Local Thermal Non-equilibrium Model Research Articles

Effect of heat source on forced convection in a partially-filled porous channel under LTNE condition

An analysis of forced convection is presented within a channel partially filled by porous medium inserted in the core, with the inclusion of internal heat source in fluid and solid phases. By employing Brinkman extended Darcy model and local thermal non-equilibrium (LTNE) model in porous region, exact solutions are obtained including fluid velocity, solid and fluid temperatures and Nusselt number, and pertinent parameters' effects on heat transfer enhancement are performed. In addition, the solutions are also compared to that by applying the local thermal equilibrium (LTE) assumption and the LTE validity is discussed. The results find that for a partially-filled porous channel, existed heat source terms can intensify the occurrence of the singularity in Nusselt number, especially with the variation of porous filling ratio more than one singularity points can be observed under both LTE and LTNE conditions. In addition, even if the singularity exists the Nusselt number can reach to LTE condition at a high Biot number (Bi) or at a very high solid to fluid thermal conductivity ratio (K), and at a small K the LTE also holds with the fluid heat source only. Overall, partially-filled porous systems with internal heat source have more rich thermal characteristics.

Natural convection of nanoencapsulated phase change suspensions inside a local thermal non-equilibrium porous annulus

In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle’s core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ e ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process.

Experimental based numerical approach for determination of volumetric heat transfer coefficients of modified graphite foams

Graphite-based porous materials are emerging as attractive alternatives to metals for use as heat dissipation elements in thermal management applications. While having several desirable features such as high thermal conductivity and low density, graphite foam heat sinks also tend to have low permeability that can limit transport of working fluid within the component and result in inefficient heat transfer. In order to improve their heat dissipation performance, graphite foams can be modified by channels drilled in various arrangements. However, the heat transfer characteristics of such modified graphite foams are not well characterized. In order to address this problem, we report novel empirical correlations for graphite foams modified in a specific configuration where circular channels with 2 mm diameter are drilled in graphite foam along the flow direction in a staggered arrangement. Then, volumetric heat transfer coefficients between the modified graphite foam and a stream of air are obtained by using transient single-blow technique (TSBT). The transient one-dimensional local thermal nonequilibrium (LTNE) model is employed for determination of the volumetric heat transfer coefficient from experimentally obtained data. Nine different modified graphite foam samples of various L/H ratios are studied in experiments and an empirical correlation of the form Nuv = CRea for each sample is derived. Empirical correlations for three different sample lengths (L = 27 mm, 52 mm, 76 mm) at a fixed height are also developed in the form of Nuv = CRea(L/H)b . The novel empirical correlations in question are valid for the Reynolds (Re) number varying from approximately 1000 to 10000. Results show that Nuv generally increases with the increasing value of Re and L at a fixed value of H and the uncertainties associated with Re and Nuv are evaluated to be less than 1.3% and 3.6%, respectively. Consequently, we anticipate that the proposed correlations will be useful in reliable design of a new generation of electronic devices.

Effects of bluff-body on the thermal performance of micro thermophotovoltaic system based on porous media combustion

To improve thermophotovoltaic system efficiency, a porous media combustor with a bluff-body as the flame holder was proposed. A two-dimensional numerical simulation of premixed hydrogen/air combustion inside a planar porous media channel with the local thermal non-equilibrium model was conducted. Effects of the bluff-body flame holder on mean wall temperature and system efficiency were examined. By inserting the bluff-body, the blowout limits of the planar porous media combustor for ϕ = 0.6, 0.8, 1.0, 1.2 are increased by 33%, 19%, 12%, 20%, respectively. Numerical results show that the flame stabilization is dominated by flow and heat recirculation. Further analysis reveals the mechanism of heat transfer on flame stabilization due to three heat recirculation paths. Considering the view factor and the external quantum efficiency, the system efficiency with the bluff-body is increased by 14.72% as compared to the one without the bluff-body at ϕ = 0.8, vin = 4 m/s.

