Local Equilibrium Conditions Research Articles

A High-Order Well-Balanced Discontinuous Galerkin Method for Hyperbolic Balance Laws Based on the Gauss-Lobatto Quadrature Rules

In this paper, we develop a high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules. Important applications of the method include preserving the non-hydrostatic equilibria of shallow water equations with non-flat bottom topography and Euler equations in gravitational fields. The well-balanced property is achieved through two essential components. First, the source term is reformulated in a flux-gradient form in the local reference equilibrium state to mimic the true flux gradient in the balance laws. Consequently, the source term integral is discretized using the same approach as the flux integral at Gauss-Lobatto quadrature points, ensuring that the source term is exactly balanced by the flux in equilibrium states. Our method differs from existing well-balanced DG methods for shallow water equations with non-hydrostatic equilibria, particularly in the aspect that it does not require the decomposition of the source term integral. The effectiveness of our method is demonstrated through ample numerical tests.

Emergence hour-by-hour of features in the kilonova AT2017gfo

The spectral features in the optical/near-infrared counterparts of neutron star mergers (kilonovae, KNe) evolve dramatically on hourly timescales. To examine the spectral evolution, we compiled a temporal series that was complete at all observed epochs from 0.5 to 9.4\,days of the best optical/near-infrared (NIR) spectra of the gravitational-wave detected kilonova AT2017gfo. Using our analysis of this spectral series, we show that the emergence times of spectral features place strong constraints on line identifications and ejecta properties, while their subsequent evolution probes the structure of the ejecta. We find that the most prominent spectral feature, the 1\ P Cygni line, appears suddenly, with the earliest detection at 1.17\,days. We find evidence in this earliest feature for the fastest yet discovered kilonova ejecta component at 0.40--0.45$c$. Across the observed epochs and wavelengths, the velocities of the line-forming regions span nearly an order of magnitude, down to as low as 0.04--0.07$c$. The time of emergence closely follows the predictions for because combines rapidly under local thermal equilibrium (LTE) conditions. The transition time between the doubly and singly ionised states provides the first direct measurement of the ionisation temperature. This temperature is highly consistent with the temperature of the emitted blackbody radiation field at a level of a few percent. Furthermore, we find the KN to be isotropic in temperature, that is, the polar and equatorial ejecta differ by less than a few hundred Kelvin or \( 5\)<!PCT!>, in the first few days post-merger based on measurements of the reverberation time-delay effect. This suggests that a model with very simple assumptions, with single-temperature LTE conditions, reproduces the early kilonova properties surprisingly well.

Gas Kinematics and Dynamics of Carina Pillars: A Case Study of G287.76-0.87

We study the kinematics of a pillar, namely G287.76-0.87, using three rotational lines of 12CO(5-4), 12CO(8-7), 12CO(11-10), and a fine structure line of [O i] 63 μm in southern Carina observed by SOFIA/GREAT. This pillar is irradiated by the associated massive star cluster Trumpler 16, which includes η Carina. Our analysis shows that the relative velocity of the pillar with respect to this ionization source is small, ∼1 km s−1, and the gas motion in the tail is more turbulent than in the head. We also performed analytical calculations to estimate the gas column density in local thermal equilibrium (LTE) conditions, which yields N CO as (∼0.2–5) × 1017 cm−2. We further constrain the gas’s physical properties in non-LTE conditions using RADEX. The non-LTE estimations result in nH2≃105cm−3 and N CO ≃ 1016 cm−2. We found that the thermal pressure within the G287.76-0.87 pillar is sufficiently high to make it stable for the surrounding hot gas and radiation feedback if the winds are not active. While they are active, stellar winds from the clustered stars sculpt the surrounding molecular cloud into pillars within the giant bubble around η Carina.

Spatial Distribution of C4H and c-C3H2 in Cold Molecular Cores

C4H and c-C3H2, as unsaturated hydrocarbon molecules, are important for forming large organic molecules in the interstellar medium. We present mapping observations of C4H (N = 9−8) lines, c-C3H2 (J Ka,Kb = 21,2–10,1), and H13CO+ (J = 1−0) toward 19 nearby cold molecular cores in the Milky Way with the IRAM 30 m telescope. C4H 9–8 was detected in 13 sources, while c-C3H2 was detected in 18 sources. The widely existing C4H and c-C3H2 molecules in cold cores provide material to form large organic molecules. Different spatial distributions between C4H 9–8 and c-C3H2 2–1 were found. The relative abundances of these three molecules were obtained under the assumption of local thermodynamic equilibrium conditions with a fixed excitation temperature. The abundance ratio of C4H to c-C3H2 ranged from 0.34 ± 0.09 in G032.93+02 to 4.65 ± 0.50 in G008.67+22. A weak correlation between C4H/H13CO+ and c-C3H2/H13CO+ abundance ratios was found, with a correlation coefficient of 0.46, which indicates that there is no tight astrochemical connection between C4H and c-C3H2 molecules.

