Local Thermal Equilibrium Assumption Research Articles

Analytical solutions of fluid flow and heat transfer in a partial porous channel with stress jump and continuity interface conditions using LTNE model

Forced convection heat transfer is analytically performed in a channel partially filled with porous media located at two inner walls under local thermal non-equilibrium (LTNE) condition. A constant heat flux is imposed at the channel walls. The Brinkman extended Darcy model is applied in the porous region and the stress jump and continuity conditions are employed at the interface. Exact solutions are obtained for velocity, pressure drop, the fluid and solid temperatures and Nusselt number. The effects of pertinent parameters on the fluid flow and heat transfer are conducted. Furthermore, the solution for the Nusselt number is compared to that by applying the local thermal equilibrium (LTE) assumption and the validity of the LTE is examined. It is shown that by applying LTNE model for different solid to fluid effective thermal conductivity ratios (K) and Biot numbers (Bi), the variations of Nusselt number with hollow ratio include three types of curves, which are: a maximized Nusselt number occurs at a small optimum hollow ratio, Nusselt number monotonically decreases by increasing hollow ratio and a minimized Nusselt number occurs at a small hollow ratio, respectively. For high K, a small critical value of S at which the Nusselt number reaches to LTE Nusselt number occurs and it lowers with the increase of Bi number and the decrease of Darcy number; while for low K, the LTNE Nu number versus hollow ratio is almost the same with LTE Nu number and therefore the LTE is valid. The stress jump at the interface is found to have negligible effect on the Nusselt number and the pressure drop, except in a high Darcy number with a low stress jump coefficient where the calculation of pressure drop need to account for the stress jump effect at the interface and the Nusselt numbers for both LTE and LTNE models slightly differs from the case of stress continuity interface condition.

Numerical simulation of ballistic electron dynamics and heat transport in metallic targets exposed to ultrashort laser pulse

The role of ballistic electrons generated during ultrashort pulse laser (USPL) absorption in metallic targets was investigated in a wide range of laser intensities using our developed simulation package FEMTO-2D. The simulation package is based on the numerical solution of the two-temperature model with the assumption of local thermal equilibrium for electron and lattice subsystems within the simulation cell at any time step. Electron thermodynamic parameters were calculated through the processes of material transition from the cold solid state into the dense plasma state during and after the pulse based on the collision theory. The appropriate model for temperature dependent thermodynamic parameters allows defining the heat transport during an early stage of the USPL-matter interaction directly, without relying on the effective absorption depth model. The study investigated, for the first time, using integrated computer simulation the role of ballistic electrons in energy transfer and heat conduction during USPL deposition. The simulation predictions of the electron heat transport dynamics during and shortly after the laser pulse were benchmarked for the gold target against available experimental data and were able to confirm the dominant role of the ballistic electrons in the initial heat propagation within 100–120 nm of the target at laser intensities below 1013 W/cm2.

Positivity-preserving scheme for two-dimensional advection–diffusion equations including mixed derivatives

In this work, we propose a positivity-preserving scheme for solving two-dimensional advection–diffusion equations including mixed derivative terms, in order to improve the accuracy of lower-order methods. The solution of these equations, in the absence of mixed derivatives, has been studied in detail, while positivity-preserving schemes for mixed derivative terms have received much less attention. A two-dimensional diffusion equation, for which the analytical solution is known, is solved numerically to show the applicability of the scheme. It is further applied to the Fokker–Planck collision operator in two-dimensional cylindrical coordinates under the assumption of local thermal equilibrium. For a thermal equilibration problem, it is shown that the scheme conserves particle number and energy, while the preservation of positivity is ensured and the steady-state solution is the Maxwellian distribution.

