Thermal Nonequilibrium Research Articles

First principles simulation of reacting hypersonic flow over a blunt wedge

This article presents molecular-level analysis of a reactive, near-continuum, Mach 21 nitrogen flow over a blunt wedge using the direct molecular simulation (DMS) method. The flow conditions lead to internal energy excitation and dissociation in the flow field, resulting in thermal and chemical nonequilibrium in the flow. Thermal nonequilibrium in the vibrational mode is observed to extend to the molecular level, where the vibrational energy distributions at various points in the flow field are observed to be non-Boltzmann. Furthermore, this is the first reactive DMS calculation where the wall is assumed to be isothermal and full momentum accommodation of the particles is enforced, hence incorporating viscous wall effects. Since the DMS method uses a quantum mechanically generated interaction potential as its only modeling input, all thermochemical and transport properties of the flow field can directly be attributed to the ab initio potential energy surface. Using the DMS solution as a benchmark, this article assesses the performance of Navier–Stokes computational fluid dynamics solutions using lower fidelity two-temperature models. Two models are chosen as points of comparison: the well-known Park two-temperature model and the recently developed modified Marrone and Treanor model.

Extreme-ultraviolet fine structure and variability associated with coronal rain revealed by Solar Orbiter/EUI HRIEUV and SPICE

Context. Coronal rain is the most dramatic cooling phenomenon of the solar corona. Recent observations in the visible and UV spectrum have shown that coronal rain is a pervasive phenomenon in active regions. Its strong link with coronal heating through the thermal non-equilibrium (TNE) – thermal instability (TI) scenario makes it an essential diagnostic tool for the heating properties. Another puzzling feature of the solar corona in addition to the heating is its filamentary structure and variability, particularly in the extreme UV (EUV). Aims. We aim to identify observable features of the TNE-TI scenario underlying coronal rain at small and large spatial scales to understand the role it plays in the solar corona. Methods. We used EUV datasets at an unprecedented spatial resolution of ≈240 km from the High Resolution Imager (HRI) in the EUV (HRIEUV) of the Extreme Ultraviolet Imager (EUI) and SPICE on board Solar Orbiter from the perihelion in March and April 2022. Results. EUV absorption features produced by coronal rain are detected at scales as small as 260 km. As the rain falls, heating and compression is produced immediately downstream, leading to a small EUV brightening that accompanies the fall and produces a fireball phenomenon in the solar corona. Just prior to impact, a flash-like EUV brightening downstream of the rain, lasting a few minutes, is observed for the fastest events. For the first time, we detect the atmospheric response to the impact of the rain on the chromosphere, and it consists of upward-propagating rebound shocks and flows that partly reheat the loop. The observed widths of the rain clumps are 500 ± 200 km. They exhibit a broad velocity distribution of 10 − 150 km s−1and peak below 50 km s−1. Coronal strands of similar widths are observed along the same loops. They are co-spatial with cool filamentary structure seen with SPICE, which we interpret as the condensation corona transition region. Prior to the appearance of the rain, sequential loop brightenings are detected in gradually cooler lines from coronal to chromospheric temperatures. This matches the expected cooling. Despite the large rain showers, most cannot be detected in AIA 171 in quadrature, indicating that line-of-sight effects play a major role in the visibility of coronal rain. The AIA 304 and SPICE observations still reveal that only a small fraction of the rain can be captured by HRIEUV. Conclusions. Coronal rain generates EUV structure and variability over a wide range of scales, from coronal loops to the smallest resolvable scales. This establishes the major role that TNE-TI plays in the observed EUV morphology and variability of the corona.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator.

Gauge theory and thermalization are both topics of essential importance for modern quantum science and technology. The recently realized atomic quantum simulator for lattice gauge theories provides a unique opportunity for studying thermalization in gauge theory, in which theoretical studies have shown that quantum thermalization can signal the quantum phase transition. Nevertheless, the experimental study remains a challenge to accurately determine the critical point and controllably explore the thermalization dynamics due to the lack of techniques for locally manipulating and detecting matter and gauge fields. We report an experimental investigation of the quantum criticality in the lattice gauge theory from both equilibrium and nonequilibrium thermalization perspectives, with the help of the single-site addressing and atom-number-resolved detection capabilities. We accurately determine the quantum critical point and observe that the Néel state thermalizes only in the critical regime. This result manifests the interplay between quantum many-body scars, quantum criticality, and symmetry breaking.