Numerical study on natural convection of Ag–MgO hybrid/water nanofluid inside a porous enclosure: A local thermal non-equilibrium model

This paper investigates the natural convection of Ag-MgO/water nanofluids within a porous enclosure using a Local Thermal Non-Equilibrium (LTNE) model. The Darcy model is applied to simulate the flow dynamics throughout the porous medium. Using non-dimensional parameters, the dimensionless form of the prevailing equations has been derived. Finally, the Galerkin finite element method is utilized to solve governing equations using a non-uniform structured grid, numerically. The key parameters of this study are Rayleigh number (10 ≤ Ra ≤ 1000), porosity (0.1 ≤ ε ≤ 0.9), nanoparticles volume fraction (0 ≤ φ ≤ 0.02), interface convective heat transfer coefficient (1 ≤ H ≤ 1000), and the thermal conductivity ratio of two porous phases (1 ≤ γ ≤ 10). It is indicated that dispersing Ag–MgO hybrid nanoparticles in the water strongly decreases the transport of heat through two phases of the porous enclosure. For glass ball and aluminum foam, by increasing the H from 1 to 1000, Qhnf would be 1.33 and 5.85 times, respectively, at φ = 2%.

SOLAR HYDROGEN PRODUCTION BY THERMOCHEMICAL REACTION: DEVELOPMENT OF A PACKED-BED REACTOR

Solar water splitting is a promising process for the storage and conversion of sunlight power into clean-burning hydrogen gas, this paper presents a CFD analysis of hydrogen production via a proposed packed bed thermochemical receiver/reactor system. The idea of this study is the use of packed bed of spherical ceramic particles coated with active redox ferrite materials. The first step is an endothermic reaction, nickel ferrite (NiFe2O4) dissociate thermally into nickel oxide (NiO), ferrous oxide (FeO) and oxygen at 1473 K, this reaction take place under 2 KW concentrated solar energy. The second is the hydrolysis step at 1073 K to form hydrogen and NiFe2O4, the latter is recycled to the first step for a new production cycle. The CFD code solves the momentum, energy and species transport equations. The temperature fields of the reactor solid & the fluid phases were attained using the local thermal non-equilibrium model (LTNE). The LTNE model sources terms were computed through the user-defined functions to couple the energy equations of the fluid phase and solid phase. The complete model was used to analyse numerically the reaction through the packed bed in order to predict the thermal behavior under different conditions (inlet velocity, packing arrangement and solar concentrated flux).

Effects of multilayer porous ceramics on thermochemical energy conversion and storage efficiency in solar dry reforming of methane reactor

In solar thermochemical systems, the utilization of porous ceramics plays an important role in the enhancement of heat transfer and optimization of reaction conditions, thereby effectively improving the energy conversion and storage efficiency. Compared with the common filling pattern of one-layer porous ceramic (1-LPC), novel changes in the thermal and chemical characteristics can be induced using multilayer porous ceramics (MPCs). To determine whether MPCs have advantages over 1-LPC in solar thermochemical applications, a numerical model was established in this study by combining computational fluid dynamics with dry reforming of methane reaction kinetics. The local thermal non-equilibrium model coupled with the P1 approximation was adopted to solve the solar radiation diffusion and convective heat transfer problems, while the non-Darcy flow effect was considered to predict the momentum dissipation resulting from the porous ceramics. Based on this, the effects of layer number, gap position, porosity, and cell size were investigated to find the optimal application strategies for MPCs. The simulation results indicate that a large temperature gradient in the first gap between two layers of MPCs can usually reduce the wall heat loss and improve the thermal efficiency, but has no universal effect on improving the solar-to-fuel efficiency. Under the current operational conditions, although improvement of the solar-to-fuel efficiency by approximately 0.03%–2.43% can be obtained using a 4-LPC in the cases of high porosities (ϕ⩾0.86) and large mean cell sizes (dp⩾7mm), 1-LPC remains the most reliable filling pattern with a wider range of applications and stable performance.

Thermal instability of an Oldroyd-B fluid-saturated porous layer: implications of pressure gradient and LTNE temperatures

A local thermal nonequilibrium model is used to investigate the instability of an Oldroyd-B fluid-saturated horizontal layer of porous medium by imposing a constant pressure gradient in the horizontal direction and maintaining a constant temperature difference between the boundaries. The flow in the porous medium is studied by a modified Darcy–Oldroyd-B model. The problem has been transformed into a generalized complex eigenvalue problem and solved numerically by utilizing the Galerkin method. The pressure gradient and/or the viscoelasticity of the fluid instill oscillatory instability. The influence of constant horizontal pressure gradient is to hasten the onset of oscillatory convection: a result of contrast noticed in Newtonian fluids. The impact of constant horizontal pressure gradient is to increase the critical frequency of oscillations and to increase the size of convection cells. Besides, the effect of viscoelastic parameters on the oscillatory onset diminishes in the presence of pressure gradient. For the Maxwell fluid, instability sets in earlier compared to an Oldroyd-B fluid. The numerical results obtained under the limiting case are shown to be in excellent agreement with the published ones.