Solar energy latent thermal storage by phase change materials (PCMs) in a honeycomb system

A computational investigation of a honeycomb system with Phase Change Materials (PCM) for solar energy applications is accomplished. The system is a solid honeycomb structure made in checkerboard matrix using parallel squared channels, half of them are filled with PCM and in the other the Heat Transfer Fluid (HTF) passes through. Transient regime numerical simulations are created for different channels per unit of length (CPL). The Solid-liquid PCM is paraffin wax. A comparison between the direct honeycomb model (Model A) and a porous medium model (Model B) is carried out. The model B is modelled with the extended Darcy-Brinkman law using the Local Thermal Equilibrium (LTE) assumption for heat exchange between solid and liquid zones. By the results of the direct honeycomb model, the characteristics such as permeability, effective thermal conductivity and interfacial heat transfer are evaluated and then compared with the porous medium model. Numerical simulations were carried out using the Ansys-Fluent code. Results in terms of melting time and temperature fields as function of time are presented.

Numerical Study of Heat Transfer Enhancement for a Flat Plate Solar Collector by Adding Metal Foam Blocks

Numerical study has been conducted to investigate the thermal performance enhancement of flat plate solar water collector by integrating the solar collector with metal foam blocks.The flow is assumed to be steady, incompressible and two dimensional in an inclined channel. The channel is provided with eight foam blocks manufactured form copper. The Brinkman-Forchheimer extended Darcy model is utilized to simulate the flow in the porous medium and the Navier-Stokes equation in the fluid region. The energy equation is used with local thermal equilibrium (LTE) assumption to simulate the thermofield inside the porous medium. The current investigation covers a range of solar radiation intensity at 09:00 AM, 12:00 PM, and 04:00 PM on the 8th of July 2016 under Iraq climate conditions, and a range of Reynolds number of (207<Re<625). The results show that the insertion of metal foam blocks caused a reduction in the absorber plate temperature and the possible enhancement in the heat transfer coefficient is more than 80% and as a result, the collector exhaust temperature will increase.

Applicability of the local thermal equilibrium assumption in the performance modelling of CSP plant rock bed thermal energy storage systems

Gas-solid packed beds have been widely studied as a cost-effective means of thermal energy storage in concentrating solar power (CSP) plants. Typically, the operation of packed beds in such systems is modelled by accounting for a finite rate of heat transfer between the fluid and solid media. This approach requires the coupled solution of the fluid- and solid-phase energy equations, which is computationally-costly, especially for year-long performance simulations. The local thermal equilibrium assumption, which assumes an infinite inter-phase heat transfer rate, can be applied to reduce the complexity and thus computational cost of packed bed models. However, the implications of making such an assumption in the context of CSP thermal energy storage system performance modelling is poorly understood. In fact, the application of the approach in long-term simulations has not been investigated before. This work addresses the topic by comparatively evaluating the performance of local thermal equilibrium and local thermal non-equilibrium models in the annual simulation of an air-rock packed bed, hypothetically operating in an open volumetric receiver CSP plant. The level of inter-model agreement is assessed in terms of annual bed exergy yield, bed blowing work, and plant power generation time. In addition, solution times are compared to establish the extent of computational cost savings. A parametric study examining the effect of variations in key bed design parameters on inter-model agreement is also conducted. The results obtained provide a clear indication of the strengths and weaknesses of either modelling approach, as well as of the suitability of the local thermal equilibrium assumption in general.

Mixed convective heat transfer in an enclosure containing a heat-generating porous bed under the influence of bottom injection

The present study numerically models the process of heat removal from a heat-generating porous bed with cold fluid injection from the bottom of the bed. This type of situation is encountered during post-accident situations in nuclear reactors and involves augmentation of heat removal capacity with forced coolant injection from the bottom. A steady-state analysis is carried out with the assumption of laminar flow regime and without accounting for phase change. Darcy-Brinkmann-Forchheimer approximation and local thermal equilibrium assumption are adopted for modelling the momentum and energy equations in porous media, respectively. It is observed that the fluid flow is determined based on the dominancy of the two co-existing flow mechanisms viz. inertial flow due to forced fluid injection and buoyancy-driven flow due to heat generation within the porous bed. In addition, permeability of the porous media significantly affects the flow mechanism, especially near the fluid inlet. Heat transfer characteristics closely follow the flow mechanism established within the enclosure.