Numerical study on transient response of transpiration cooling with hydrocarbon fuel as coolant

A transient non-thermal equilibrium model was established to solve the transient process of transpiration cooling, which considers the influence of cracking reaction. The occurrence of cracking reaction leads to the increase of inlet pressure, thermal diffusion coefficient and heat transfer coefficient and effectively reduces the temperature of porous matrix. In the absence of external oscillation excitation, the change rate of porous matrix temperature and fluid temperature with heating time gradually decreases. In the case of unsteady heat flux, the oscillation amplitude of fluid parameters near the outlet of porous media is larger. The increase of thermal conductivity of solid matrix can effectively restrain the temperature oscillation caused by external heat flux, but the amplitude of coolant supply pressure increases with the increase of thermal conductivity, which is not conducive to the supply of coolant. The amplitude of reaction heat is the smallest when the frequency of coolant mass flux and heat flux is the same. The greater inlet pressure oscillation is formed when the coolant supply cycle period is lower than the cycle period of heat flux.

Calibration Method for Airborne Infrared Optical Systems in a Non-Thermal Equilibrium State.

Airborne infrared optical systems equipped with multiple cooled infrared cameras are commonly utilized for quantitative radiometry and thermometry measurements. Radiometric calibration is crucial for ensuring the accuracy and quantitative application of remote sensing camera data. Conventional radiometric calibration methods that consider internal stray radiation are usually based on the assumption that the entire system is in thermal equilibrium. However, this assumption leads to significant errors when applying the radiometric calibration results in actual mission scenarios. To address this issue, we analyzed the changes in optical temperature within the system and developed a simplified model to account for the internal stray radiation in the non-thermal equilibrium state. Building upon this model, we proposed an enhanced radiometric calibration method, which was applied to the absolute radiometric calibration procedure of the system. The radiometric calibration experiment, conducted on the medium-wave channel of the system within a temperature test chamber, demonstrated that the proposed method can achieve a calibration accuracy exceeding 3.78% within an ambient temperature range of -30 °C to 15 °C. Additionally, the maximum temperature measurement error was found to be less than ±1.01 °C.

Nonthermal Equilibrium Process of Charge Carrier Extraction in Metal/Insulator/Organic Semiconductor/Metal (MIOM) Junction

This paper presents the concept and experimental evidence for the nonthermal equilibrium (NTE) process of charge carrier extraction in metal/insulator/organic semiconductor/metal (MIOM) capacitors. These capacitors are structurally similar to metal/insulator/semiconductor/(metal) (MIS) capacitors found in standard semiconductor textbooks. The difference between the two capacitors is that the (organic) semiconductor/metal contacts in the MIOM capacitors are of the Schottky type, whereas the contacts in the MIS capacitors are of the ohmic type. Moreover, the mobilities of most organic semiconductors are significantly lower than those of inorganic semiconductors. As the MIOM structure is identical to the electrode portion of an organic field-effect transistor (OFET) with top-contact and bottom-gate electrodes, the hysteretic behavior of the OFET transfer characteristics can be deduced from the NTE phenomenon observed in MIOM capacitors.

A 3D numerical model of controlled drug delivery to solid tumor by means of mild microwave hyperthermia-activated thermo-sensitive liposomes

A computational 3D analysis of liposomal drug delivery to investigate the effectiveness of this innovative therapy as an alternative to conventional chemotherapy is shown in this study. The temperature field evolution is obtained via the Local Thermal Non-Equilibrium (LTNE) bioheat model by including both variable porosity and blood vessels sizes to describe the local structure of the investigated tissue. Heating is induced by means of a microwave antenna directly inserted in tumor tissue, supplying a pulsating power to avoid tissue necrosis. Interstitial flow and drug diffusion are modeled by means of Darcy's law and convection-diffusion equations, respectively; Starling's law is included to simulate transcapillary exchange. After validating the model with available literature data, the results show that liposomal drug delivery leads to a 10% improvement in therapeutic outcomes (i.e., Fraction of Killed Cells, FKC). It is also proved that considering blood flow in the LTNE porous media model yields a more realistic evolution of drug diffusion and subsequent FKC, while severe tissue damage is avoided because of the pulsating power supply. This study highlights the potential benefits of using liposomal drug delivery in cancer chemotherapy via microwave-induced heating.