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

AbstractBy adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study.

Battery thermal management with thermal energy storage composites of PCM, metal foam, fin and nanoparticle

This study aims to analyze the thermal performance of the passive thermal management system (TMS) of the 18,650 lithium-ion battery with application of phase change materials (PCM). To improve performance of TMS, nanoparticles, fins and porous metal foam are used beside the PCM, and their effects on the system performance are compared. The local thermal non-equilibrium (LTNE) model and non-Darcy law are considered to simulate the nano-PCM melting inside the porous media. Numerical results are validated through previously published experimental data and results are presented for two, 4.6 W and 9.2 W, heat generation rates. Sole effects of adding nanoparticles to the PCM, utilizing different numbers of fins, and application of the metal foam on the system performance are scrutinized. Results indicated that the porous-PCM composition performs more efficiently than the nano-PCM and the fin-PCM ones. In addition, ΔTavg, battery parameter is introduced and its variations are analyzed to judge about the effect of each technique to reduce the battery mean temperature. Using the porous-PCM led to 4–6 K reduction in the battery mean temperature with respect to the pure PCM. Moreover, for the porous-PCM composition a delay is observed in the PCM melting initiation time that can adversely affect the performance of battery TMS.

Impact of side injection on heat removal from truncated conical heat-generating porous bed: thermal non-equilibrium approach

Effective removal of heat from the heat-generating porous bed, particularly in a confined space, is essential due to its implications on thermal management and system safety. The safety aspect becomes particularly important during post-accident heat removal from decay heat-generating debris in nuclear reactors, as well as thermal management of self-igniting coal stockpiles. In spite of detailed research on thermal convection through porous media, only a handful of studies have considered mixed convective heat transport involving heat-generating porous bed along with external fluid injection. The situation, however, demands an in-depth analysis due to the associated practical implications. The present work addresses one cooling method providing side injection of cold fluid and assuming a typical conical heat-generating porous bed located centrally within a fluid-filled cylindrical enclosure. The study is carried out in a general way to suit other applications. The dimensionless governing equations, along with the boundary conditions in a two-dimensional coordinate system, are solved numerically assuming laminar and incompressible flow along with the Boussinesq approximation. The analysis is carried utilizing the local thermal non-equilibrium model within the porous bed. Injection of cold fluid can markedly affect the convective heat transport rate. Porous media permeability considerably influences the flow mechanism. The major findings of this study can be very useful in improving the management of thermal energy removal from self-igniting coal stockpiles, grain storages, porous debris, etc. Heat transport intensification from heat-generating porous bed is analyzed by injecting coolant through the sidewall and considering liquid water as the working medium. The impacts of pertinent parameters on the thermal convection characteristics are illustrated using the average Nusselt number and energy flux vectors.

Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor

To improve flammability and radiation efficiency, a divergent porous media combustor is proposed and numerically studied. The local thermal non-equilibrium model is used to consider the temperature difference between gas and solid matrix. Effects of equivalence ratio, the wall thermal conductivity, solid matrix thermal conductivity, and divergent ratio on combustion characteristics, radiation efficiency, and flammability limits are studied. The results show that the divergent channel extends the blowout limit by 186% and obtains a maximum radiation efficiency of 29.3%, increased by 70% compared with the straight channel. A smaller wall thermal conductivity is recommended considering the flammability range and radiation efficiency. A careful choice of solid matrix thermal conductivity and the divergent ratio is suggested to balance their opposing effects on the radiation efficiency and the flammability.