Performance evaluation of a flat-plate solar collector filled with porous metal foam: Experimental and numerical analysis

Experimental and numerical investigations on the effect of porous metal foam on the performance of a flat-plate solar collector have been carried out in this study. The numerical solution is based on the control-volume approach and local thermal equilibrium assumption between the fluid-porous material phase to get the optimum thickness of the porous medium and also evaluate the thermal performance and pressure drop in the porous channel collector. The numerical results exhibit that the maximum thermal performance is obtained in a porous layer dimensionless thickness greater than 0.8, which the fully filled channel is selected in the present study. In the experimental section, an ASHRAE standard is used to examine the effects of metal foam on the solar collector performance at different flow rates. The numerical solution results have been validated against the experimental results, and a reasonable agreement has been achieved. The numerical and experimental results have shown that using the porous medium enhances the maximum thermal efficiency and Nusselt number up to 18.5% and 82%, respectively.

Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional, Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model

Effect of local thermal non-equilibrium (LTNE) on onset of Brinkman–Benard convection and on heat transport is investigated. Rigid–rigid and free–free, isothermal boundaries are considered for investigation. The assumption of LTNE leads to an ‘advanced onset’ situation compared to that predicted by the local thermal equilibrium (LTE) assumption. This results in the ‘enhanced heat transport’ situation in the problem. Asymptotic analysis for small and large values of inter-phase heat transfer coefficient is also carried out on critical Rayleigh number, critical wave number and Nusselt number. In respect of boundary influences on onset and heat transport, it is found that classical results hold even under the LTNE assumption. The other parameters’ influences on onset and heat transport are qualitatively similar in LTNE and LTE cases.

A numerical study on the impact of thermal alterations in porous media during hot fluid injection process employing a modified Boussinesq model

The Oberbeck-Boussinesq (OB) approximation is widely employed as a simplifying assumption for density-dependent flow problems. It reduces the governing differential equations to simpler forms, which can be handled analytically or numerically. In this study, a modified OB model is formulated to account for the variation of rock permeability and porosity with temperature during the hot fluid injection process in an oil-saturated porous medium under the assumption of local thermal equilibrium (LTE). The mathematical model is solved numerically using a fully implicit control volume finite difference discretization with the successive over relaxation (SOR) method to handle the non-linearity. Subsequently, the numerical model is validated with the analytical solution of the simplified problem successfully. Through detailed sensitivity analyses, the simulation results reveal the hot fluid injection rate as the most important operational parameter to be optimized for a successful thermal flood. The numerical runs show that that for single-phase core-flood simulation, the effect of temperature on the rock absolute permeability and porosity can be neglected without introducing any significant errors in the estimated recovery and temperature profile.

VALIDATION OF LOCAL THERMAL EQUILIBRIUM ASSUMPTION IN A VASCULAR TISSUE DURING INTERSTITIAL HYPERTHERMIA TREATMENT

In this paper, the validity of local thermal equilibrium assumption in a tissue-like porous medium is investigated numerically, with an interstitial heat source. The study is based on comparison between two three-equation local thermal nonequilibrium (LTNE) model and one-equation local thermal equilibrium (LTE) model. The LTNE model is validated by an steady-state 1D analytical solution which is presented for first time. The presented results indicate the small temperature difference between fluid and solid phases in heat-affected region, which leads to considerable errors in prediction of tissue thermal behavior. According to records, increasing perfusion rate or intensity of heat source increases the differences between LTE and LTNE models. It is found that in a counter-current vascular tissue if the perfusion rate of blood into tissue becomes higher, the prediction error of LTE model will be more considerable. Moreover, the higher the intensity of heat source is, the greater the difference between LTE and LTNE models is. These findings could be extended to heat transfer modeling of actual tissue during various interstitial hyperthermia treatments.