Numerical simulation of Darcy–Forchheimer flow of Casson ternary hybrid nanofluid with melting phenomena and local thermal non-equilibrium effects

The Casson fluid flow over a stretching sheet is studied in this work in the presence of porous media with melting heat transfer and chemical reaction, combining nanoparticles of Ti4Al6V,AA7072 and AA7075 with a base fluid of sodium alginate (NaAlg). The porous medium Darcy Forchheimer effect is included in the momentum equation. Through the effects of melting, the process of heat transfer is described. In order to explore the features of heat transmission in the absenteeism of LTECs (local thermal equilibrium conditions), the current study employs a mathematical model that has been simplified. For both the solid and liquid phases, the LTNE model yields two different fundamental thermal gradients. This proposed model compares the YOM (Yamada-Ota model) and XM (Xue model), two well-known trihybrid nanofluid models, in terms of performance. After applying the proper transformations, modulated non-linear PDEs (partial differential equations) are simplified in ODEs (ordinary differential equations) and the bvp4c method is used to solve them numerically. A graphic discussion of the relevant factors' significance on the pertinent fields has been presented. It is observed that the Casson ternary hybrid nanofluid temperature and velocity distributions predominate at higher melting parameter. The solid phase's heat transport rate rises with an upsurge in the interphase heat transfer parameter.

A Broad Line-width, Compact, Millimeter-bright Molecular Emission Line Source near the Galactic Center

A compact source, G0.02467–0.0727, was detected in Atacama Large Millimeter/submillimeter Array 3 mm observations in continuum and very broad line emission. The continuum emission has a spectral index α ≈ 3.3, suggesting that the emission is from dust. The line emission is detected in several transitions of CS, SO, and SO2 and exhibits a line width FWHM ≈ 160 km s−1. The line profile appears Gaussian. The emission is weakly spatially resolved, coming from an area on the sky ≲1″ in diameter (≲104 au at the distance of the Galactic center, GC). The centroid velocity is v LSR ≈ 40–50 km s−1, which is consistent with a location in the GC. With multiple SO lines detected, and assuming local thermodynamic equilibrium (LTE) conditions, the gas temperature is T LTE = 13 K, which is colder than seen in typical GC clouds, though we cannot rule out low-density, subthermally excited, warmer gas. Despite the high velocity dispersion, no emission is observed from SiO, suggesting that there are no strong (≳10 km s−1) shocks in the molecular gas. There are no detections at other wavelengths, including X-ray, infrared, and radio. We consider several explanations for the millimeter ultra-broad-line object (MUBLO), including protostellar outflow, explosive outflow, a collapsing cloud, an evolved star, a stellar merger, a high-velocity compact cloud, an intermediate-mass black hole, and a background galaxy. Most of these conceptual models are either inconsistent with the data or do not fully explain them. The MUBLO is, at present, an observationally unique object.

Development of Node-centered finite-volume diffusion method on triangle mesh for detonation propagation simulation in insensitive high explosives

This study presents a numerical simulation of detonation waves in insensitive high explosives (IHE). A direct numerical simulation (DNS) method of detonation waves propagation was developed. It solves two-dimensional reactive Euler equations by using a semi-discrete node-centered finite-volume (NCFV) scheme on triangle mesh. Employing ZND model analytical solution as the initial condition, the upper and lower boundary conditions were designed as local sonic equilibrium conditions. The DNS method was validated using steady detonation wave propagation experimental results for tri-amino-tri-nitro-benzene (TATB) based explosives. The two-dimensional steady detonation propagation of the circular arc experiments was completed using a non-embedded technique (electric and optical fibre probe velocimetry). The comparison results demonstrate that the numerical method can provide a good prediction of the pseudo-steady-state detonation wave front propagation and the angular speed.

