Local Thermal Non-equilibrium Research Articles

Analysis of Heat Flux Distribution during Brush Seal Rubbing Using CFD with Porous Media Approach

This paper discusses the question of heat flux distribution between bristle package and rotor during a rubbing event. A three-dimensional Computational Fluid Dynamics (3D CFD) model of the brush seal test rig installed at the Institute of Thermal Turbomachinery (ITS) was created. The bristle package is modelled as a porous medium with local non-thermal equilibrium. The model is used to numerically recalculate experimentally conducted rub tests on the ITS test rig. The experimentally determined total frictional power loss serves as an input parameter to the numerical calculation. By means of statistical evaluation methods, the ma in influences on the heat flux distribution and the maximum temperature in the frictional contact are determined. The heat conductivity of the rotor material, the heat transfer coefficients at the bristles and the rubbing surface were identified as the dominant factors.

Thermal Energy Discharging Performance of Metal Foam/Paraffin Composite Phase Change Material at Pore Scale

Abstract In this research, thermal energy discharging performance of metal foam/paraffin composite phase change material (MFPC) is investigated at pore scale through direct simulation. A thermal transport model is first developed for heat discharging of MFPC by incorporating the involved effects of solidification phase transition, foam structure, and paraffin volume shrinkage. With this model, the detailed phase interface evolutions, temperature fields, and heat flux distributions of MFPC are numerically obtained and analyzed. It is found that once phase change heat discharging of MFPC begins, the solidification front of paraffin quickly forms and extends along the foam skeleton, which results in remarkably extended thermal transport interface to release latent heat as well as improved spatial synergy in phase change. The effect of local thermal nonequilibrium between porous metal foam and paraffin proves to be intrinsic and significant, providing an efficient inner driving force for enhancing latent heat discharging within MFPC. The overall energy discharging performance of MFPC unit is remarkably improved as compared with pure paraffin unit, evidenced by a large enhancement in latent heat release rate (more than three times) with only small reduction (2.6%) in heat capacity. Simultaneously, it is found that the paraffin-air interface for MFPC unit descends much faster than that for pure paraffin unit due to accelerated volume shrinkage of solidified paraffin within metal foam, resulting in a threefold enhancement in thermally driven dynamic response rate. This study can help more deeply understanding the energy discharging performance of MFPC and providing fundamental guidance for its application in miniaturized thermal systems.

Pennes\u2019 bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation

The objective of this study was to compare three different heat transfer models for radiofrequency ablation of in vivo liver tissue using a cooled electrode and three different voltage levels. The comparison was between the simplest but less realistic Pennes’ equation and two porous media-based models, i.e. the Local Thermal Non-Equilibrium (LTNE) equations and Local Thermal Equilibrium (LTE) equation, both modified to take into account two-phase water vaporization (tissue and blood). Different blood volume fractions in liver were considered and the blood velocity was modeled to simulate a vascular network. Governing equations with the appropriate boundary conditions were solved with Comsol Multiphysics finite-element code. The results in terms of coagulation transverse diameters and temperature distributions at the end of the application showed significant differences, especially between Pennes and the modified LTNE and LTE models. The new modified porous media-based models covered the ranges found in the few in vivo experimental studies in the literature and they were closer to the published results with similar in vivo protocol. The outcomes highlight the importance of considering the three models in the future in order to improve thermal ablation protocols and devices and adapt the model to different organs and patient profiles.

