6.

Anomalous thermal conductivity in amorphous niobium pentoxide thin films: A correlation study between structure and thermal properties

Niobium pentoxide (Nb2O5) based thin films are predominantly used in optical filters, solar cells, electrochromic devices, sensors and microelectronic devices. The temperature-dependent thermophysical properties of Nb2O5 films are crucial for the performance and reliability of such devices. Within this work, for the first time, the thermal properties of sputter deposited Nb2O5 films are correlated with their structural properties at different length scales. Thermal measurements were carried out by time-domain thermoreflectance, yielding a thermal conductivity of 3.0±0.3 W/mK at 25 °C for crystalline Nb2O5 films, which decreases to 2.6±0.2 W/mK at 450 °C. In contrast, amorphous Nb2O5 films had a thermal conductivity of 2.2±0.2 W/mK below 275 °C. Above 275 °C, an abrupt increase in thermal conductivity up to a maximum value of 2.8±0.2 W/mK at 325 °C was recorded. The average and local structure are determined by in-situ high-temperature X-ray diffraction and in-situ high-temperature Raman spectroscopy, respectively. These characterization techniques together enable to cross-correlate structural and thermal properties of Nb2O5 thin films highlighting the observed peculiarity of the thermal conductivity. This substantial increase in thermal conductivity cannot be linked to any macroscopic phase change but rather to a local phase rearrangement near the crystallization temperature, evidenced by temperature-dependent Raman spectra analysis. This study serves as a guide to engineering future Nb2O5 based thin film devices and for their reliability optimization.

Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach.

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e., propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equationof the prototypical β-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. Our main findings are as follows. (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equationto study thermal propagation.

Abnormally high thermal conductivity in fivefold twinned diamond nanowires

Fivefold twins (5FTs), discovered nearly 200 years ago, are a common multiply twinned structure that usually dramatically deteriorate the thermal transport properties of nanomaterials. Here, we report the anomalous thermal conductivity (κ) in a novel fivefold twinned diamond nanowires (5FT-DNWs). The κ of 5FT-DNWs is effectively enhanced by the defects of 5FT boundaries, and non-monotonically changes with the cross-sectional area (S). Above the critical S = 7.1 nm2, 5FT-DNWs shows a constant value of κ, whereas below it, there appears a sharp increase in κ with decreasing S. More importantly, 5FT-DNWs with minimal S show a superior κ over the bulk diamond. By confirming the Normal-process-dominated scattering event, it is demonstrated that the phonon hydrodynamic behavior plays a determinative role in abnormally high κ of 5FT-DNWs with small S. The super-transported phonon hydrodynamic phenomenon unveiled in the twinned diamond nanowires may provide a new route for pursuing highly thermally conductive nanomaterials.

Anomalous Thermal Conductivity in Amorphous Niobium Pentoxide Thin Films: A Correlation Study between Structure and Thermal Properties

Anomalous Thermal Conductivity in Amorphous Niobium Pentoxide Thin Films: A Correlation Study between Structure and Thermal Properties

Anomalous Thermal Conductivity Induced by High Dispersive Optical Phonons in Rubidium and Cesium Halides

Anomalous Thermal Conductivity Induced by High Dispersive Optical Phonons in Rubidium and Cesium Halides

Quantum oscillations, magnetic breakdown and thermal Hall effect in Co3Sn2S2

Co3Sn2S2 is a ferromagnetic semi-metal with Weyl nodes in its band structure and a large anomalous Hall effect below its Curie temperature of 177 K. We present a detailed study of its Fermi surface and examine the relevance of the anomalous transverse Wiedemann Franz law to it. We studied Shubnikov-de Haas oscillations along two orientations in single crystals with a mobility as high as cm2 V−1 s−1 subject to a magnetic field as large as ∼60 T. The angle dependence of the frequencies is comparable with density functional theory (DFT) calculations and reveals two types of hole pockets (H1, H2) and two types of electron pockets (E1, E2). An additional unexpected frequency emerges at high magnetic field. We attribute it to magnetic breakdown between the hole pocket H2 and the electron pocket E2, since it is close to the sum of the E2 and H2 fundamental frequencies. By measuring the anomalous thermal and electrical Hall conductivities, we quantified the anomalous transverse Lorenz ratio, which is close to the Sommerfeld ratio () below 100 K and deviates downwards at higher temperatures. This finite temperature deviation from the anomalous Wiedemann–Franz law is a source of information on the distance between the sources and sinks of the Berry curvature and the chemical potential.

Effect of Exfoliated Graphene on Thermal Conductivity Enhancements of Graphene-Ironoxide Hybrid Nanofluids: Experimental Investigation and Effective Medium Theories

Reasoning of particular mechanism of anomalous thermal transport behaviours are not identified yet for the nanofluids. In this study, iron oxide (Maghemite: MH) and graphene (Gr) flake dispersed deionized water (DW) hybrid nanofluid system were developed for the first time to evaluate the thermal conductivity (TC) enhancements along with the analysis of anomalous TC behavior implementing modified effective medium theories (EMTs). A solvo-thermal two-step method was used to develop the MH nanoparticle and exfoliated Gr flake dispersed hybrid nanofluids with different compositions. Stability of as-prepared hybrid nanofluids were monitored using Ultraviolet-Visible (UV-Vis) spectroscopy. The maximum sedimentation rate was observed ~ 8.4 % after 600 hours. The results showed an overall maximum TC enhancement of ~ 43 % at 25 °C. EMTs were modified with the consideration of flat geometry of Gr flake. It is found that, modified EMTs with the crumpled factor (due to the non-flatness or crumple of Gr flake) of ~ 0.205 the predicted effective TC enhancements are agreed with the experimental TC’s of Gr-NMP/MH-DW hybrid nanofluids samples. The estimated crumple factor value of exfoliated Gr flakes using images analysis was also found nearly similar (~ 0.232). This agreement exposed that, Gr flake’s with negligible thickness compared to its extremely wide basal plane dimensions and its non-flatness or crumpled geometry in the nanofluids have the leading impacts on the effective TC properties of the Gr flake dispersed nanofluids. This modified model opens the new doors to analyse the insight of the thermophysical properties of various types of nanofluids by introducing potential other parameters.