Local Thermal Non-equilibrium Research Articles

Modeling and characterizing the thermal and kinetic behavior of methane hydrate dissociation in sandy porous media

Methane hydrates (MHs) are deemed to be a potential energy source to meet the overwhelmingly growing demand for natural gas. The production of MHs involves many controlling processes such as heat transfer, fluid dynamics and hydrate reaction kinetics. Local thermal equilibrium (LTE) between solid and fluid phases was typically assumed when modeling the hydrate production, however, in many cases the local thermal non-equilibrium (LTNE) caused by the complex heat transfer processes at the pore scale cannot be neglected. In this work, a LTNE model was adopted to reflect the multiple heat transfer forms associated with hydrate dissociation and gas-liquid flow, particularly the solid-fluid interfacial convective heat transfer and the Joule-Thomson effect. The LTNE phenomenon and Joule-Thomson effect were hinted by a hydrate dissociation experiment carried out for model verification. The results show that the average estimation errors of temperature, cumulative gas and water production profiles between experiment and LTNE model were 7.70%, 6.63% and 4.02%, respectively, which are considerably better than those of the traditional LTE model (16.44%, 11.74% and 10.89%, respectively). A tenfold increase of interfacial convective heat transfer coefficient could reduce the local solid-fluid temperature difference by about 78.5%. A special focus was given to the Joule-Thomson effect which seemed to have less impact at the experimental condition in this work but become more significant when the gas saturation exceeds 40%. This work could add further insights into the thermal performance during hydrate dissociation in porous media, help to reveal the thermo-kinetic relationship at the pore scale and provide a more accurate estimation of the hydrate dissociation dynamics. It could be potentially employed to optimize the methane hydrate production strategies, minimize the risk of hydrate re-formation and maximize the overall energy recovery efficiency.

Impact of using single heated obstacle on natural convection inside porous cavity under non-Darcy flow and thermal non-equilibrium model: A comparison between horizontal and vertical heated obstacle arrangements

The current study implements a numerical investigation on natural convection inside non-Darican porous duct to analyse the actions of using a single heated obstacle attached horizontally/vertically at the heated surface under Local thermal non-equilibrium (LTNE). Importance has been given on how the heated obstacle length and its position manipulate the enhancement of natural convection. Solutions confirm that Nu is extremely depends on ratio of thermal conductivity (Kr), obstacle length (Z), obstacle position (X), modified Rayleigh number (Ra*) and inertia coefficient (Fs/Pr*) as compared to heat transfer coefficient (H). Results display that the rising in Z leads to recede free convection activity as compared to the smallest one, where Z and X have extremely impact on Nu. Results displayed that Nus, Nuf and NuT obtained for the horizontal case are higher than vertical case, which reveals a better thermal performance. Optimum enhancement in Nu has been observed when using small Z and it horizontally attached at higher place inside the duct. The density of LTNE regime is extremely reduced with rising in H, Kr and Ra* and reducing in Z and Fs/Pr*. Finally, the horizontal heated obstacle can be advised to be used in heat exchanger for techniques implementing porous media.

Experimental evidence for local thermal non-equilibrium during heat transport in sand representative of natural conditions

When modelling heat transport in hydrogeological systems, a standard assumption is local thermal equilibrium (LTE), which implies that the porous medium temperature at the interface between the solid and fluid instantaneously reaches equilibrium. Few studies have investigated the validity of the LTE assumption and its violation, also known as local thermal non-equilibrium (LTNE), as well as its impact on the accuracy of heat transport models. While the theoretical conditions under which LTNE occurs in natural groundwater flow have recently been revealed, these have not yet been experimentally verified. We examined the applicability of the LTE assumption by conducting systematic laboratory experiments using eight distinct flow velocities (Reynolds number, Re < 0.37) through sand (0.76 mm grain size), injecting both heat and solute as tracers and observing the response at multiple points downstream. Theoretical heat transport parameters were calculated from solute tracer experiments by applying a retardation factor, and the results were subsequently compared to the actual parameters estimated from heat tracing. Our experimental results confirm that the LTE assumption can be violated under natural groundwater flow conditions, and that LTNE impacts thermal dispersion coefficients more significantly than thermal front velocities. The largest differences between the predicted and estimated thermal transport parameters were 112% and 13% for the dispersion coefficients and velocities, respectively. Our results demonstrate that LTNE effects need to be considered in heat transport modelling especially when analyzing thermal dispersion coefficients.