Conjugate local thermal nonequilibrium and non‐Darcy flow inside porous enclosure: Analysis of localized heating and cooling arrangements

AbstractThis study covers a simulation on conjugate free convective in a porous enclosure containing a side wall thickness and partially heated and cooled from sides under the considerations of local thermal nonequilibrium (LTNE) and non‐Darcy flow. Interest has been focused on how the side wall thickness and the locations of cooled and heated parts affect the effectiveness of the Nusselt number (Nu). Three different cases of localized heating and cooling locations have been implemented for the following ranges: scaled heat transfer coefficient (), wall to fluid thermal conductivity ratio (), modified Rayleigh number (), wall width (), inertial parameter (), and thermal conductivity ratio (). Outcomes show that and the locations of cooled and heated parts have remarkable impacts on all the Nusselt numbers. The intensity of LTNE region considerably relies on , and . The total average NuT is highly dependent on , , , , and as compared to H. The increase in leads to change of the convective mechanism to conductive mode. The rise in guides to increase Nu, where can control the flow strength. The actions of on Nuf is more evident than Nus. For low H and Kr, the size of LTNE zone is considerably affected by H as compared to Kr although Kr has a high influence on Nu. For high Kr and H, the LTNE zone has closely vanished. Findings display that the Case 2 provided the highest Nu for all tested parameters except the case of . Finally, it is evident that for the problems that employed solid conduction wall with localized heating and cooling sections, Case 2 is recommended for future use in the applications that implement a porous medium and depend on free convection.

A Two-Domain Local Thermal Non-equilibrium Analysis for Forced Convection in a Transpiration-Cooled Channel Filled with a Porous Medium

A Two-Domain Local Thermal Non-equilibrium Analysis for Forced Convection in a Transpiration-Cooled Channel Filled with a Porous Medium

Natural Convection of Variable Viscosity Fluid in a Partially Porous Cube Having Heat-generating Element Under Local Thermal Non-Equilibrium Model

Natural Convection of Variable Viscosity Fluid in a Partially Porous Cube Having Heat-generating Element Under Local Thermal Non-Equilibrium Model

Three-dimensional non-Darcy free convective heat transfer flow in a bidisperse porous medium within a cubical cavity

Heat transport in porous media, especially in a bidisperse porous matrix, has recently received considerable attention due to its diverse real-life applications in applied science and engineering. In the current study, we employ the Darcy-Brinkman-Forchheimer model and three temperature equations incorporating the local thermal nonequilibrium conditions among the fluid and the porous matrix to examine the three-dimensional free convective heat transfer flow in a bidisperse permeable matrix inside a cubical cavity. The Galerkin weighted residual finite element method simulates the model's non-dimensional governing equations. We examine the effects of the significant model parameters on the flow and heat domains considering (104 ≤ Raf ≤ 106), (103 ≤ Rap ≤ 106), (10−3 ≤ Daf ≤ 10−1), (10−4 ≤ Dap ≤ 10−2),(0.7 ≤ ϕ ≤ 0.9) and (0.4 ≤ ε ≤ 0.7). It is found that the average Nusselt number in the macrophase, microphase, and solid matrix increased with the increase of the macro porosity for about 7.18%, 7.06%, and 9.86%, respectively, when it rises from 0.7 to 0.9. Furthermore, increasing the micro-porosity enhances the rate of heat transfer. As the Raleigh number advances, there is a noticeable increase in heat transfer in both the macrophase and the microphase.

