Local Thermal Equilibrium Research Articles

NUMERICAL INVESTIGATION OF FORCED CONVECTION HEAT TRANSFER AROUND AND THROUGH AN ELLIPTICAL POROUS CYLINDER

Convection heat transfer from a heated elliptical porous cylinder in the incompressible and laminar cross-flow is studied numerically. The effects of Darcy number (10<sup>-6</sup> ≤ Da ≤ 10<sup>-2</sup>), aspect ratio (0.2 ≤ AR ≤ 5), Prandtl number (0.7 ≤ Pr ≤ 70), Reynolds number (10 ≤ Re ≤ 40), on the average Nusselt number (Nu), as well as the lift and the drag coefficients are investigated. Two types of thermal boundary conditions for porous cylinder are investigated: uniformly distributed heat source and constant temperature. The fluid flow in the porous medium is numerically simulated by the superficial velocity model. Additionally, the energy equation in the porous medium is simplified by the local thermal equilibrium (LTE) hypothesis. It is concluded that the aspect ratio of the elliptical cylinder has a great influence on the heat transfer and fluid flow characteristics of this problem. Results show that increasing the Darcy number increases the Nusselt number and decreases the drag coefficient of the porous cylinder. Moreover, values of Da smaller than 10<sup>-4</sup> resemble the fluid flow and heat transfer characteristics of the impermeable solid cylinder.

DOUBLE-DIFFUSIVE CONVECTION-REACTION FLOW IN A SQUARE ENCLOSURE FILLED WITH POROUS MEDIUM

In this work, we analyze the double-diffusive convection-reaction of a binary mixture in a square enclosure filled with a porous media, with constant temperatures and concentrations at the two vertical walls and adiabatic and impermeable horizontal walls. The boundaries of the enclosure are under chemical equilibrium. The porous medium is assumed to be in local thermal equilibrium (LTE) state and the solubility of the dissolved salts depends on temperature. The two-dimensional steady-state flow rate is determined by a non-Darcy (Darcy-Brinkman) model, and the entire governing equations are solved using the usual SIMPLE-R finite-volume methodology. It has been found that as the reaction rate increases in the system the salt precipitation also increases, causing a decrease in overall mass transfer rate. Also, the chemical reaction tends to decrease the overall heat transfer-rate.

Observations and modeling of spectral line asymmetries in stellar flares

Context. Stellar flares are energetic events occurring in stellar atmospheres. They have been observed on various stars using photometric light curves and spectra. On some cool stars, flares tend to release substantially more energy than solar flares. Spectroscopic observations have revealed that some spectral lines exhibit asymmetry in their profile in addition to an enhancement and broadening. Asymmetries with enhanced blue wings are often associated with coronal mass ejections, while the origin of red asymmetries is currently not well understood. A few mechanisms have been suggested, but no modeling has been performed so far. Aims. We observed the dMe star AD Leo using the 2-meter Perek telescope at Ondřejov observatory, with simultaneous photometric light curves. In analogy with solar flares, we modeled the Hα line emergent from an extensive arcade of cool flare loops and explain the observed asymmetries using the concept of coronal rain. Methods. We solved the non-LTE (departures from local thermal equilibrium) radiative transfer in Hα within cool flare loops taking the velocity distribution of individual rain clouds into account. For a flare occurring at the center of the stellar disk, we then integrated radiation emergent from the whole arcade to obtain the flux from the loop area. Results. We observed two flares in the Hα line that exhibit a red wing asymmetry corresponding to velocities up to 50 km s−1 during the gradual phase of the flare. Synthetic profiles generated from the model of coronal rain have enhanced red wings that are quite compatible with observations.