Macroscopic model for solidification in porous media

A macroscopic model for solidification of pure metal in porous media is derived using the volume averaging method. Solidification starts when the infiltration of the porous mould is completed and therefore the phase change problem involving three phases (liquid and solid metal, mould) is governed by diffusion. The upscaled model is first characterized by the local thermal equilibrium assumption (LTE) between the liquid and the solid metallic phases leading to one energy conservation equation for the equivalent metallic phase. On the other hand, local thermal non-equilibrium (LTNE) between the equivalent continuous metallic phase and the mould is considered, giving rise to two coupled energy conservation equations. The associated closure problems are derived and numerically solved allowing for the determination of the effective transport properties. Numerical solutions of the macroscopic model are qualitatively compared with available experiments.

Instability and Route to Chaos in Porous Media Convection

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

Extracting temperature and transverse flow by fitting transverse mass spectra and HBT radii together

Single particle transverse mass spectra and HBT radii of identical pion and identical kaon are analyzed with a blast-wave parametrization under the assumptions of local thermal equilibrium and transverse expansion. Under the assumptions, temperature parameter [Formula: see text] and transverse expansion rapidity [Formula: see text] are sensitive to the shapes of transverse mass [Formula: see text] spectrum and HBT radius [Formula: see text]. Negative and positive correlations between [Formula: see text] and [Formula: see text] are observed by fitting [Formula: see text] spectrum and HBT radius [Formula: see text], respectively. For a Monte Carlo simulation using the blast-wave function, [Formula: see text] and [Formula: see text] are extracted by fitting [Formula: see text] spectra and HBT radii together utilizing a combined optimization function [Formula: see text]. With this method, [Formula: see text] and [Formula: see text] of the Monte Carlo sources can be extracted. Using this method for A Multi-Phase Transport (AMPT) model at Relativistic Heavy Ion Collider (RHIC) energy, the differences of [Formula: see text] and [Formula: see text] between pion and kaon are observed obviously, and the tendencies of [Formula: see text] and [Formula: see text] versus collision energy [Formula: see text] are similar with the results extracted directly from the AMPT model.

Study of heat and mass transfer of water evaporation in a gypsum board subjected to natural convection

The present paper reports a numerical study to investigate the drying of rectangular gypsum sample based on a diffusive model. Both vertical and low sides of the porous media are treated as adiabatic and impermeable surfaces plate. The upper face of the plate represents the permeable interface. The energy equation model is based on the local thermal equilibrium assumption between the fluid and the solid phases. The lattice Boltzmann method (LBM) is used for solving the governing differential equations system. The obtained numerical results concerning the moisture content and the temperature within a gypsum sample were discussed. A comprehensive analysis of the influence of the mass transfer coefficient, the convective heat transfer coefficient, the external temperature, the relative humidity and the diffusion coefficient on macroscopic fields are also investigated. They all presented results in this paper and obtained in the stable regime correspond to time superior than 4000 s. Therefore the numerical error is inferior to 2%. The experimental data and the descriptive information of the approach indicate an excellent agreement between the results of our developed numerical code based on the LBM and the published ones.

Heat transfer and parameterization in local thermal non-equilibrium for dual porosity continua

Processes of coupled fluid flow and heat transport in fractured porous media are of interest in many different natural and industrial applications. Often it is difficult to represent all features of a system in an adequate parameterization. The dual porosity model allows parameterization for pore space and fractures separately, representing high permeable fractures and high porous host rock at the same time. Local thermal non-equilibrium models (LTNE) overcome the limiting assumption of instantaneous local thermal equilibrium between fluid and rock phase in heat transport, which has been shown to be preferential in several scenarios. In this work we derive a LTNE model for a dual porosity fluid flow model, considering heat transfer between rock and both fluid domains, pore space and fractures, as well as heat transport between the two fluid domains, linked to mass transfer. This enables a well-defined parameterization for fluid and heat transport and allows deeper insights into heat transport processes. We test our model for some standard scenarios in the context of geothermal application.Our results indicate in comparison to a standard fluid-rock model, that water stored in low permeable regions of the host rock need to be considered in heat transfer models, otherwise the heat stored is underestimated. Pore water acts as an additional heat reservoir for the host rock, generating higher production temperatures in the reservoir compared with an equivalent fluid flow model also using LTNE. Only in regions with high pressure gradient between pore and fracture fluid, heat transfer due to mass transfer is significant and it is the smallest heat transfer process under any scenario tested. Our model can be easily adopted to other simulation tools and be extended with more, also dynamic, constitutive relationships for a stronger coupling between heat transport and fluid flow separately for porous matrix and fractures.