Thermosolutal LTNE Porous Mixed Convection Under the Influence of the Soret Effect

Abstract The onset of thermosolutal convection in a fluid-saturated porous medium in the presence of a horizontal pressure gradient and the Soret effect under the two-temperature model of local thermal nonequilibrium (LTNE) is investigated. The Darcy model with the time-dependent velocity term in the momentum equation is employed together with the Oberbeck–Boussinesq approximation. The eighth-order eigenvalue differential equation obtained by employing linear stability analysis is solved using Galerkin's method of weighted residuals (GMWR) and also analytically. The onset of convection instills through oscillatory rather than stationary mode, and the critical stability parameters for the same are determined. The horizontal pressure gradient reinforces together with the solute concentration gradient and the scaled interphase heat transfer coefficient in evidencing mixed behavior on the criterion for the onset of oscillatory convection. Besides, the similarities and differences between the results of thermal and thermosolutal LTNE porous mixed convection are discerned.

Critical review on local thermal equilibrium and local thermal non-equilibrium approaches for the analysis of forced convective flow through porous media

Scientific community from the field of thermo-fluidics have focused extensive attention towards investigating techniques of enhancing the heat transfer in varied thermal systems. One of the most suitable techniques for augmenting the heat transfer is incorporating porous medium into thermal systems. The transport processes through porous media, which consists of a fluid phase and a solid matrix, can be modelled by either considering both to be in thermal equilibrium or in thermal non-equilibrium. Hence, two different modelling strategies viz. local thermal equilibrium (LTE) model and local thermal non-equilibrium (LTNE) model have been employed by different researchers. In this work, a comprehensive review of the published literatures in respect of the modelling approaches used for determining the implications of embedding porous media in different thermal systems from the perspective of heat transfer and entropy generation has been presented. The effects of various key determinants on the fluid flow, heat transfer characteristics and entropy generation in thermal systems are discussed. This discussion is then followed by a critical assessment of the applicability of LTE and LTNE approaches. At the end, conclusions and recommendations about the less explored systems and the areas that needs further investigations are summarized.

Mono- and Multi-Objective CFD Optimization of Graded Foam-Filled Channels.

Graded foam-filled channels are a very promising solution for improving the thermal performance of heat sinks because of their customized structures that leave large amounts of room for heat transfer enhancement. Accordingly, this paper proposes a comprehensive optimization framework to address the design of such components, which are subjected to a uniform heat flux boundary condition. The graded foam is achieved by parameterizing the spatial distributions of porosity and/or Pores Per Inch (PPI). Mono- and multi-objective optimizations are implemented to find the best combination of the foam’s fluid-dynamic, geometrical and morphological design variables. The mono-objective approach addresses the Performance Evaluation Criterion (PEC) as an objective function to maximize the thermal efficiency of graded foams. The multi-objective approach addresses different objective functions by means of Pareto optimization to identify the optimal tradeoff solutions between heat transfer enhancement and pressure drop reduction. Optimizations are performed by assuming a local thermal non-equilibrium in the foam. They allowed us to achieve a 1.51 PEC value with H* = 0.50, ReH = 15000, iε = iPPI = 0.50, ε(0) = 0.85, ε(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and ks→f = 104 as the design variables. For the three multi-objective functions investigated, one can extrapolate the optimum from the Pareto front via the utopia criterion, obtaining = 502 W/m2 K and Δp = 80 Pa, = 2790 and f = 42, = 0.011, and Δp* = 91. The optimal solutions provide original insights and guidelines for the thermal design of graded foam-filled channels.