Polarization in heavy ion collisions: A theoretical review

In these proceedings I discuss the recent progress in the theory of spin polarization in relativistic fluids. To date, a number of studies have begun to examine the impact of the shear tensor on the local spin polarization and whether this contribution can restore agreement between the measurements and the predictions obtained from a polarization induced by the gradients of the plasma. I present the derivation of the spin polarization vector of a fermion at local thermal equilibrium and I discuss the role of pseudo-gauge transformations and of dissipative effects. I list what we can learn from the polarization measured at lower energies. Finally, I discuss possible applications of spin polarization measurements in relativistic heavy ion collisions.

A parameter-free model for temperature and pressure profiles in luminous, stable stars

The historic, classical thermodynamic model of star interiors neglects luminosity (𝐿), and consequently predicts ultrahigh central solar temperatures (𝑇 ~ 15 × 106 K). Modern models yield similar 𝑇 profiles mostly because local thermal equilibrium and multiple free parameters are used. Instead, long-term stability of stars signifies disequilibrium where energy generated equals energy emitted. We assume that heat is generated in a shell defining the core and use Fourier’s model, which describes diffusion of heat, including via radiation, to predict the 𝑇 profile. Under steady-state, power 𝐿 transmitted through each shell is constant above the zone of energy generation. Hence, 𝐿 is independent of spherical radius (𝑠), so the Stefan-Boltzmann law dictates 𝑇(𝑠), and material properties are irrelevant. Temperature is constant in the core and proportional to 𝐿¼𝑠−½ above. A point source core sets the upper limit on 𝑇(𝑠), giving 𝑇average = (6/5)𝑇surface. Core size or convecting regions little affect our results. We also construct a parameter-free model for interior pressure (𝑃) and density (ρ) by inserting our 𝑇(𝑠) formula into an ideal gas law (𝑃/ρ 𝛼 𝑇) while using the equation for hydrostatic gravitational compression. We find 𝑃 𝛼 𝑠−3, ρ 𝛼 𝑠−5/2, and ρaverage = 6 × ρsurface. Another result, 𝐿 𝛼 mass3.3, agrees with accepted empirical rules for main sequence stars, and validates our model. The total solar mass already “burned” suggests that fusion occurs near 𝑠surf/400 where 𝑃 ~ 0.5 × 1012 Pa, in agreement with H-bomb pressure estimates. Implications are discussed.

A NUMERICAL STUDY OF AXIAL CONDUCTION IN A FLUID-SATURATED POROUS-FILLED DUCT UNDER A LOCAL THERMAL NON-EQUILIBRIUM MODEL

This study analyses the influence of axial conduction and Biot number on the forced convective heat transfer characteristics in a duct filled with porous material that is thermally developing under local thermal non-equilibrium (LTNE). Channel walls are subjected to heat flux. The unidirectional flow in the porous region corresponds to the Darcy Brinkman model. A successive accelerated replacement (SAR) approach has been used to obtain numerical solutions. The investigations further quantify the impact of the Biot number on heat transfer enhancement. For fluid-solid phases, dimensionless temperatures, and local Nusselt number (<i>Nu<sub>ξ</sub></i>), profiles are given in the present investigation. Validation of fully developed conditions for LTNE is done. The axial conduction effect is more at the low Peclet number <i>Pe<sub>H</sub></i> for all the Biot numbers Bi. For large <i>Pe<sub>H</sub></i>, the axial conduction effect is negligible. The <i>Nu<sub>ξ</sub></i> decreases as the ratio of thermal conductivities, <i>κ</i> and <i>Bi</i>, increases. LTNE is equivalent to local thermal equilibrium (LTE) for a large Bi.

To the derivation of relativistic hydrodynamic equations for a rarefied non-ideal gas system of high-energy particles in the framework of Tsallis statistics

The paper discusses the construction of non-extensive relativistic dissipative hydrodynamics of an anomalous hadronic fluid on the basis of relativistic kinetic equation, obtained earlier in the context of the Tsallis statistics, characterized by the nonextensivity parameter q, and taking into account correlation effects (by rejecting the standard hypothesis of molecular chaos) in the collision term for heavy ions. It is shown that some specific form of local thermal equilibrium quark-gluon matter is described by a generalized version of the relativistic Yüttner distribution. With the help of this distribution all thermodynamic parameters of state are defined in explicit form. Linear constitutive relations and transport coefficients such as shear viscosity, bulk viscosity and heat conductivity are derived from the linearized collision integral written in the Anderson-Witting form and evaluated using a relaxation time approximation. The designed non-extensive relativistic fluid dynamics is designed to simulate a wide range of phenomena in astrophysics, cosmology and high-energy physics.

