Thermal Non-equilibrium Conditions Research Articles

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition: application of the clique polynomial method and physics-informed neural networks

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition: application of the clique polynomial method and physics-informed neural networks

Physics-informed Hermite neural networks for wetted porous fin under the local thermal non-equilibrium condition: application of clique polynomial method

Physics-informed Hermite neural networks for wetted porous fin under the local thermal non-equilibrium condition: application of clique polynomial method

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

AbstractA fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.

A numerical study comparing the performance of a self-aspirating domestic LPG porous burner and that of a conventional LPG burner

The study involves in the design of a domestic two-layer self-aspirating porous burner that operates at a thermal load of 1 kW using liquefied petroleum gas (LPG). The porous burner is intended to function within India’s standard domestic regulator fuel inlet pressure of 3000 Pa. For the same thermal load, this work also provides a numerical comparison between the domestic conventional burner and the designed porous burner. For both porous and conventional burners, a full-scale 3D model is developed to calculate the flow, combustion, heat transfer to the cooking vessel, thermal efficiency, and emissions. The combustion process of both burners is numerically computed using a detailed chemical kinetic mechanism of LPG combustion, the San Diego Mechanism (SDM) with 57 species and 268 reactions are used. The porous burner is simulated using a non-thermal equilibrium condition to better calculate the heat recirculation within the porous domain. The self-aspirated porous burner has an equivalence ratio ϕ of 0.75 at 1 kW and an efficiency of 84.2%; conventional burner at the same load had an efficiency of 68%. 10 and 6 parts per million (ppm), respectively, are the measured CO and NOx emissions from the domestic porous burner and 660 and 80 ppm for domestic conventional burner, respectively.

Numerical simulation of chemical reactive flow of Boger fluid over a sheet with heat source and local thermal non-equilibrium conditions

In this article, the effect of nonlinear heat source on chemical reactive flow of magnetized Boger fluid over a sheet with Marangoni convection and porous medium is explored. In the modelling, local thermal non-equilibrium (LTNE) conditions and heat sources are taken into account. The unique heat transport for both liquid and solid phases is provided by the LTNE model, which is based on thermal equations. As a result, various temperature profiles are used in this work for both the solid and fluid phases. It is essential for streamlining industrial procedures, improving material processing methods, comprehending biological systems like blood flow for medicine delivery, determining the environmental impact of pollutant dispersion, and increasing the effectiveness of oil and gas transportation. This model supports crucial decision-making processes in numerous disciplines by offering insights into the intricate interplay between reactive fluids, heat transmission, and chemical reactions. The appropriate similarity variables are used to compress the model equation system, and the shooting method and the conventional bvp4c solver are then used to solve the system numerically. Optimal homotopy approach is used to achieve residual errors. There are suggested best estimates for auxiliary variables. Results show that for larger values of the solvent fraction parameter, Boger fluid exhibits an enhanced velocity profile and a declining thermal profile of the liquid phase. The concentration and thermal profiles of both the solid and liquid phases are declined and enhanced the velocity of the Boger fluid for higher values of the Marangoni convection parameter.

Flow structure and cooling effect of seeping gas film in supersonic turbulent boundary layer

Seeping gas film cooling is an active cooling method that involves injecting a cooling gas film into the boundary layer through porous media. In this study, a sintered wire mesh porous material is used to generate the gas film through seepage flow. The flow of the gas film in the supersonic turbulent boundary layer is observed using nanometer particle plane laser scattering technology, while the temperature distribution of the porous wall surface is measured by infrared thermometry. It is observed that as the injection rate of the gas film exceeds 0.2 %, the supersonic turbulent boundary layer thickens significantly. The rate of thickness growth is promoted from 5.5 % to 17.1 % as the injection rate increases from 0.3 % to 0.8 %. Additionally, the injection of the gas film induces an oblique shock wave, and the shock angle increases with the enhancement of the injection rate, resulting in an uneven cooling effect along the injector length. The transient cooling efficiency of the seeping gas film under thermal non-equilibrium conditions is analyzed. The results indicate that the temperature amplitude on the porous wall surface decreases significantly when the injection rate is promoted from 0.2 % to 0.3 %. However, continuing to increase the coolant injection rate does not lead to a more significant improvement in cooling efficiency. When the injection rate reaches 0.5 %, the relative cooling efficiency reaches 50 %–60 %, which is much lower than the predicted values of the thin film theory.