On Numerical Modeling of Thermal Performance Enhancementof a Heat Thermal Energy Storage System Using a Phase Change Material and a Porous Foam

In this investigation, a comprehensive numerical analysis of the flow involved in an open-ended straight channel fully filled with a porous metal foam saturated and a phase change material (paraffin) has been performed using a single relaxation time lattice Boltzmann method (SRT-LBM) at the representative elementary volume (REV) scale. The enthalpy-based approach with three density functions has been employed to cope with the governing equations under the local thermal non-equilibrium (LTNE) condition. The in-house code has been validated through a comparison with a previous case in literature. The pore per inch density (10≤PPI≤60) and porosity (0.7≤ε≤0.9) effects of the metal structure were analyzed during melting/solidifying phenomena at two Reynolds numbers (Re = 200 and 400). The relevant findings are discussed for the LTNE intensity and the entropy generation rate (Ns). Through the simulations, the LTNE hypothesis turned out to be secure and valid. In addition, it is maximum for small PPI value (=10) whatever the parameters deemed. On the other hand, high porosity (=0.9) is advised to reduce the system’s irreversibility. However, at a moderate Re (=200), a small PPI (=10) would be appropriate to mitigate the system irreversibility during the charging case, while a large value (PPI = 60) might be advised for the discharging case. In this context, it can be stated that during the melting period, low porosity (=0.7) with low PPI (=10) improves thermal performance, reduces the system irreversibility and speeds up the melting rate, while for high porosity (=0.9), a moderate PPI (=30) should be used during the melting process to achieve an optimal system.

NUMERICAL INVESTIGATION OF HEAT TRANSFER IN A DEVELOPING THERMAL FIELD IN THE POROUS-FILLED DUCT UNDER LOCAL THERMAL NONEQUILIBRIUM: CONSTANT WALL HEAT FLUX

NUMERICAL INVESTIGATION OF HEAT TRANSFER IN A DEVELOPING THERMAL FIELD IN THE POROUS-FILLED DUCT UNDER LOCAL THERMAL NONEQUILIBRIUM: CONSTANT WALL HEAT FLUX

COMBINED EFFECT OF INTERNAL HEATING AND THROUGH-FLOW IN A NANOFLUID SATURATED POROUS MEDIUM UNDER LOCAL THERMAL NONEQUILIBRIUM

In this paper the combined effect of internal heating and through-flow in a porous medium layer saturated by nanofluid is studied under local thermal nonequilibrium. Free-free isothermal boundaries have been considered for the analysis. The Brinkman model is used for the porous medium. The nanofluid is assumed to be incorporated with the effect of thermophoresis and Brownian motion. The particles, fluid, and solid-matrix are at different temperatures, i.e., a three temperature model has been used for local thermal nonequilibrium (LTNE). To investigate the onset of convection and heat/mass transfer both linear and nonlinear stability analysis have been featured. We conclude that the effects of internal heating and through-flow play a vital role in the heat and mass transfer inside the system.

Evaluation of heat extraction performance of multi-well injection enhanced geothermal system

• Model of multiple-injection and one-production is established using local thermal non-equilibrium. • Effects of reservoir and injection-production parameters on EGS performance were investigated. • Increasing of injection temperature can increases production temperature and prolongs EGS life. • Thermal extraction rate increases with the injection-production distance increases. • Heat recovery rates of four different injection-production well patterns are compared. The well layout can provide fluid channels, which is important for enhanced geothermal system (EGS), then the thermal energy in the rock mass can be used for heat extraction and power generation. The heat extraction rate analysis of injection-production well patterns can provide reference for the heat extraction condition of EGS. Based on the local thermal non-equilibrium theory and random fracture model, the EGS model of four injection and one production was established in this paper. Effects of reservoir parameters and injection-production parameters on production temperature and thermal extraction rate were studied. The results show that the injection temperature and injection-production distance are important parameters that affecting the thermal performance of the EGS. Increasing injection temperature can increases the production temperature and prolongs the EGS life. When the injection temperature increases from 293.15 K to 323.15 K, the production temperature increases from 340.04 K to 354.21 K. The higher the injection-production distance is, the higher the thermal extraction rate is. When the injection-production distance increases from 210 m to 325 m, the thermal extraction rate increases from 41.9% to 56.4%. In addition, heat extraction rates of four injection-production well patterns were compared and analyzed. The heat extraction performance of three-injections and one-production is obviously better than other methods. For the heating demand, the heat extraction rate of this well pattern is 60.34% and its service life is 39.7a. For power generation demand, its heat extraction rate of the well pattern is 55.9%, and its life is 32.7a.