Integrated system model of spray flash vacuum distillation with internal heat recovery

This study proposed an integrated system model for an original spray flash vacuum distillation system that enhances and leverages the thermal non-equilibrium of the flash process via active vapor extraction to realize an internal heat recovery feature, in which partial heat from hotter vapor is recovered to cooler spray residue within the same stage of feed circulation. This system contains four interlinked sub-systems: (1) an evaporation chamber in which a vacuum-promoted spray flash vaporization occurs, with an active vapor extraction and an outflow of evaporation-cooled brine, (2) a recirculation loop of feed-brine mixture, with the circulation pump, feed heater, and spray nozzle, (3) a hybrid dual-condenser combination, with the internal heat recovery from condensing vapor to the recirculating feed and a secondary cooling by an external coolant, and (4) a vacuum source that maintains vacuum conditions to the entire system as well as discharges the non-condensable gases. The pressure of vapor phase, as the major interlinked operation parameter, is in order of sequential decrease from the evaporation chamber, through condensers, to the vacuum source while the depressurization level in each sub-system is strongly coupled with other transport characteristics such as flash vapor generation in the evaporation chamber or condensing vapor flow in condensers. Thus, the integrated system model is composed of four sub-models to describe the key processes in such four sub-systems. For the modeling validation, a lab-scale experimental system is developed to provide relevant measurements. Comparisons between model predictions against measurements show a good match. Major process characteristics (such as spray flash rate, yield rate, and operating temperatures and pressures) and operational thermodynamic characteristics (such as thermal consumption and heat recovery efficiency) are investigated parametrically. The system's multivariate impacts concerning distillate yield rate and heat recovery effectiveness are also studied with varied operating parameters. Results indicate the pronounced thermal non-equilibrium feature arising from the spray flash process can be effectively utilized via the internal heat recovery design of our system to recover up to more than half of the heat from the yield vapor. Meanwhile, the developed system model can effectively analyze various operational and parametric effects, proving valuable for system design and optimized operation.

Pore-scale evaluation on a volumetric solar receiver with different optical property control strategies

Pore-scale flow and heat transfer model is built for a volumetric solar receiver subjected to highly concentrated irradiation, in order to provide insight into the detailed thermal and hydrodynamic performance. Direct three-dimensional simulations on the coupled radiation-convection-conduction are performed based on the Weaire-Phelan structure which is used to represent the open-cell ceramic foam absorber. The energy conversion characteristics with two ceramic materials (SiC and Al2O3) are firstly predicted and compared. And then several cases focused on the control approaches for the optical property (absorption/reflection/emission) of the solar absorber are introduced and investigated, including gradient surface absorptivity, spectral selectivity, and combination design of semi-transparent and opaque configuration. The results show that a moderate volumetric effect can be achieved at very low inlet fluid velocity for both ceramic materials, however presenting low conversion efficiency. Increasing the inlet velocity could enlarge the thermal non-equilibrium between solid and fluid phases and lower the outlet temperature. SiC absorber shows improved performance compared to Al2O3 absorber, and the efficiency changes obviously with the inlet velocity, while a variation of 24% is found. The optical property of the absorber front region significantly affects the overall performance. Decreasing absorptivity design and spectral selective design both show positive impact, especially for the Al2O3 absorber with an increment by 33% in efficiency relative to the basic one. Among the different strategies, spectral selective improvement shows the best effectiveness. Besides, adding porous fused silica as the front absorber layer can effectively move the high-temperature area inward at a cost of small decrement in efficiency, herein, honeycomb structure shows preponderance compared to the foam silica.

Detection of sulfur mustard simulants using the microwave atmospheric pressure plasma optical emission spectroscopy method.

Sulfur mustard (SM) is one kind of highly toxic chemical warfare agent and easy to spread, while existing detection methods cannot fulfill the requirement of rapid response, good portability, and cost competitiveness at the same time. In this work, the microwave atmospheric pressure plasma optical emission spectroscopy (MW-APP-OES) method, taking the advantage of non-thermal equilibrium, high reactivity, and high purity of MW plasma, is developed to detect three kinds of SM simulants, i.e., 2-chloroethyl ethyl sulfide, dipropyl disulfide, and ethanethiol. Characteristic OES from both atom lines (C I and Cl I) and radical bands (CS, CH, and C2) is identified, confirming MW-APP-OES can preserve more information about target agents without full atomization. Gas flow rate and MW power are optimized to achieve the best analytical results. Good linearity is obtained from the calibration curve for the CS band (linear coefficients R 2 > 0.995) over a wide range of concentrations, and a limit of detection down to sub-ppm is achieved with response time on the order of second. With SM simulants as examples, the analytical results in this work indicate that MW-APP-OES is a promising method for real-time and in-site detection of chemical warfare agents.

