Local Thermal Non-equilibrium Research Articles

A fully coupled thermo-poroelastic model for energy extraction in naturally fractured geothermal reservoirs: sensitivity analysis and flow simulation

The development of a novel method for modelling fluid flow and heat transfer in naturally fractured geothermal reservoirs represents a significant advancement in geothermal energy research. This Study presents a hybrid approach, which combines discrete fracture and single continuum techniques, to effectively capture the complex interactions between fluid flow and heat transfer in geothermal fractured reservoirs. In addition, the incorporation of the local thermal nonequilibrium method for simulating heat transmission accounts for the disparities in temperature between the rock matrix and the fluid, providing a more realistic representation of heat transfer processes. The study also presents a fully coupled thermo-poro-elastic framework that integrates fluid flow and heat transfer to comprehensively evaluate reservoir responses to injection/production scenarios. This coupled approach allows for the prediction of changes in reservoir properties, such as permeability and porosity, under varying fluid pressure and temperature conditions. The application of the proposed model to evaluate a geothermal reservoir’s long-term response to injection/production scenarios provides valuable insights into the reservoir’s behaviour and potential energy production capacity. The sensitivity analysis further enhances the model’s utility by identifying the key reservoir parameters that significantly influence the thermal depletion of the reservoir. Overall, this novel modelling approach holds promise for improving the understanding and management of naturally fractured geothermal reservoirs, contributing to the optimization of geothermal energy extraction strategies.

Linear and weakly nonlinear analyses of double‐diffusive convection in porous media with chemical reaction using LTNE model

AbstractThe onset of convection in a horizontal porous layer with chemical reaction and local thermal nonequilibrium is investigated. The nondimensional governing equations have been solved using the normal mode technique, which results in an eigenvalue problem. The analytical expressions for both stationary and oscillatory Rayleigh numbers are obtained. The effect of different parameters has been investigated and presented. The amplitude equation is derived using weakly nonlinear theory. Nusselt number is calculated using an amplitude equation to investigate heat transport. When modeling a fluid‐saturated porous medium, previous research on double‐diffusive convection has uniformly operated under the assumption of local thermal equilibrium (LTE) between the fluid and solid phases at all points within the medium. This standard practice assumes a minimal temperature gradient between the phases at any given location. However, in practical scenarios involving high‐speed flows or significant temperature differentials between the fluid and solid phases, the LTE assumption proves insufficient.

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.

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.

Numerical and thermal resistance analysis on the cryogenic porous medium heat exchanger with liquid channel

The porous medium heat exchanger has been increasingly utilized in cryogenic applications, especially in the milli-Kelvin region. This study focuses on the porous medium heat exchanger with liquid channel commonly used in the dilution refrigerator and proposes a numerical model, which applies the local thermal non-equilibrium (LTNE) model coupled with N–S equations and Brinkman-Forchheimer model. Comparing with literature results validates the numerical model. By analyzing the heat transfer characteristics of the heat exchanger, a thermal resistance network model is developed to capture the heat transfer mechanism. The results show that the total thermal resistance mainly depends on the fluid conductive thermal resistance and Kapitza thermal resistance inside the porous medium. The fluid conductive thermal resistance dominates at higher temperature while the Kapitza thermal resistance dominates at lower temperature. The expression of critical temperature is derived to determine the priority of reducing thermal resistance. At cryogenic temperatures, the porous medium serves to bypass the significant Kapitza thermal resistance by introducing much lower thermal resistances, while at normal temperatures, the porous medium reduces the overall thermal resistance by incorporating a parallel thermal resistance but without magnitude difference.

Numerical assessment of thermomagnetic convection of ferrofluid in a porous cavity employing a local thermal nonequilibrium model

Utilizing a two-temperature model, this study investigates the thermomagnetic convection of a ferrofluid within a porous cavity. The cavity is heated from the bottom and cooled from the sides to establish thermo-gravitational convection, whereas the thermomagnetic convection is induced by permanent magnets. The equations that govern flow and heat transfer are discretized using the finite volume method and the SIMPLE algorithm. The first part of the study evaluates the impact of the permanent magnet’s position on the flow pattern and ferrofluid and solid temperature fields. The results showed that positioning the magnet at the bottom of the cavity enhances heat transfer rate. The second part investigates the impact of the distance between two magnets at different magnetic, Rayleigh, and Darcy numbers, as well as the conduction ratio. The numerical findings exhibit that the heat transfer rate attains a peak at a certain distance between the magnets, depending on the Rayleigh number. With increasing Rayleigh number and conduction ratio, or decreasing Darcy number, the role of the magnetic field in improving heat transfer becomes less important. It is observed that thermomagnetic convection is replaced by thermo-gravitational one at high conduction ratios. The study emphasizes the need to use a local thermal non-equilibrium model in porous media with high magnetic and Darcy numbers, as well as large conduction ratios, to accurately capture the heat transfer phenomenon. It is observed that by placing two magnets at an appropriate distance, the heat transfer rate could be augmented by more than 136%.