THERMAL NON-EQUILIBRIUM EFFECTS ON THE INSTABILITY MECHANISM IN A NON-NEWTONIAN JEFFREY FLUID SATURATED POROUS LAYER

In this work, the impact of local thermal nonequilibrium (LTNE) state on the convective instability of non-Newtonian Jeffrey fluid in a porous matrix is analyzed using a two-field temperature model. In view of the linear stability concept, the onset conditions for the convective instability are obtained analytically in terms of critical Rayleigh-Darcy number RD,c. The results demonstrate that the stability of the system improves with interphase heat-transmit parameter NHT , while it decreases with the Jeffrey parameter λ and altered thermal conductivities ratio γ. Some existing outcomes in the literature are also recuperated as specific states from this examination.

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

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

Local Thermal Non-Equilibrium Analysis of the Combined Conjugate Natural Convection and Thermal Radiation in a Porous Inclined Enclosure Occupied with Cu-Al2o3 Hybrid Nanofluid

Local Thermal Non-Equilibrium Analysis of the Combined Conjugate Natural Convection and Thermal Radiation in a Porous Inclined Enclosure Occupied with Cu-Al2o3 Hybrid Nanofluid

Natural convection of a binary liquid in cylindrical porous annuli/rectangular porous enclosures with cross-diffusion effects under local thermal non-equilibrium state

The present article reports an analytical study of the double diffusive natural convection (DDNC) in cylindrical porous annuli (CPA) and rectangular porous enclosures (RPE), which are handled in a unified way using the curvature parameter, saturated by a binary liquid under the assumption of local thermal non-equilibrium (LTNE) state. The buoyancy forces (thermal and solutal) driving the flow are assumed to be induced by the maintenance of constant and uniform heat and mass fluxes applied along the vertical (radial) walls and insulation of both horizontal walls of the annuli/rectangular enclosures. The Darcy-Boussinesq equations with LTNE assumption between the fluid and solid phases are employed to model the problem of DDNC in a binary liquid-saturated porous medium with cross-diffusion effects. The analytical results are obtained by employing the Oseen-linearization transformation technique in the study. The influence of various dimensionless parameters on heat and mass transports of the system are depicted using the Nusselt and Sherwood numbers and isotherms plots, and the obtained results are analysed with the physical explanation. Special attention is given to understand the effect of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system. Different aspect ratio values are chosen to obtain the results of three types of CPA/RPE (shallow, square and tall). Among these CPA/RPE, maximum and minimum heat and mass transports are achieved in the cases of shallow and tall CPA/RPE, respectively. The results of the pure thermal convection problem is obtained at the zero value of buoyancy ratio and solute Rayleigh number. The increasing value of N magnifies the heat and mass transports in the system due to the augmented buoyancy effect resulted from the thermal and solutal gradients. The increase of solid inner cylinder radius, by fixing its volume, makes the annulus slender which yields to decrease the heat and mass transports in the system. The effects of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system are clearly brought out. The results of LTE model are obtained at the infinite value of ratio of porosity modified thermal conductivities, γ, as a particular case of the present model. From the study, we conclude that the shallow porous annulus and tall rectangular enclosure are best suited in the design of heat removal and heat storage systems, respectively.