Numerical study of laminar pulsed impinging jet on the metallic foam blocks using the local thermal non-equilibrium model

In this study, thermal performance of an impingement jet with the presence of porous block is numerically investigated. The study is comprised of two main parts. At first, a parametric study is conducted on the steady impingement jet with porous block. Later, the effect of porous block is assessed on the pulsative impingement jet. The effect of different pulsation frequencies and amplitudes is analyzed on the heat transfer between the jet and porous block. In order to model the thermal performance, the local thermal non-equilibrium model is applied to the system. An entropy generation study was also conducted in order to investigate the system’s performance from second law of thermodynamics point of view. In addition to the mentioned studies, by utilizing the energy density flux vector, different regimes of heat transfer in various cases are demonstrated and some of the trends obtained in parametric study are justified. The results suggest that porous block can change the Nusselt number distribution on the target plate. A more flattened Nusselt number distribution is observed with the presence of porous blocks. While lower frequencies and amplitudes of pulsation do not affect the thermal performance of the jet, higher ones have a moderate effect on the heat transfer rate of the impinging jet.

Impact of local thermal non-equilibrium on temporal thermo-hydro-mechanical processes in low permeable porous media

The thermo-hydraulic-mechanical (THM) response of low permeable media is of crucial significance in thermal fracturing for production of unconventional shale oil, enhanced geothermal systems, and waste disposal. During such processes, pore pressures and stresses change in a spatiotemporal manner due to hydraulic and thermal loadings. From the viewpoint of the energy balance equation, the available theoretical studies can be classified as local thermal equilibrium (LTE), and local thermal non-equilibrium (LTNE) models. LTE models consider identical temperature for different phase of the porous system. LTNE models allow different temperature variations in solid and fluid phases of a porous medium. Current LTNE studies are weakly-coupled – not incorporating thermo-osmosis. This paper presents novel coupled LTNE thermo-poroelastic solutions in a transversely isotropic saturated porous medium, incorporating thermo- osmosis effect. Solutions are obtained for permeable and impermeable boundaries. Thermo-osmosis is found to have a very different effect in case of LTNE versus LTE, resulting in a fundamentally different THM response. LTNE effect analysis reveals different THM responses under different heat transfer properties at the solid-fluid interface in low permeable strata.

Numerical Simulation of Effects of Bioheat Transfer Characteristics of Malignant Melanoma on Thermal Conductivity Measurements.

In our previous study, we successfully detected a difference in the effective thermal conductivity between an invasive melanoma lesion and healthy skin, through clinical experiments conducted on melanoma patients. We found that the effective thermal conductivity of the lesions correlated with the tumor thickness, suggesting that it may be correlated with the prognostic risk of melanoma. However, the bioheat transfer mechanisms of the correlation remained unknown. The aim of this study was to numerically investigate the effects of the bioheat transfer characteristics of malignant melanoma on thermal conductivity measurements and explore the cause of the difference in the effective thermal conductivity between lesions and healthy skin. We used two different bioheat transfer models, the Pennes model and local thermal nonequilibrium model, and investigated the cause of the aforementioned differences by varying the bioheat transfer parameters associated with the thermophysical properties and blood flow of a tumor. The calculation results indicated that the contribution of the blood flow can be dominant in a measurement comprising the use of a guard-heated thermistor probe. Therefore, we found that it is necessary to take into consideration the contribution of the convective term to the effective thermal conductivity of the lesion in order to explain the clinical data of a Stage IV invasive melanoma.

Numerical investigation of two-phase flow in a horizontal porous evaporator with localised heating using non-Darcian flow and two equations model

In this article, a new mathematical model, based on the modified enthalpy formulation of Two-Phase Mixture Model (TPMM), is developed by considering non-Darcy flow and Local Thermal Non-Equilibrium (LTNE) conditions to describe numerically the two-dimensional problems of the complete evaporation process inside an asymmetrically heated porous evaporator. The governing equations have been discretised using Finite Volume Method (FVM) on a fixed non-staggered grid layout. The in-house code has been validated against experimental data and the results show good agreement between them. Three different models have been employed for the partitioning of the wall heat flux. Only the effect of the heat flux has been analysed, while all other parameters and properties have been kept fixed during the present investigation. The numerical simulations indicated that the locally high heat flux significantly influences the working fluid flow performances, and lead to extend the superheated vapour region towards the exit of the evaporator. The results also show that the two-phase zone significantly expanded in the axial direction and does not occupy a large portion inside the channel due to the energy transport through the two-phase region is significantly higher in the flow direction as compared to the transverse direction, caused by the decrease in the effective diffusion coefficient in this region and higher axial velocity. Numerical analysis reveal that the different models for the partitioning of the wall heat flux have almost no influence on the overall predictions, except in the vicinity of the wall. The results clearly demonstrate that the numerical simulations with the modified h-formulation by considering non-Darcy law and LTNE model are indispensable for the problem of complete evaporation process, particularly under the high both heat flux and inlet velocity conditions.