Spatial and Temporal Analysis of Quiescent Coronal Rain over an Active Region

The solar corona produces coronal rain, hundreds of times colder and denser material than the surroundings. Coronal rain is known to be deeply linked to coronal heating, but its origin, dynamics, and morphology are still not well understood. The leading theory for its origin is thermal instability (TI) occurring in coronal loops in a state of thermal nonequilibrium (TNE), the TNE-TI scenario. Under steady heating conditions, TNE-TI repeats in cycles, leading to long-period EUV intensity pulsations and periodic coronal rain. In this study, we investigate coronal rain on the large spatial scales of an active region (AR) and over the long temporal scales of EUV intensity pulsations to elucidate its distribution at such scales. We conduct a statistical study of coronal rain observed over an AR off limb with Interface Region Imaging Spectrograph and Solar Dynamics Observatory imaging data, spanning chromospheric to transition region (TR) temperatures. The rain is widespread across the AR, irrespective of the loop inclination, and with minimal variation over the 5.45 hr duration of the observation. Most rain has a downward (87.5%) trajectory; however, upward motions (12.5%) are also ubiquitous. The rain dynamics are similar over the observed temperature range, suggesting that the TR emission and chromospheric emission are colocated on average. The average clump widths and lengths are similar in the SJI channels and wider in the AIA 304 Å channel. We find ubiquitous long-period EUV intensity pulsations in the AR. Short-term periodicity is found (16 minutes) linked to the rain appearance, which constitutes a challenge to explain under the TNE-TI scenario.

Quantification of model-form uncertainties affecting the calibration of a carbon nitridation model by means of Bayesian Model Averaging

Severe epistemic uncertainties not only can affect the prescription of parameters within a given model but also the choice of models we make to interpret and infer from experimental data. In this work, we incorporate experimental, parametric and model-form uncertainties in the calibration of a carbon nitridation model. The model-form uncertainties considered stem from the different modeling choices that are taken as valid representations of a set of plasma wind tunnel experiments. To this end, we define a Bayesian Model Averaging strategy where the marginal posteriors of the nitridation reaction efficiencies are weighted by the marginalized likelihoods of the experimental data for each proposed model. First, Bayes factors are computed to possibly discard invalid models. The baseline model, a thermal equilibrium stagnation line flow with nitridation as only surface reaction, performs as well as all the alternative models proposed, which range from adding surface recombination reactions to considering thermal non-equilibrium in the gas and gas-surface interface. The presence of nitrogen recombination reactions is shown to broaden the support of the nitridation marginal posteriors considerably, allowing it to take on larger values. Lastly, a Bayesian model averaged Arrhenius law for the nitridation efficiencies is computed for a range of surface temperatures.

Modeling enhanced geothermal systems using a hybrid XFEM–ECM technique

Heat extraction from Enhanced Geothermal Systems (EGS) involves several multi-physics coupling processes, including the seepage through the fractured porous media, the thermal exchange between the working fluid and the matrix, and the deformation of fractured porous media, which play essential roles in exploiting the geothermal energy contained in hot dry rocks. In this study, a fully coupled numerical model for Thermo-Hydro-Mechanical simulation of EGS is presented based on the local thermal non-equilibrium using the eXtended Finite Element Method (XFEM) and Equivalent Continuum Method (ECM). The ECM can provide the equivalent tensors of not only fluid permeability but also solid compliance, which is an essential feature for coupled Thermo-Hydro-Mechanical simulation of fracture networks. In the model, the XFEM is employed for large-scale fractures to capture the mass and heat transfer between the fracture and matrix more accurately, while the ECM is applied on the network of small-scale fractures since considering their details explicitly is not usually cost-effective. Hence, the proposed model benefits from the advantages of both methods, and it allows for managing between accuracy and cost. The model is validated against the analytical solutions of heat transfer in porous media as well as single fracture problems. Moreover, its flexibility and applicability are shown by assessing the effects of the connectivity of fractures, characteristics of fracture networks, coupling conditions, and local thermal non-equilibrium assumption on the EGS simulation results. It is observed that the network connectivity and fracture alignment are both influential in the early thermal breakthrough; however, each can take dominance under different conditions. The results show the proposed computational model is a promising tool for estimation of the heat mining performance of EGS.