Experimental Investigations of Heat Transport Dynamics in a 1d Porous Medium Column

The present study involves the experimental investigation of heat transport due to the forced convective flow through a thermally isolated porous medium column.The experiments regard the observation of thermal breakthrough curves obtained through a hot flow injection in correspondence of two thermocouples positioned along a thermally isolated column of porous medium. The experiment has been carried out for three flow rates in order to investigate the critical issues regarding heat transport phenomena such as the relationship between the thermal dispersion with the flow velocity and the validity of the local thermal equilibrium assumption between the fluid and solid phase.

Failure of Local Thermal Equilibrium in Quantum Friction.

Recent progress in manipulating atomic and condensed matter systems has instigated a surge of interest in nonequilibrium physics, including many-body dynamics of trapped ultracold atoms and ions, near-field radiative heat transfer, and quantum friction. Under most circumstances the complexity of such nonequilibrium systems requires a number of approximations to make theoretical descriptions tractable. In particular, it is often assumed that spatially separated components of a system thermalize with their immediate surroundings, although the global state of the system is out of equilibrium. This powerful assumption reduces the complexity of nonequilibrium systems to the local application of well-founded equilibrium concepts. While this technique appears to be consistent for the description of some phenomena, we show that it fails for quantum friction by underestimating by approximately 80% the magnitude of the drag force. Our results show that the correlations among the components of driven, but steady-state, quantum systems invalidate the assumption of local thermal equilibrium, calling for a critical reexamination of this approach for describing the physics of nonequilibrium systems.

A dynamic heat transfer coefficient between fractured rock and flowing fluid

Estimation of heat production remains a major challenge for geothermal industry. In continuum mechanics two main approaches need to be separated to model heat transfer between fluid and rock: local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE). While LTNE does not require the strong assumption of instantaneous local thermal equilibrium, the parameters for explicit heat transfer between rock and fluid are only loosely defined. This work focuses on the heat transfer coefficient between rock walls and flowing fluid. Based on an experimental setup with simple geometry and a steady state scenario, we derive a dynamic heat transfer coefficient dependent on fracture aperture, flow velocity and thermal parameters. We compare our model to experimental data and achieve a good agreement for most temperatures. In comparison to a static heat transfer coefficient, a dynamic coefficient changes the fluid and rock temperature distribution in the fractured system. We then show possible extensions of our dynamic approach with a simulation on reservoir scale. In opposite to existing models and empiric approaches our model intrinsically adjusts to spatial heterogeneity and temporal changes in flow and temperature field. The model is based on well-defined physical parameters which can be easily obtained from standard laboratory tests and dependent on characteristic variables like velocity and rock temperature. Our model can be extended by including more constitutive relationships linking permeability, fracture aperture, fluid pressure and heat transfer.

Heat transfer enhancement of PCM melting in 2D horizontal elliptical tube using metallic porous matrix

In this study, the melting process of ice as a phase-change material (PCM) saturated with a nickel–steel porous matrix inside a horizontal elliptical tube is investigated. Due to the low thermal conductivity of the PCM, it is motivated to augment the heat transfer performance of the system simultaneously by finding an optimum value of the aspect ratio and impregnating a metallic porous matrix into the base PCM. The lattice Boltzmann method with a double distribution function formulated based on the enthalpy method, is applied at the representative elementary volume scale under the local thermal equilibrium assumption between the PCM and porous matrix in the composite. While reducing or increasing the aspect ratio of the circular tubes leads to the expedited melting, the 90 $$^{\circ }$$ inclination of each elliptical tube in the case of the pure PCM melting does not affect the melting rate. With the reduction in the porosity, the effective thermal conductivity and melting rate in all tubes promoted. Although the natural convection is fully suppressed due to the significant flow blockage in the porous structure, the melting rates are generally increased in all cases.