First Extragalactic Detection of Thermal Hydroxyl (OH) 18 cm Emission in M31 Reveals Abundant CO-faint Molecular Gas

The most abundant interstellar molecule, molecular hydrogen (H2), is practically invisible in cold molecular clouds. Astronomers typically use carbon monoxide (CO) to trace the bulk distribution and mass of H2 in our galaxy and many others. CO observations alone fail to trace a significant component of molecular gas known as “CO-dark” molecular gas, which can be probed with molecules such as OH and CH. We present an extremely sensitive pilot search for the 18 cm hydroxyl (OH) lines in the Andromeda galaxy (M31) with the 100 m Robert C. Byrd Green Bank Telescope. We successfully detected the 1665 and 1667 MHz OH lines in faint emission. The 1665/1667 MHz line ratio displays the characteristic 5:9 ratio predicted under conditions of local thermodynamic equilibrium. To our knowledge, this is the first detection of nonmaser 18 cm OH emission in another galaxy. We compare our OH and H i observations with archival CO (1–0) observations. Our OH detection position overlaps with the previously discovered Arp Outer Arm in CO. Our best estimates show that the amount of H2 traced by OH is 100%–140% higher than the amount traced by CO in this sight line. The amount of dark molecular gas implied by dust data supports this conclusion. We conclude that the 18 cm OH lines hold promise as a valuable tool for mapping of the “CO-dark” and “CO-faint” molecular gas phase in nearby galaxies, especially with upcoming multibeam, phased-array feed receivers on radio telescopes, which will allow for drastically improved mapping speeds of faint signals.

EMISSA: Exploring millimetre indicators of solar-stellar activity III. Comparison of Ca II indices and millimetre continua in a 3D model atmosphere

Amongst several spectral lines, some of the strongest chromospheric diagnostics are offered by the Ca II H K lines. These lines can be used to gauge the temperature stratification of the atmosphere since the line core and wings are formed in different regions of the solar atmosphere. Furthermore, the Ca II lines act as tracers for the magnetic structure of the solar atmosphere, as the line cores are formed in the upper chromosphere even though they are formed in non-local thermodynamic equilibrium (NLTE). In contrast, the formation of millimetre (mm) continuum radiation occurs under local thermodynamic equilibrium (LTE) conditions. As a result, the brightness temperatures obtained from observations with the Atacama Large Millimetre/Submillimetre Array (ALMA) offer a complementary perspective on the activity and thermal structure of stellar atmospheres. The overall aim is to establish more robust solar/stellar activity indicators using ALMA observations in comparison with classical diagnostics, such as the s index and infrared triplet (IRT) index. We employed the 1.5D radiative transfer codes RH1.5D and advanced radiative transfer (ART) to compute the synthetic spectra for the Ca II lines and the millimetre (mm) continua, respectively. These calculations were performed using an enhanced network atmosphere model, which incorporates non-equilibrium hydrogen ionisation generated by the state-of-the-art 3D radiation magnetohydrodynamics (rMHD) Bifrost code. To account for the limited spatial resolution of ALMA, we simulated the effect using a Gaussian point spread function (PSF). Additionally, we analysed the correlations and slopes of scatter plots between the Ca II indices and mm continuum for the original and degraded resolutions, focusing on the entire simulation box, quiet Sun regions, and enhanced network patches separately. The activity indices generated from these lines could further be used to compare the spectra of Sun-like stars with the solar spectrum. We present a comparative study between synthetic continuum brightness temperature maps at mm wavelengths (0.3 mm to 8.5 mm) and the Ca II activity indices; namely, the s index and infrared triplet (IRT) index. The Ca II activity indices and mm brightness temperatures are weakly correlated at the high resolution, with the highest correlation observed at a wavelength of 0.3 mm, corresponding to ALMA band 10. As the resolution decreases, the correlation consistently increases. Conversely, the slopes exhibit a decreasing trend with increasing wavelength, while the degradation of resolution does not noticeably affect the calculated slopes. As the spatial resolution decreases, the standard deviations of the Ca II activity indices and brightness temperatures decrease, while the correlations between them increase. However, the slopes do not exhibit significant changes. Consequently, these relationships could be valuable for calibrating the mm continuum maps obtained through ALMA observations.