Influence of periodicity on natural convection in a square porous cavity due to non-uniform heat under LTNE state

In this article, the influence of the local thermal non-equilibrium (LTNE) state on free convection in a square cavity filled with fluid-saturated porous medium is investigated numerically. The steady-state flow is induced due to sinusoidal heat distributed on the side walls of the cavity and insulated of the horizontal walls. The coupled flow governing equations are solved numerically by using the finite volume method (FVM) consisting of the SIMPLER (Semi-Implicit Method for Pressure Linked Equation Revised) Algorithm. The numerical simulations of temperature and stream-function contours are carried out for the non-Darcy model. The developed code is validated with existing numerical and present computed results for the case of a square enclosure associated with non-uniform heat source. Then, the present numerical results are analyzed over a range of physical parameters, like periodicity parameter ( N ≥ 1 ), interface heat transfer coefficient ( 10 − 2 ≤ H ≤ 10 2 ), porosity scaled thermal conductivity ratio ( 10 − 2 ≤ γ ≤ 10 2 ), with a fixed Rayleigh number ( Ra = 10 6 ), Darcy number ( Da = 10 − 4 ), Prandtl number (Pr = 0.71), and porosity ( ε = 0.8 ). To study the impacts of these key parameters on the fluid flow behavior and isotherm patterns of fluid as well as solid phase in the porous-square enclosure. From present numerical experiments that the structure of flow is controlled by multicellular structure with rotating clockwise and anticlockwise directions in the entire results. The flow dynamics are highly affected by the periodicity parameter (N) under LTNE circumstances. The characteristics of the local Nusselt number have the point of inflection and the maximum magnitude of it increases with N. The significant effect of H is found on the heat transfer rate of fluid phase but it is negligible on the heat transfer rate of solid phase. However, the influence of γ is found reverse in nature on the heat transfer rate of fluid as well as solid phase when as compared to the effect of H.

Thermal analysis of natural convection in rectangular porous fin wetted with CNTs nanoparticles and thermal radiation

AbstractIn the present investigation, the phenomenon of heat conduction in rectangular shaped porous fin wetted with nanofluid (a mixture of carbon nanotube [CNT] with water as base liquid) is examined using the local thermal non‐equilibrium (LTNE) paradigm. The heat transport mechanism involving the nanofluid and solid phases is represented by the dimensional thermal governing ordinary differential equations (TGODEs). These equations are transformed into nonlinear ordinary differential equations (ODEs) using relevant non‐dimensional variables. To solve the resultant dimensionless TGODEs, probabilists collocation method with Hermite polynomials (PCMHPs) is utilized. This study of temperature analysis has examined the characteristics of internal and exterior radiation, convection, and thermal conductivity to determine the attributes affecting heat transfer. For both the nanofluid and solid phase aspects, temperature distribution characteristics are revealed in tables and graphs. Subsequently, it is determined that as surface‐ambient radiation parameter levels decreased, the temperature profile of both solid and nanofluid phase augmented. The temperature variance among the solid and nanofluid phases decreased with an escalation in the wet porous parameter. The numerical outcomes illustrate that the presented PCMHP approach is not only convenient to execute but also provides accurate results.

Numerical investigation on transpiration cooling with phase change based on multiphysics coupled finite element method

Transpiration cooling with phase change is an efficient active thermal protection method in aerospace. However, conducting numerical simulation of transpiration cooling with phase change is still a challenge, because porous flow, heat transfer and phase change are coupled with each other, which lead to numerical difficulties. In this article, the previous model is modified and the Zero Thickness Area Model (ZTAM) is proposed, which improves the efficiency and convergence significantly. In addition, the local thermal nonequilibrium effect and latent heat can be considered. To verify this ZTAM model, one-dimensional control equations of mass, momentum, and energy transpiration are solved using finite element method. Furthermore, the position of phase change is determined by fixed point iteration numerical algorithm, which shows good convergence. Finally, the influence on cooling effect by heat flux, coolant mass flow rate, porosity and pore diameter is investigated numerically.