Effect of Rarefaction on Thermal and Chemical Non-Equilibrium for Hypersonic Flow With Different Enthalpy and Catalytic Wall Conditions

AbstractCompressibility and rarefaction effect plays an essential role in the design and study of objects experiencing hypersonic flows. The presence of chemical and thermal non-equilibrium in hypersonic flows increases the complexity of estimating aerothermodynamic properties, which are essential for developing thermal protection systems and the aerothermodynamic design of hypersonic vehicles. In this study, the hy2Foam solver, developed in an OpenFOAM framework by hyStrath group, is used to understand the effect of Knudsen number (which in turn depends on the altitude) and freestream enthalpy variation on the surface aerothermodynamic properties such as pressure, heat flux, velocity slip, temperature jump, and flow field variables such as species concentration and temperature, in five-species air flow over a cylinder, for both noncatalytic and fully catalytic wall conditions. The novelty of the work lies in reporting the effect of rarefaction on thermal and chemical non-equilibrium (associated with hypersonic flows), and thus on the surface properties under different enthalpy and wall catalytic conditions. It has been shown that the rarefaction effect is more pronounced on the vibrational temperature component and for high enthalpy gas. The surface wall heat flux and the chemical reaction rate among the species decrease with rarefaction. The skin friction coefficient is one of the most sensitive properties, while the pressure coefficient has been the least susceptible to non-equilibrium effects. The stagnation points heat flux at different Knudsen numbers shows good agreement with the existing correlation in literature for both low and high enthalpy flows, which further establishes the validity of the study done in this work.

Natural convection due to lateral uniform heat flux in a slender porous cavity saturated with nanofluid: Departure from LTE state

The present article deals with the influence of the local thermal nonequilibrium (LTNE) state on natural convection in an enclosure filled with nanofluid-saturated porous medium. The flow is induced due to the maintenance of constant heat flux on the vertical walls and insulation of horizontal walls. The Darcy model has been adopted to describe the flow governing equations. These equations are solved numerically by using the alternate direction implicit method and analytically by applying parallel flow assumptions valid for large aspect ratios. Boundary layer analysis is performed to report the boundary layer thickness ( δ x ∼ 2 1 / 2 ( k nf / k f ) 1 / 10 ( R a T ) − 1 / 5 ) as well as the heat transfer rate of nanofluid ( N u nf ∼ ( k nf / k f ) − 1 / 5 R a T 2 / 5 ) . The combined effect of LTNE state parameters (interface heat transfer coefficient (H), porosity scaled thermal conductivity ratio (γ)) and volume fraction of nanoparticle ( ϕ ) is addressed on the flow dynamics and heat transfer mechanism. Rigorous analysis, indicates that the average heat transfer rate of nanofluid and solid porous matrix are increasing function of H and γ, however, the role of γ is accelerated for a relatively high value of H. For increasing the value of γ from 1 to 10, the enhancement in the heat transfer rate of nanofluid is reported to be up to 27% at 10% volume fraction of nanoparticles. The average Nusselt number of nanofluid, as well as solid phase, are reduced when the value of ϕ is increased under the LTNE circumstances. Furthermore, the flow structure is controlled by unicellular structure with rotating anticlockwise direction in the entire study. For the very small value of H the temperature distribution in the solid porous matrix is mainly by conduction mode and distribution is linear, however, for a relatively high value of H the distribution in the same is controlled by both conduction as well as convection, and it will be more pronounced for the higher value of γ.