COMPUTATIONAL MODELING FOR THE PERFORMANCE PREDICTION OF QUAD-SECTOR ROTARY AIR PREHEATER AND COMPARATIVE STUDY WITH TRI-SECTOR AND BI-SECTOR ROTARY AIR PREHEATERS

Rotary air preheaters are mainly used to improve the economy of a steam power plant by preheating the air with the help of hot flue gases from the boiler. Modern steam power plants are preferring tri-sector and quad-sector rotary air preheaters over bi-sector due to their better performance and lower leakage. In the present work, thermal behavior of a quad-sector rotary air preheater is the focus using computational fluid dynamics. The porous media approach is used for numerical simulation assuming local thermal equilibrium condition between fluid and solid. The performance of the air preheater is accessed by effectiveness and pressure drop. Porosity is estimated for four different cell shapes, which are used in the rotary preheater core for numerical investigation. The study reveals that the core consisting of a triangular cell has the highest effectiveness. The effect of porosity on performance is also investigated for various cell shapes. The effect of important operating parameters, such as rotor speed, aspect ratio, and mass flow rate of fluids on the effectiveness, as well as pressure drop is investigated for a quad-sector rotary air preheater. The study ends with a comparative performance analysis between bi-, tri-, and quad-sector rotary air preheaters. The performance of quad-sector air preheater is found to be better than other two preheaters in terms of effectiveness, whereas its pressure drop is maximum.

Melting performance enhancement of febro-hydrodynamic carreau non-Newtonian PCM in porous media: A geometrical evaluation

In this paper melting of a carreau non-Newtonian PCM in the space between two concentric horizontal tubes, which is partially filled with porous material with different shapes but same area, is investigated numerically. A magnetic source is located in the center of the geometry for melting process of PCM to occur in the presence of ferro-hydrodynamic effects. Porous material is made of Cu that covers the cross-section of the inner tube. In addition, the space between inner and outer tubes is saturated with paraffin-wax PCM. Flow of melted paraffin-wax is considered as a Carreau non-Newtonian, laminar and incompressible flow with viscous dissipation that is evaluated in a specific time interval. Boussinesq approximation is valid for the PCM. Also local thermal equilibrium condition is assumed between the porous and the PCM. Galerkin finite element method has been utilized to solve the problem. Results showed that melting rate is higher for the third model in comparison other models. Also effects of the magnetic number depends on the shape of the porous medium. Therefore, that increase in the magnetic number, increasingly enhances the progress of the melting front in the second case. Moreover, effects of Carreau index, Stefan number, and porosity on the melting process are studied.

Analysis of heat transfer using Local thermal non‐equilibrium conditions for a non‐Newtonian fluid flow containing Ti6Al4V and AA7075 nanoparticles in a porous media

AbstractThe accurate forecasting of thermal processes is one of the primary concerns of those working in the area of heat transfer as well as those in the energy research community. The present investigation makes use of a simplified mathematical model as an illustration in order to investigate the properties of heat transport under the lack of local thermal equilibrium conditions. The LTNE model results in two distinct primary thermal gradients, one for the fluid phase and another for the solid phase. The non‐Newtonian fluid flow containing Ti6Al4V and AA7075 nanoparticles with a base fluid sodium alginate over a stretching sheet in a porous media with magnetic effect is studied here. The shooting approach is used to transform the resultant equations of boundary value problems into initial value problems, which are subsequently solved using Runge–Kutta–Fehlberg 45 process. The impact of pertinent parameters on the involved fields have been discussed graphically. Results reveal that the increase in porosity and magnetic parameters value decreases velocity and increases thermal performance. An upsurge in inter‐phase heat transfer parameter increases the heat transport rate of solid phase but, decreases the liquid phase heat transport rate.