Cadmium concentrations in pore waters can largely increase during soil incubation: Artefacts with consequences for Cd limits in fertilisers

A sound evaluation of the cadmium (Cd) mass balance in agricultural soils needs accurate data of Cd leaching. Reported Cd concentrations from in situ studies are often one order of magnitude lower than predicted by empirical models, which were calibrated to pore water data from stored soils. It is hypothesized that this discrepancy is related to the preferential flow of water (non-equilibrium) and/or artefacts caused by drying and rewetting soils prior to pore water analysis. These hypotheses were tested on multiple soils (n = 27) with contrasting properties. Pore waters were collected by soil centrifugation from field fresh soil samples and also after incubating the same soils (28 days, 20 °C), following two drying-rewetting cycles, the idea being that chemical equilibrium in the soil is reached after incubation. Incubation increased pore water Cd by a factor 4, on average, and up to a factor 16. That increase was statistically related to the decrease of pore water pH and the increase of nitrate, both mainly related to incubation-induced nitrification. After correcting for both factors, the Cd rise was also highest at higher pore water Ca. This suggests that higher Ca in soil enlarges Cd concentration gradients among pore classes in field fresh soils because high Ca promotes soil aggregation and separation of mobile from immobile water. Several empirical models were used to predict pore water Cd. Predictions exceeded observations up to a factor 30 for the fresh pore waters but matched well with those of incubated soils; again, deviations from the 1:1 line in field fresh soils were largest in high Ca (>0.8 mM) soils, suggesting that local equilibrium conditions in field fresh soils are not found at higher Ca. Our results demonstrate that empirical models need recalibration with field fresh pore water data to make accurate soil Cd mass balances in risk assessments.

Effect of Femtosecond Ultraviolet and Infrared Laser Wavelength on Plasma Characteristics of Metals, Ceramics and Glass Samples Using Femtosecond Laser-Induced Breakdown Spectroscopy.

In this work, we present studies on the effect of laser wavelengths on the laser-induced plasma characterization using a femtosecond (fs) ytterbium-doped potassium-gadolinium tungstate (Yb:KGW) laser. Plasma plumes of copper, steel, ceramics, and glass samples were induced using a multiple shot of 200 fs laser pulses with 1030 nm and 343 nm wavelengths at fixed laser fluence () and analyzed using the laser-induced breakdown spectroscopy (LIBS) technique. Time-resolved fs-LIBS measurements were performed on the same set of samples and under the same experimental conditions. For the calculation of plasma parameters, the set of spectral lines of Cu(I) (for copper sample), Fe(I) (for steel sample), and Ca(I), K(I) (for glass and ceramics samples) were observed. The plasma electron temperature and density were evaluated from the Boltzmann plots and Stark-broadening profiles of the plasma spectral lines, assuming the local thermodynamic equilibrium condition. Time-resolved plasma temperature and electron density for fs-LIBS using ultraviolet (UV) and infrared (IR) laser wavelengths were analyzed and no significant dependence on fs laser wavelength was observed for any of the samples. However, for all samples the signal-to-noise ratio (SNR) significantly increased using UV laser radiation: copper (), steel (), glass (), and ceramics (). Therefore, by using a fs UV laser wavelength for laser-induced breakdown spectroscopy experiments, for certain materials the SNR and at the same time the limit of detection can be significantly enhanced.

On thermodynamic stability of black holes. Part I: classical stability

We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria are quite generic and well-established in classical thermodynamics, but they have not been fully utilized in black hole physics. We show how weaker or incomplete conditions could lead to misleading or incorrect results for the thermodynamic stability of the system. We also stress the importance of finding all possible local heat capacities in order to fully describe the classical equilibrium picture of black holes. Finally, we thoroughly investigate the critical and phase transition curves and the limits of the classical analysis. This paper is the first in the line of intended works on thermodynamic stability of black holes in modified theories of gravity and holography.