Solid–liquid phase transition simulated by the lattice Boltzmann model: from pore scale to representative elementary volume scale

Purpose This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems. Design/methodology/approach Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given. Findings This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices. Originality/value A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

Importance of thermophoretic particles deposition in ternary hybrid nanofluid with local thermal non-equilibrium conditions: Hamilton–Crosser and Yamada–Ota models

This article exhibits a brief study of magneto ternary hybrid nanofluid flow with thermophoretic particle deposition and porous medium based on the extended version of model, known as the Yamada-Ota and Hamilton Crosser models. Thermophoretic particle deposition, which is important in both aero-solution and electrical engineering, is one of the most fundamental methods for transferring small particles across a heat gradient. This suggested model's goal is to evaluate how well Hamilton-Crosser and Yamada-Ota, two trihybrid nanofluid models, perform. Advanced heat transfer systems, in particular the creation of effective cooling and heating technologies, may benefit from this research. Researchers can develop more efficient heat exchangers, boost thermal management in electronic devices, and increase energy efficiency in industrial processes by better understanding how thermophoretic particles behave in complicated nanofluid systems under various conditions. By using the required similarity variables, the MATLAB solver bvp4c package handles the system of ODEs acquired from the leading PDEs to arrive at the numerical solution. The relevant parameters' effects on the relevant fields have been graphically explained. The results show that when inter-phase heat transfer parameter value grows, thermal profile and rate of heat transfer decrease of liquid phase. With regard to heat and mass transfer effectiveness, the Yamada-Ota model performs better than the Hamilton Crosser trihybrid nanofluid model.

Slip boundary conditions effect on bidispersive convection with local thermal non-equilibrium: Significant findings

We examine a theory concerning heat convection within a porous material characterized by a skeletal structure comprising macropores and, additionally, cracks or fissures leading to a network of micro pores. Brinkman theory and slip conditions were considered applicable within the macropores, while exclusively Darcy theory was applied within the micropores. This represents a scenario of thermal convection within a double-porosity porous medium. The theory accommodates non-equilibrium thermal conditions, allowing for the possibility that the temperature of the solid skeleton differs from that of the fluid present in either the macro or micro pores. Importantly, the model permits independent fluid velocities and pressures within both the macro and micro pores. We conducted both linear and nonlinear stability assessments, with a specific focus on assessing how slip boundary conditions affect the stability of the system. Once we pinpointed the onset of instability, we calculated the critical Rayleigh number as a variable dependent on the slip coefficient. Additionally, we provided numerical results that outline the thresholds for stability and instability.

Quantum gates based on two strongly coupled harmonic oscillators in thermal non-equilibrium conditions

We consider two strongly coupled harmonic oscillators (TSCHO) exposed by a bosonic bath in thermal non-equilibrium conditions (TNEC). To explain TNEC, we use the Tsallis statistics. To obtain the system's time evolution, we use the Liouville-von Neumann master equation. We find that the q-dependence of the entanglement of formation (EOF) gives EOFq<1 ≤ EOFq=1 ≤ EOFq>1.The effects of squeezing and coupling between two oscillators on EOF are analyzed. We apply our method to obtain the outputs of SWAP and CONT gates in TNEC exposed to the environment. We find that for different q-regions, the squeezing and hopping coefficients affect the amount of entanglement and its death slope after the CNOT-gate operation.

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise.Article HighlightsA two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem.The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven.Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

The Onset of Darcy–Brinkman Convection in a Porous Layer with Mutual Impact of Thermal Non-Equilibrium and Non-Uniform Temperature Gradients

The two-field thermal conditions of local thermal nonequilibrium (LTNE) were used to investigate linear stability of thermal convection in a liquid-saturated, porous layer via the extended Brinkman–Darcy model for different non-uniform basic thermal gradients. The critical values were numerically computed by the Galerkin method for rigid isothermal boundaries. The impact of LTNE and different forms of non-uniform basic temperature gradients on the onset of porous convection was examined. The porosity modified conductivity ratio has no influence on system stability at a small inter-phase heat transport coefficient limit. However, for higher values of the inter-phase heat transport coefficient, an increase in the porosity modified conductivity ratio hastens the onset of convection. An increase in the Darcy number delays the convective motions. The results for different basic temperature profiles are symmetric qualitatively. In addition, the possibility of control of convection by a basic temperature profile was studied in detail.