Integral Transform Solution of Porous Medium Models for Heat Sinks Subject to Periodic Heat Loads

Abstract Analysis of the energy transport in thermal microdevices modeled as a porous medium under periodic heat loads is conducted using integral transforms. Coupled eigenvalue problems are employed and a single set of coupled ordinary differential equations conveying all information on the temperature fields in both the solid and fluid phases are reached, allowing for a relatively straightforward treatment of the local thermal nonequilibrium (LTNE) formulation. This characteristic proved instrumental in finding out that the local thermal equilibrium (LTE) hypothesis is inadequate for unsteady problems. The solid phase is shown to have a significant role on inducing thermal lag in the fluid, which may be severe, depending on the dimensions and operational conditions. In general, devices comprised of larger fractions of solid material and with poorer heat transfer characteristics are more prone to having larger thermal lag along them. These conclusions may be relevant to a wide range of applications such as electronics cooling, battery thermal management, solar energy harvesting, among others.

Validation of ablation model for polyethylene using pulsed x-ray and proton exposures

The surface erosion of polyethylene is interrogated using pulsed x rays at the Z Machine (Sandia National Laboratories) and with proton beams at the Gamble II generator (Naval Research Laboratory) to validate a coupled model for volumetric thermal ablation, photoionization, finite-rate decomposition, and molecular recombination of radicals. The intense radiation pulses (up to ∼1014W/m2 over tens of nanoseconds) are used to generate one-dimensional vapor flows with low ionization fractions and a simplified geometry compared to typical laser ablation, allowing for evaluation of the model under local thermal equilibrium conditions. Areal momentum carried by the ensuing uniaxial hydrodynamic shock is used to indicate the extent of ablation. The threshold fluence for ablation is found to be in close correspondence with the bulk melt transition, and reasonable agreement with the model is obtained for peak temperatures in polyethylene up to 5500 K and heating rates up to 1011K/s where thermal decomposition reactions are also active.

Laser induced breakdown spectroscopy of aluminum incorporated with metallic nanoparticles

Laser-Induced Breakdown Spectroscopy is a promising spectroscopic technique with a vast spectrum of applications in fields concerned with identification and detection of elements. But it faces some limitations due to self-absorption, noise due to matrix effect and line broadening resulting in low emission signal. This research proposes LIBS signal enhancement by incorporation of metal nanoparticles (Cu, Mg, Au) on Al surface and compares their effect. The successful optical emissions enhancement is achieved as the emission intensities of Al- and Na- lines of three coated samples are compared with those of uncoated Al. The Electron Temperature has been evaluated by Boltzmann plot and an increase in Electron Temperature has been observed with the incorporation of nanoparticles to the aluminum surface as compared to the untreated aluminum, due to more plasma emissions. The Electron Number Density of the aluminum plasma did not have much effect with the incorporation of Nanoparticles. The Local Thermal Equilibrium condition has been satisfied and checked by Mc Whirter’s Criterion. The incorporation of metal nanoparticles can be declared as an effective method not only for LIBS signal enhancement but also better detection of trace elements which were not observed without the use of Nanoparticles.