Empirical test of the Kelvin relation in thermoelectric nanostructures

Thermoelectric (TE) nanostructures with dimensions of ∼100 nm can show substantially better TE properties compared to the same material in the bulk form due to charge and heat transport effects specific to the nanometer scale. However, TE physics in nanostructures is still described using the Kelvin relation (KR) Π = αT, where Π is the Peltier coefficient, α the thermopower, and T the absolute temperature, even though derivation of the KR uses a local equilibrium assumption (LEA) applicable to macroscopic systems. It is unclear whether nanostructures with nanostructures with dimensions on the order of an inelastic mean free path satisfy a LEA under any nonzero temperature gradient. Here, we present an experimental test of the KR on a TE system consisting of doped silicon-based nanostructures with dimensions comparable to the phonon–phonon and electron–phonon mean-free-paths. Such nanostructures are small enough that true local thermodynamic equilibrium may not exist when a thermal gradient is applied. The KR is tested by measuring the ratio Π/α under various applied temperature differences and comparing it to the average T. Results show relative deviations from the KR of |(Π/α)/T − 1| ≤ 2.2%, within measurement uncertainty. This suggests that a complete local equilibrium among all degrees of freedom may be unnecessary for the KR to be valid but could be replaced by a weaker condition of local equilibrium among only charge carriers.

Measurement of medium-voltage AC air arc temperature and particle number density based on dual-wavelength Moiré deflection technology

AC air arcs are generated in medium-voltage (MV) power systems under the effect of harsh weather conditions, equipment aging, and high penetration of distributed generation, threatening equipment and public safety. The arc current and temperature are low due to the wide application of arc suppression devices. In this scenario, the MV AC air arc does not satisfy the local thermodynamic equilibrium (LTE) condition. In addition, the repeated arcing and extinguishing processes further complicate the arc discharge mechanism, which bring challenges in the modeling and detection of MV AC air arcs. Experimental methods are a direct and efficient approach to determine the properties of arc plasmas. In this study, a dual-wavelength Moiré deflection diagnostic system was established to determine the time evolution of the particle density and radial distribution of the temperature in an MV AC air arc without relying on the LTE assumption. The electron number density and heavy particle number density change transiently during the arc discharge process and change gradient along the radial direction. The heavy particle temperature and electron temperature were then calculated based on the measured particle number density. During the arcing stage, the temperature of the electrons exceeded that of the heavy particles significantly, and the arc deviated from LTE. Finally, the limitations of the traditional single-wavelength Moiré deflection method are analyzed. The classic single-wavelength Moiré deflection method, while capable of estimating heavy particle temperature in plasma, exhibits a significant error in electron density estimation compared to the dual-wavelength Moiré deflection method.

Collisional excitation of propyne (CH3CCH) by He atoms

Context. A detailed interpretation of the detected emission lines of environments where propyne (or methyl acetylene, CH3CCH) is observed requires access to its collisional rate coefficients with the most abundant species in the interstellar medium, namely, helium (He) or molecular hydrogen (H2). Aims. We present the first three-dimensional potential energy surface (3D PES) for the CH3CCH-He molecular complex. We study the dynamics of the collision and report the first set of rate coefficients for temperatures up to 100 K for the collisional excitation of the lowest 60 ortho rotational levels and 60 para rotational levels of CH3CCH by He atoms. Methods. We computed the 3D PES with the explicitly correlated coupled-cluster with a single-, double-, and perturbative triple-excitation method in conjunction with the augmented correlation-consistent triple zeta basis set (CCSD(T)-F12a/aug-cc-pVTZ). The 3D PES was then fitted to an analytical function and scattering computations of pure rotational (de-)excitation of CH3CCH by collision with He atoms were performed. State-to-state cross-sections were computed using the close coupling method for total energies up to 100 cm−1 and with the coupled states approximation at higher energies for both the ortho- and para- symmetries of CH3CCH. Results. The PES we obtained is characterised by a large anisotropy and a potential well depth of 51.04 cm−1. By thermally averaging the collisional cross-sections, we determined the quenching rate coefficients for kinetic temperatures up to 100 K. A strong and even Δj propensity rule at almost all collision energies is present for CH3CCH-He complex. To evaluate the impact of rate coefficients on the analysis of observations, we carried out non-local thermodynamic equilibrium radiative transfer computations of the excitation temperatures and we demonstrate that local thermodynamic equilibrium conditions are not typically fulfilled for the propyne molecule.

A Mode-Coupling Model of Colloid Thermophoresis in Aqueous Systems: Temperature and Size Dependencies of the Soret Coefficient.