Mathematical modeling of microwave liver ablation with a variable-porosity medium approach

Background and objectivesThermal ablation of tumors plays a key role to fight cancer, since it is a minimally invasive treatment which involves some advantages compared to surgery and chemotherapy, such as shorter hospital stays and consequently lower costs, along with minor side effects. In this context, computational modeling of heat transfer during thermal ablation is relevant to accurately predict the obtained ablation zone in order to avoid tumor recurrence risk caused by incomplete ablation, and the same time to save the surrounding healthy tissue. The aim of this work is to develop a more realistic porous media-based mathematical model to simulate a microwave thermal ablation (MWA) of an in vivo liver tumor surrounded by healthy tissue. MethodsThe domain is made up of a spherical tumor bounded by a cylindrical healthy liver tissue. The simulated microwave antenna is a 14 G HS Amica-Gen Probe, and the supplied power of 60 W is applied for 300 s and 600 s. The model consists in coupling modified Local Thermal Non Equilibrium (LTNE) equations with the electromagnetic equations. The LTNE equations include a variable porosity function which fits the porosity changing from the tumor core to the rim based on experimental measures in in vivo cases. Moreover, four different blood vessels’ uniform distributions are investigated to compare the effects of different vascularizations of the considered target tissue. ResultsThe results are shown in terms of temperature fields, ablation diameters and volumes based on the Arrhenius thermal damage model with 99% of cell death probability. The outcomes show a very good agreement with a clinical study on human patients with hepatocellular carcinoma using the same antenna and energy setting, when terminal arteries distribution is included. ConclusionsIn this work, an in vivo microwave ablation of liver tumor surrounded by healthy tissue is modeled with a variable-porosity medium approach based on experimental measures. The outcomes shown for distinct vascularizations underline the key relevance of modeling more and more accurately tumor MWA, by considering increasingly realistic features, avoiding tumor recurrence, and improving both medical protocols and devices.

Radiation and heat generation aspects on MHD convection of nanofluids in inclined wavy porous double lid-driven enclosures having obstacles: local thermal non-equilibrium

The present contribution focuses on the thermal non-equilibrium handling of an unsteady mixed convection nanofluid flow within two-sided wavy and two-sided lid-driven porous enclosures due to the impact of the thermal radiation and inclined magnetic field. The forced convection situation is due to the movements of the left irregular and top regular boundaries. This pattern accounts for such impacts as the inter-phase heat transfer factor impact, the modified conductivity ratio and the thermal radiation aspects. The cavity includes apart heated wall of length b subjected to external Cu water (with particle diameter less than 100 nm) nanofluid. The governing equations have been solved utilizing Galerkin finite element (GFE) approach with CBS algorithm. Numerical outcomes for the flow and heat transfer for the fluid and solid phases are determined for miscellaneous combinations of the physical factors. Graphical and tabular outcomes pointing out interesting features of the physics of the problem are presented and discussed. The forced convection mode is dominance at higher values of and low values of Hartmann number Ha. Furthermore, the considered range of the nanoparameter () gives an augmentation in the rate of the heat transfer up to 14.54%.

Theoretical evaluation of bio-thermal response in human tissue subjected to pulse-laser induced hyperthermia therapy for cancer treatment