Transpiration cooling of high pressure turbine vane with optimized porosity distribution

The additive manufacturing allows to fabricate porous structures with elevated mechanical strength, which enable designers to apply transpiration cooling to gas turbine blades. However, most transpiration cooling investigations are carried out using the flat plate geometry. To understand transpiration cooling of a turbine blade better, it is necessary to conduct the investigations using real turbine blade geometry. The current study focuses on the numerical investigation and optimization of a transpiration cooled C3X vane. The C3X vane is designed with multiple porous zones whose porosities are in a range from 0.2 to 0.7. The Darcy-Brinkman-Forchheimer equation and the local thermal equilibrium model are used to simulate the flow and heat transfer in the porous zones. A surrogate-based optimization framework incorporating the Kriging method and the genetic algorithm is built to optimize the transpiration cooling performance. The numerical approach is carefully validated with the available experimental data, and then the optimization method is validated with the numerical results. The optimal designs under injection ratios of 1.2% and 2.0% are obtained, and the underlying flow structure and heat transfer physics are revealed. The results show that for an optimal transpiration cooled turbine vane design, large porosity should be applied first to the leading edge and the pressure side just downstream of the leading edge. The coolant issuing from the leading edge and the upstream pressure side convects downstream, forming an effective transpiration cooling film. The transpiration cooling film adheres well to the pressure surface, while it decays quickly on the suction surface. The temperature non-uniformity of the coolant in the plenum and the suction side endwall vortices can lead to the non-uniform surface temperature distribution along the vane height.

Multiplicity-Momentum Correlations in Relativistic Nuclear Collisions

We introduce a two-particle correlation observable that measures multiplicity-momentum correlations and may facilitate an estimate of the level of equilibration of the medium created in relativistic nuclear collisions. We calculate that multiplicity-momentum correlations should vanish in equilibrium in the Grand Canonical Ensemble, therefore non-zero measured values may indicate that the system has not reached local thermal equilibrium. Information about the level of equilibration of the system is important because many state-of-the-art models assume local equilibration either directly or through the use of an equation of state that makes this assumption. We make estimates of multiplicity-momentum correlations using PYTHIA/Angantyr and find positive values comparable in magnitude to well-measured correlations of transverse momentum fluctuations. We then outline a formalism that can use multiplicity-momentum correlations and correlations of transverse momentum fluctuations to quantify the level of partial thermalization of the system.

Effect of Magnetic Field Dependent Viscosity on Darcy-Brinkman Ferroconvection with Second Sound

The problem of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law and MFD viscosity is investigated by the method of small perturbation. The fluid motion is described using the Brinkman model. It is assumed that the fluid and solid matrices are in local thermal equilibrium. For simplified boundary conditions, the eigenvalue problem is solved exactly, and closed form solutions for stationary instability are obtained. Magnetic forces and second sound were found to enhance the beginning of Brinkman ferroconvection. However, ferroconvection is hampered when the porous parameters are increased. The results show that MFD viscosity inhibits the beginning of Darcy-Brinkman ferroconvection and that MFD viscosity stabilizing effect is decreased when the magnetic Rayleigh number is significant. Furthermore, it is demonstrated that oscillatory instability arises before stationary instability, assuming that the Prandtl and Cattaneo numbers are sufficiently large.

Numerical study of shell and tube latent thermal energy storage partially filled with metal foam and corrugated internal tube with external heat losses

In the present work, a vertical shell and tube Latent Heat Thermal Energy Storage System is analyzed. The cylinder is filled with phase change material and parts of metal foam. The inner face of the cylinder is corrugated, and it is assumed a constant temperature over the melting temperature of the paraffin wax to simulate the heat transfer. The external surface loses heat to the outside and the top and bottom surfaces are adiabatic. Paraffin wax is used as phase change material that melts over a range of temperatures and has a high latent heat of fusion. The thermal conductivity of the phase change material is low and due to this, it is enhanced with metal foam. In this numerical simulation, it is used the aluminum foam. Enthalpy-porosity theory is used to simulate the phase transition process, and the Local Thermal Equilibrium and Darcy-Forchheimer models are used to examine heat transport between the paraffin and the metal foam. Using the commercial code Ansys-Fluent, the governing equations’ solutions are calculated. In the paper, it is considered different conductivity variations on the external wall and the distinct filling ratio of metal foam. The melting time, enthalpy stored, and energy loss from the numerical simulations of the LHTESS charging phase are provided as a function of time and evaluated.