Thermophoresis allows for the manipulation of colloids in systems containing a temperature gradient. A deep understanding of the phenomena at the molecular level allows for increased control and manipulation strategies. We developed a microscopic model revealing different coupling mechanisms for colloid thermophoresis under local thermodynamic equilibrium conditions. The model has been verified through comparison with a variety of previously published experimental data and shows good agreement across significantly different systems. We found five different temperature-dependent contributions to the Soret coefficient, two from bulk properties and three from interfacial interactions between the fluid medium and the colloid. Our analysis shows that the Soret coefficient for nanosized particles is governed by the competition between the electrostatic and hydration interfacial interactions, while bulk contributions become more pronounced for protein systems. This theory can be used as a guide to design thermophoretic transport, which is relevant for sensing, focusing, and separation at the microscale.

Comparison of excitation temperature of a laser-produced plasma by combining emission and absorption spectroscopy

Measurement of the temporal evolution of laser-produced plasma temperature is very important for many of its applications, and several plasma diagnostic tools are routinely used by researchers. However, it is very challenging to measure the properties of the plasma at the early and late times of its evolution using a single diagnostic tool. In this study, we combined emission and laser absorption spectroscopy to compare the excitation temperatures of a laser-produced uranium plasma system. Several U I transitions in the near-infrared spectral range (775–800 nm) were considered, and the Boltzmann plot method was used to measure the excitation temperatures using both emission and absorption spectroscopy. Emission spectroscopy provided early-time temperature measurements of the plasma up to times 2–20 µs, while absorption spectroscopy provided temperature measurements at late times of plasma evolution (for times 5–80 µs). The emission and absorbance of U I transitions were found to follow the Boltzmann distribution, indicating the plasma is likely in the state of local thermodynamic equilibrium even at late times of its lifetime. The emission and absorption-based time-resolved excitation temperatures demonstrated good agreement at earlier times (≤15 µs) in the overlapped temporal region, while a deviation in the measured values was seen at times (≥15 µs), and potential reasons for such a disagreement are discussed.

LIBS analysis of tritium in thin film-type samples

Evaluating the mole fraction of hydrogen isotopes in a solid is a difficult task. Few methods allow it to be achieved. LIBS is a laser method based on the electronic excitation of elements and the spontaneous emission of characteristic optical lines. On a sample containing hydrogen isotopes, α-type lines can allow the estimate of their total mole fraction. In addition, LIBS is a discriminating method because it can separate the contributions of isotopes. This paper reports the implementation of this method on thin film-type samples containing hydrogen and tritium.They consist of nanometric layers of palladium and titanium on a silicon substrate. Under irradiation of nanosecond laser pulses reaching a fluence of the order of 200 J cm−2, LIBS was performed in argon at atmospheric pressure. A detailed spectroscopic study is performed around the Tα line of wavelength 656.039 nm of the Balmer series (n=3→2) of tritium. An analysis based on the reconstruction of the spectrum under conditions of local thermodynamic equilibrium is carried out. This leads to the estimate of the tritium mole fraction.

Irreversible Thermodynamics of Seawater Evaporation

Under typical marine conditions of about 80% relative humidity, evaporation of water from the ocean is an irreversible process accompanied by entropy production. In this article, equations are derived for the latent heat of irreversible evaporation and the related nonequilibrium entropy balance at the sea surface. To achieve this, linear irreversible thermodynamics is considered in a conceptual ocean evaporation model. The equilibrium thermodynamic standard TEOS-10, the International Thermodynamic Equation of Seawater—2010, is applied to irreversible evaporation under the assumption of local thermodynamic equilibrium. The relevance of local equilibrium conditions for irreversible thermodynamics is briefly explained. New equations are derived for the mass flux of evaporation and for the associated nonequilibrium enthalpies and entropies. The estimated entropy production rate of ocean evaporation amounts to 0.004 W m−2 K−1 as compared with the average terrestrial global entropy production of about 1 W m−2 K−1.

Numerical study on mixed convection heat transfer of copper-water nanofluid in a porous cavity with an isothermal solid block in local thermal non-equilibrium

This manuscript reports a numerical study on mixed convection heat transfer of Cu-water nanofluid in a porous cavity with an isothermal solid block in the state of local thermal non equilibrium. The set of governing equations are solved by finite volume method combined with SIMPLE algorithm. Through streamlines and isothermal contour plots as well as the average Nusselt number, the impact of various parameters like the nanoparticle concentration, Richardson number, Darcy number, and inter phase heat transfer coefficient is highlighted. The main findings indicate that the Local thermal non-equilibrium state (H = 1, 10) produces the maximum heat transfer rate than the local thermal equilibrium state (H = 1000).