Effects of porous medium filling on thermally developing forced convection in a parallel plate channel

This study obtains the semi-analytical solutions and explores the thermal characteristics of a thermally developing flow in a parallel plate channel, partially filled with a porous medium at the core, while considering local thermal non-equilibrium conditions, and viscous dissipation for the first time. The developing temperature field, for a porous medium filling of volume fraction fixed at 0.9, indicates an increasing difference in temperature between the solid and fluid phases with the axial distance. Besides, heat flux bifurcation starts in the entrance region as more heat diffuses to the solid at the interface, more markedly with a decreasing Darcy number, Da. When the thermal transport is dominated by interstitial heat transfer between solid and fluid in the porous medium, the thermal entrant length is the shortest. An increasing amount of porous medium filling with such quality and an increasing Da tend to shorten the thermal entry length. Nonetheless, as a lower Da porous media convects more heat away from the interface, it expedites the thermal development in cases where interstitial heat transfer in porous medium is poor. With an increasing porous medium fraction, the impact of viscous dissipation on heat transfer magnifies at the entrance region, thereby reducing the effectiveness of porous medium insert.

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.

Coupled THM formulation and wellbore analytical solution in naturally fractured media during injection/production

The heat extraction efficiency, storage, and safety of carbon dioxide (CO2) sequestration and methane (CH4) injection/post-production in naturally fractured formations have attracted significant interest. However, these studies require the examination of complex thermal-hydraulic-mechanical (THM) interacting processes, which include muti-discipline coupling and phase changes. Energy transfer mechanisms and thermally induced hydraulic and mechanical responses are critical for energy extraction efficiency , surface design optimization, and safety evaluation. The THM response in the wellbore, where fluids are injected and circulated, provides key information for design evaluation. A fully coupled formulation was developed based on a dual-porosity model to simulate the THM responses of a wellbore in naturally fractured aquifers under non-isothermal, two-phase fluid flow, and non-hydrostatic loading conditions. Local thermal non-equilibrium (LTNE) conditions are imposed for energy transportation between the fracture and matrix systems in the fissured porous solid skeleton. Different physical parameters reflecting various rock types and fracture characteristics are defined for the corresponding THM behavior models. Analytical solutions for the temperature perturbation and pressure changes in single-phase fluid flow in the vicinity of a wellbore in fissured media are developed to simulate the injection and production processes. Simulating a non-isothermal fluid circulation problem along a wellbore, an newly proposed mixed Type I (Dirichlet) and II (Neumann) boundary condition is imposed to study the heat exchange efficiency between wellbore fluid and the fissured NFM. The analytical solution has the advantages of being simple, explicitly possessing direct physical parameters, and serving as a tool for validating numerical solutions. The impacts of the newly proposed boundary condition on the near-well responses and THM results from the newly developed solution may be used to simulate the injectivity, storage capacity, reproduction, and design of supercritical carbon (scCO2) and CH4 are discussed.

Activated dissociation of H2 on the Cu(001) surface: The role of quantum tunneling

The activation and dissociation of hydrogen molecules (H2) on the Cu(001) surface are studied theoretically. Using first-principles calculations, the activation barrier for the dissociation of H2 on Cu(001) is determined to be ∼ 0.59 eV in height. It is found that the electron transfer from the copper substrate to H2 plays a key role in the activation and breaking of the H–H bond, and the formation of the Cu–H bonds. Two stationary states are identified at around the critical height of bond breaking, corresponding to the molecular and the dissociative states, respectively. Using the transfer matrix method, we also investigate the role of quantum tunneling in the dissociation process along the minimum energy pathway (MEP), which is found to be significant at or below room temperature. At a given temperature, the tunneling contributions due to the translational and the vibrational motions of H2 are quantified for the dissociation process. Within a wide range of temperature, the effects of quantum tunneling on the effective barriers of dissociation and the rate constants are observed. The deduced energetic parameters associated with the thermal equilibrium and non-equilibrium (molecular beam) conditions are comparable to experimental data. In the low-temperature region, the crossover from classical to quantum regime is identified.