Characteristics of synovial trihybrid nanofluid activation energy and Marangoni convective flow: A Computational framework of local thermal non-equilibrium

The impact of nonlinear heat source and activation energy on magnetized Synovial trihybrid nanofluid Marangoni convective flow across a sheet combining two viscosity models is investigated in this study. Heat sources, activation energy, and conditions of local thermal non-equilibrium (LTNE) are all considered in the modelling. Based upon energy equations, the LTNE model provides unique heat transport for both liquid and solid phases. This leads to the utilization of different temperature profiles for the fluid and solid phases in this work. A trihybrid fluid is created by combining the basic fluid blood with MWCNT (multi-wall carbon nanotubes), SWCNT (single-wall carbon nanotubes) and sliver nanoparticle. This study significant potential in several fields. The effects of parameters on friction between joints are examined, which aids in the analysis of the lubricant nature of Synovial trihybrid nanofluid. A significant finding of the current work is that the thermal profiles decrease with higher values of the Concentration-dependent viscosity parameter, but the velocity profile increases. An increase in the inter-phase heat transfer characteristic raises the liquid phase's thermal profile while lowering the solid phase's thermal profile.

Optimizing of a metal foam-assisted solar air heater performance: a thermo-hydraulic analysis of porous insert placement.

A numerical assessment of the heat transfer efficacy of a solar air heater (SAH) was carried out. The SAH is supplied with a porous metal foam layer to improve thermal mixing. Both the local thermal non-equilibrium (LTNE) and Darcy-extended Forchheimer (DEF) models were employed to forecast fluid and thermal transport within the partly filled SAH channel. The analysis was performed for various values of dimensionless foam layer lengths ( ), pore densities ( ), and Reynolds numbers ( ) at a fixed value of layer thickness ( ). Based on the position of the porous layer, three distinct arrangements, marked as Case 1, Case 2, and Case 3, were explored. Regarding the parameters examined, the findings indicate a definite improvement in the average Nusselt number ( ), but unfortunately, the friction factor also increases unfavorably. By reducing the length of the porous layer, a reasonable reduction in heat transfer rate and a significant decrease in pressure drop were noticed. The results showed about 26.64%, 48.73%, and 70.74% reductions in pressure drop by reducing the dimensionless foam length from 1 to 0.25, 0.5, and 0.75 respectively for at . On the other side, there are only about 11.05%, 23.11%, and 40.78% reductions in . The exhaustive analysis of the thermal performance of SAH was conducted using the thermal performance factor (TPF), which considers the trade-off between the SAH channel's potential for improved heat transmission and its cost for pressure loss. The TPF may reach a maximum of 2.82 compared to the empty channel when the metal foam layer is inserted with , for , and .

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.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Stability of penetrative convective currents in local thermal non-equilibrium

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection

The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

Effects of local thermal non-equilibrium on hydraulic stimulation efficiency of enhanced geothermal systems

Motivated by hydraulic stimulation of enhanced geothermal systems, the present paper investigates the coupled thermo-hydro-mechanical response of a geothermal well imbedded in a thermoporoelastic medium, subjected to a non-isothermal fluid flux and convective cooling on the borehole surface. Our focus centers on the effect of local thermal non-equilibrium (LTNE) on the temporal-spatial evolution of temperatures, pore pressure, and stresses, where the solid and fluid phases have two distinct temperatures and local heat transfer between the two phases is addressed. We employ integral transform and load decomposition techniques to derive analytical solutions in the Laplace domain. This methodology allows us to disentangle and separate the individual contributions to changes in pore pressure and stresses from fluid injection and convective heat transfer. The results reveal that compared to the classical local thermal equilibrium model, the thermally induced pore pressure is slightly lower under LTNE conditions. The LTNE has a significant influence on the temporal evolution of thermally induced stresses, especially in the vicinity of the wellbore.

An Analytical Study of the Impact of an Inclined Magnetic Field on Couette Flow with Jeffrey Fluid under Local Thermal Non-Equilibrium (LTNE) and Viscous Dissipation

In this work, we examine the effects of viscous dissipation and local thermal non-equilibrium (LTNE) on Couette flow in a duct filled with a porous media under the influence of an angled magnetic field. The bottom plate of the duct is in motion and subjected to a constant heat flux, while the top plate remains stationary and adiabatic. The Jeffrey fluid flow model is consistent with the unidirectional flow in the porous zone. The studies provide more precise measurements of the effects of the Jeffrey parameter (λ), inclined angle (ϕ), Hartmann number (MW), thermal conductivity ratio (ν), Brinkman number (BrW), and Biot number (BiW) on improving heat transmission. The governing equations are solved analytically. The present investigation gives dimensionless temperatures for fluid-solid phases and fully developed Nusselt number (FDNN) profiles. Variation of Jeffrey parameter, inclined angle, Brinkman number, and Hartman number in the temperature field in both phases and FDNN. Furthermore, the temperature in the solid phase is higher than the temperature in the fluid phase for the Jeffrey parameter and Hartman number in the Couette flow, which supports LTNE validation.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.