Magneto convection for a nanofluid layer with local thermal non-equilibrium (LTNE) model: A realistic approach

Linear thermal instability of a horizontal nanofluid layer considering thermally non-equilibrium effect by applying magnetic field is investigated. Analysis is done with more practical boundary conditions on volume fraction of nanoparticles i.e. zero nanoparticle flux is considered across free-free boundaries. A two-temperature model has been introduced in order to consider the influence of thermally non-equilibrium phases (fluid and particle). Local thermal non-equilibrium (LTNE) means that there is a difference in temperature between the two phases that cannot be neglected. LTNE model has acquainted three parameters modified thermal diffusivity ratio, modified thermal capacity ratio and Nield number in addition to the Chandrasekhar number which was introduced due to magnetic field. Results are interpreted analytically as well as graphically. It is found that system stability enhances by enhancing the values of Chandrasekhar number, modified thermal diffusivity ratio, modified thermal capacity ratio and falls with the rise in Nield number, Lewis number, concentration Rayleigh number and modified diffusivity ratio. Critical wave number tends to its local thermal equilibrium (LTE) when there is no interaction among the particle and fluid phases and also when both the phases act as a single phase due to having identical temperatures. Further, critical values of two different nanomaterials (alumina and copper) immersed in base fluid water is compared. It is found that with in thermally non-equilibrium conditions among the phases along with revised boundary conditions copper–water nanofluid is having higher critical values (critical wave number as well as critical Rayleigh number) than alumina-water nanofluid in the presence of magnetic field. Thus, stability of copper nanomaterials is more pronounced as compared to alumina nanomaterials under the above said conditions.

LTNE effects on a nanofluid layer heated and soluted from below embedded by Darcy medium

Thermosolutal convection of a nanofluid layer which is heated underneath with local thermal non-equilibrium (LTNE) effects is investigated by applying one term Galerkin approach and Darcy model. A three-temperature model is applied for considering the impact of LTNE along with Brownian motion and thermophoretic effects to account for nanoparticles. With the addition of LTNE model embedded by porous medium four non-dimensional parameters have come into existence whereas due to the presence of solute two more parameters came into picture. Numerical computations are carried out with software Mathematica and it is observed that the destabilizing influence of nanoparticles is balanced with the stabilizing effect of solute to a large extent. Further effect of solute is to enhance the stability where as there is no significant variation in thermal Rayleigh number due to LTNE effects.

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

In the paper we make linear and non-linear stability analyses of Rayleigh–Benard convection in a Newtonian, nanoliquid-saturated porous medium using local thermal non-equilibrium model (LTNE). The LTNE assumption results in advanced onset of convection and increase in heat transport when compared to that of local thermal equilibrium assumption. Free–free and rigid–rigid, isothermal boundaries are considered for investigation. The Galerkin method is used to obtain the critical eigen value. The influence of inter-phase heat transfer coefficient, ratio of thermal conductivities, Brinkman number, porous parameter on the onset of convection as well as on heat transport has been presented graphically and discussed in detail. The effect of increasing the value of porosity modified thermal conductivities advances the onset of convection and enhances the amount of heat transport whereas the remaining parameters have an opposing influence on both onset of convection as well as heat transport.

Thermomechanical response of porous biological tissue based on local thermal non-equilibrium

Understanding of heat transfer and related thermomechanical interaction in biological tissue is very important to clinical applications. It is quite natural to treat the living tissue as a porous medium, such as the living tissue in the presence of blood. Based on a non-equilibrium heat transfer model, the thermomechanical response of porous biological tissue exposed to an instantaneous thermal shock is investigated in this work. The governing equations are established based on local thermal non-equilibrium model in the context of the generalized thermoelastic theory and solved by time-domain finite-element method. The effect of porosity coefficient on the thermal-mechanical response of the porous tissue is studied and illustrated graphically. Comparisons are made between the proposed results and those from the local thermal equilibrium models to reveal the difference of these two models in terms of thermoelastic response.