Numerical simulation of thermochemical non-equilibrium flow-field characteristics around a hypersonic atmospheric reentry vehicle

A multi-physics thermochemical non-equilibrium model is established to study the flow characteristics of the plasma sheath around an atmospheric reentry demonstrator. This model includes the tight coupling of Navier–Stokes equations, 54 chemical reactions of air, and a four-temperature model. The processes of dissociation, ionization, and the internal energy exchanges of air components were successfully simulated during aerodynamic heating of the reentry vehicle. The distributions of plasma sheath temperature, the molar fraction of air species, stagnation pressure, surface pressure, and electron number density around the reentry vehicle were obtained at different flight altitudes. Additionally, to validate the numerical model developed in this study, the flow characteristics of the Radio Attenuation Measurement-C-II (RAM-C-II) vehicle are also simulated and then compared with corresponding experimental data. They show good consistency in general. It is found that when the vehicle is at a high flight altitude, there is a strong thermochemical non-equilibrium phenomenon around the vehicle. However, the plasma sheath tends to be in local thermal equilibrium at a low flight altitude. The distance from the shock layer to the stagnation point decreases with a decrease in reentry altitude from 90 to 65 km but increases with a decrease from 65 to 40 km. The electron number density in the shock layer is maximum. The distribution of the electron number density in the wake region differs significantly at different flight altitudes.

Numerical investigation on a thermoelectric generator in an exhaust automotive line with convergent metal foam

In the present paper, a 2-D steady state convective heat transfer problem in a convergent channel partially filled with aluminum foam with an external thermoelectric generator (TEG) component is numerically solved. The channel is characterized by a length equal to 272 mm and by a height of 60 mm. The TEG has the dimensions equal to 65 mm and 8.5 mm. The investigation is executed considering the Darcy-Forchheimer-Brinkman assumption and the local thermal equilibrium (LTE) hypothesis for modelling the metal foam. The exhaust gas is considered to have the same properties of the air in corresponding to the assigned temperature of the upper surface of the thermoelectric generator. The thermophysical properties are temperature independent and the thermoelectric generator is studied as a solid with an internal energy generation. The governing equations for gas, porous media and thermoelectric generator are solved by finite volume method using the Ansys-Fluent code. Different configurations of convergent metal foam are analyzed. The aluminum foams are characterized by 5 PPI and porosity equal to 0.905, 0.946 and 0.971. Results are presented in terms of temperature distributions, thermoelectric efficiency, power density, and the Energy Performance Ratio (EPR) for different gas flow rates and aluminum foam configurations. Furthermore, a comparison with the use of the same foam samples characterized by a constant section is showed for the same system. From the comparison, it is possible to deduce how the configuration with convergent channel has a more uniform temperature profile than the geometry with constant section.

Thermal control of lithium-ion batteries for electric cars by metal foam partially filled with Phase Change Material

A viable solution to environmental problems related to pollutant emissions from internal combustion engine vehicles is electric cars. The main problem with electric vehicles, which also limits their widespread use, is due to lithium batteries and in particular their thermal control. Thermal control of lithium batteries is an extremely topical issue since it is not only related to the performance of the vehicles on which they are mounted, but also to the safety of the vehicles and drivers. For this purpose, both factors internal to the battery itself and external causes such as environmental conditions must be considered.In this work, a thermal control system based on metal foams partially filled by the phase change material (PCM) was numerically investigated as a possible application for cooling lithium batteries. For this purpose, a two-dimensional numerical model was constructed in which the PCM partially fills the metal foam. The finite volume method used through the ANSYS Fluent code was used for the governing equations, which are written assuming local thermal equilibrium. Several cases were simulated for different values of the external convective heat transfer coefficient. The results obtained, are reported in terms of temperatures and liquid fractions. Comparisons with partially filled and totally filled cases by PCM in the thermal control system are reported to show the advantage obtained, in terms of thermal control, with a composite system of metal foam and PCM.