This paper aims to develop a theoretical estimation of thermal response in human tissues appearing in a hyperthermia treatment under the influence of laser-induced external heat sources. In general, to develop a theoretical investigation on bioheat transfer, the fundamental aspect is to adopt an appropriate thermal model for predicting the correct thermal response. Among the existing bioheat models, the two-temperature model is considered to be the most feasible one, as it takes into account the arterio-vascular architectural interaction in the analysis. This model is established based on the local thermal non-equilibrium (LTNE) approach. The exact solution of the two-temperature bioheat model has been established by the implementation of the combined scheme of Duhamel's theorem and the Finite integral transform method. A pulse laser heating applied externally as a therapeutic heat source is introduced newly in the area of the LTNE bioheat modelling whereas the existing research works were developed by utilizing scattering laser heat sources. The thermal response of the tissue is analyzed for different laser variables such as laser intensity, optical penetration depth, pulse laser time, and laser irradiation radius. A parametric study has been made to set a theoretical treatment protocol for hyperthermia therapy and correspondingly, the thermal field has been developed within the prescribed peak temperature spectrum for the hyperthermia treatment. The thermal field has also been investigated for various biological parameters, viz. blood perfusion rate, porosity, and pore diameter of the blood vessel. The present research outcome depicts that the hyperthermia temperature can be achieved at the optical penetration depth of 0.0005 m with the laser irradiation radius in the range of 0.004 m–0.008 m. From the present work, it can be highlighted that the health monitoring of infected tissues or the organ of the human body is necessary before processing therapeutic heating as the thermal field depends on the porosity of tissue significantly. A qualitative investigation between pulse heating and scattering laser heating depicts that pulse laser heating is a better option to choose for the thermal therapy for the curtailment of the possibility of thermally induced damage of healthy tissues. A successful verification and authentication study has been carried out between the present work and the published experimental and theoretical works.

Impact of using triple adiabatic obstacles on natural convection inside porous cavity under non-darcy flow and local thermal non-equilibrium model

This work displays a numerical investigation on free convection inside non-Darcy porous cavity having a vertical triple adiabatic obstacles under conditions of Local thermal non-equilibrium (LTNE). Interesting has been focused on how the obstacles lengths arrangements manipulates the enhancement of free convection. Based on obstacles lengths, seven cases have been tested under large ranges of heat transfer coefficient (0.1 ≤ H ≤ 100), ratio of thermal conductivity (0.1 ≤ Kr ≤ 100), obstacles length (0.25 L ≤ Z ≤ 0.75 L), modified Rayleigh number (200 ≤ Ra* ≤ 1000) and inertia coefficient (10−4 ≤ Fs/Pr* ≤ 10−2). Results indicate that the optimum improvement in Nu can be obtained when using small length of all obstacles or the obstacle length should be set in ascending order. The presence of obstacles reduces the heat transfer as compared to its absence. Therefore, the case that has a minimum obstacles length is advised to be used for applications of porous heat exchangers that involved adiabatic obstacles. A significant improvement in Nu is obtained with rising in Ra*, H and Kr and reducing in Fs/Pr*. The density of LTNE region is extremely reduced with rising in H, Kr and Ra* and reducing in Z and Fs/Pr*. The thermal equilibrium case can be reached when using large values of H and Kr.

Thermodynamic analysis of entropy generation in a horizontal pipe filled with high porosity metal foams

In the field of thermal management of electronic equipment , examining entropy generation properties is extremely useful. The entropy production experiments have been expanded to porous media using high porosity metal foams. The entropy production/generation for forced convection heat transfer in a tube is quantified via a numerical research. In the field of air stream direction, the horizontal pipe is entirely filled with nickel metal foam of 0.6 m length. For the isotropic porous metal foam zone, the Darcy-extended Forchheimer (DEF) flow is used to capture the dynamics of flow and local thermal non-equilibrium (LTNE) model is used for analyzing the heat transport phenomenon, while the k-ɛ turbulent model is used for the non-foam porous region of the tube. The effect of fully filled nickel metallic foam with different pore densities of 10, 20, and 30 metal foam with a porosity of 0.85 is being investigated. The computational solutions presented here are supported by experimental results published in the literature. The outlet exergy of the system rises with higher flow rates and falls with higher metal foam pore densities. The results of entropy generation due to thermal and fluid friction and Bejan number conceptions are also shown and discussed.

Effect of Local Thermal Nonequilibrium on the Stability of the Flow in a Vertical Channel Filled With Nanofluid Saturated Porous Medium

Abstract The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal nonequilibrium state of the fluid, particle, and solid–matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy–Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle, and solid–matrix phases separately, for the temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal nonequilibrium parameters. It is noticed that the influence of local thermal nonequilibrium (LTNE) parameters on convective instability is significant.