Combustion dynamics of high Mach number scramjet under different inflow thermal nonequilibrium conditions

To characterize the impact of thermal nonequilibrium conditions in shock-induced combustion in high Mach number scramjet engines, a comparative numerical investigation has been performed. The combustor configuration was based on the HyShot II scramjet while the total enthalpy is 3.3 MJ/kg which resembles Mach 8 flight condition. The improved delay detached eddy simulation with Park two-temperature approach in combination with the vibration-chemical coupling model was employed in the nonequilibrium simulations. It is shown that under thermal nonequilibrium inflow conditions, noticeable stratification in the thermal state exists in the circumferential direction both in the combustor section and exhaust nozzle. In the inner core where the fuel mixes with the mainstream, flow deceleration caused by the heat release leads to a sufficient transformation of energy between the vibrational and translational-rotational modes approaching the thermal equilibrium state. However, the τv,mix is quite large in the supersonic mainstream, whereby the thermal nonequilibrium dominates. For the case with higher Tv in the inflow, the fuel jet's penetration height is lower while the local viscosity is higher which results in poor mixing between the fuel and air stream. Nevertheless, a 400 K increase in inflow Tv gives a higher effective temperature, which promotes the dissociation reactions, shortens the ignition distance and yields an 8% increase in the overall combustion efficiency. With better combustion performance, an additional 6% deceleration in the supersonic mainstream and the energy exchange rate between vibrational and translational-rotational modes becomes almost four times faster at the combustor outlet, which promotes the restoration of the thermal equilibrium state. Furthermore, under higher inflow vibrational temperature, the shock-induced combustion in supersonic crossflow becomes less stable with noticeable fluctuations in combustion heat release and local static pressure.

Magnetohydrodynamic mixed convection of TiO2–Cu/water between the double lid-driven cavity and a central heat source surrounding by a wavy tilted domain of porous medium under local thermal non-equilibrium

The magnetohydrodynamic (MHD) mixed convection of heat and mass transfer is carried out using finite difference method applied inside a tilted porous cavity saturated with a hybrid nanofluid due to the presence of the double-moving lid and the heat sources. In contrast to the earlier research, various effects which are recognized by heat generation in the local thermal non-equilibrium case at the extended Brinkman Darcy model subjected to inclined magnetic field are thoroughly examined numerically. For instance, unusual observations of the cold mass surrounding the heat source emphasize that the maximum fluid temperature highly depends on the forced convection. Additionally, solid-phase temperature acts in accordance to the heat source location while fluid temperature is agitated by the moveable sides which points up the disparity at the thermal energy transportation. However, the transfer of heat and mass at the model requires a specific conduct due to the existence of damping factors. The magnetic field, for example, suppresses the fluid flow. Moreover, the thermal non-equilibrium condition deteriorates the global heat generation.

THERMAL INSTABILITY OF BLOOD-COPPER CASSON NANOFLUID SATURATED POROUS MEDIUM UNDER LTNE, ROTATION, AND THROUGH-FLOW

Because of the antibacterial characteristics of copper, the thermal instability of blood-copper (B-Cu) nanoliquid plays a crucial role in the field of medical science, specifically in the cardiovascular system. In this article, the convective instability of B-Cu nanoliquid filled in a porous medium is investigated using a Casson model. A thermal nonequilibrium condition is taken for the nanoliquid and porous matrix. The Brinkman model is used because of the high porosity of the material. The influence of rotation and through-flow (both positive and negative) over the instability has also been examined. The amount of through-flow and rate of rotation are respectively governed by Peclet number and Taylor number. A comparison between the impacts of through-flow and rate of rotation is done, and it is found that through-flow is more effective than the rate of rotation to delay the onset of convection. Both steady and unsteady weakly nonlinear analyses are performed to understand the heat transport in the system. It is concluded that the Casson nanofluid parameter has both stabilizing and destabilizing impact depending upon the rate of rotation and therefore the current work can be possibly utilized in both places where heat removal and heat conservation is required. One more important thing is observed: the effect of local thermal nonequilibrium (LTNE) can also be regulated using the Casson nanofluid parameter.