A numerical investigation of heat transfer process in paraffin/ethylene-vinyl acetate/graphene aerogel ternary composite

• The heat transfer process of Pa/EVA/GA were predicted by VAM. • The two-temperature model was adopted. • GA significantly improved heat transfer performance of Pa. • EVA increased the viscosity of paraffin and accelerated heat transfer. Melting and solidification heat transfer characteristics of different paraffin/ethylene-vinyl acetate/graphene aerogel (Pa/EVA/GA) composites were predicted by the volume-averaged method (VAM). In parameter settings, Pa/EVA was treated as fluid, and GA was set to solid. The two-temperature model based on the assumption of local thermal nonequilibrium was adopted to solve the large difference in thermal conductivity between GA and Pa/EVA. The simulation results were validated by experimental data. The numerical results denoted that GA and EVA significantly improved heat transfer performance of Pa and reduced the melting/solidification time. The heat transfer of the composites was dominated by heat conduction, as the three-dimensional skeleton of GA and the high viscosity of EVA inhibited the natural convection of paraffin. Compared with Pa/EVA 0 /GA, Pa/EVA 5 /GA and Pa/EVA 10 /GA had a higher surface heat flux, decreased the velocity of paraffin, and had a more even temperature distribution.

A study of the natural convection of water-AA7075 nanoliquids in low-porosity cylindrical annuli using a local thermal non-equilibrium model

Natural convection in nanoliquid-saturated porous cylindrical annuli due to uniform heat and mass influxes from the solid cylinder and effluxes from the outer hollow cylinder is investigated analytically. The Darcy model and the modified version of the Buongiorno two-phase model are used, and local thermal non-equilibrium between the phases is assumed. A nanoliquid-saturated porous medium made up of glass balls with a dilute concentration of AA7075 alloy nanoparticles well-dispersed in water is considered. Out of three types of annuli considered, shallow annuli provide the best heat transport and tall annuli show the worst performance. The presence of a dilute concentration of nanoparticles significantly enhances the heat transport in the system. Of nine nanoparticle shapes considered, lamina-shaped nanoparticles enhance heat transport the most. Heat transport is enhanced in the case of heat-and-mass-driven convection compared to the case of purely heat-driven convection. The results for a rectangular enclosure are obtained as a particular case of the present study. Two asymptotic routes that take us to the results of thermal equilibrium are shown. The vanishing limit of the concentration Rayleigh number yields the result for a single-phase model. Results for the base-liquid-saturated porous medium form a limiting case of the present study. We conclude that a shallow cylindrical annulus saturated with water-AA7075 lamina-shaped alloy nanoparticles is best suited for heat transfer due to its high effective thermal conductivity in comparison with that of other shaped nanoparticles and a tall rectangular enclosure saturated by water is best suited for heat storage applications.

The Role and Effects of Thermal Radiation on the Non-equilibrium Heat Transfer in a Porous Filled Enclosure

In this paper, the temperature differential between the solid and liquid phases in considering of combined conduction-convection-radiation heat transfer in porous media is investigated. Simultaneous solution of the solid and fluid energy equations encompasses local thermal nonequilibrium, with volumetric radiative heat flux needed in the solid-phase energy equation. The two energy equations together with the radiative heat transfer equation are simultaneously solved using the Chebyshev spectral method. The influences of the Planck numbers, the optical thicknesses, the scattering albedos, and the emissivities of the bounding walls on the thermal behavior are investigated. The results show that: (1) When Pl increases above 20, the effect of radiation on the flow and thermal field can be ignored. (2) Changing ⌖L has a significant effect on the solid phase temperature while, the effect is little on the fluid phase temperature. (3) For ω = 1.0, the distribution of θS − θf seems to be centrally symmetric. (4) θS − θf are always positive except for εW = 1.0.

Cattaneo-LTNE Effects on the Stability of Brinkman Convection in an Anisotropic Porous Layer

The stability of Brinkman local thermal nonequilibrium anisotropic porous convection under the impact of Cattaneo law of heat conduction in solid is investigated. In the analysis, anisotropies in permeability and thermal (solid and fluid phases) conductivities are highlighted. Condition for stationary onset and oscillatory onset is obtained by carrying out linear instability analysis. A novel result is that the instability occurs through oscillatory mode against the stationary convection perceived in the absence of Cattaneo effect. The relative magnitudes of governing parameters on the initiation of oscillatory instability are delineated in detail. The thermal and mechanical anisotropies inflict stabilizing and destabilizing effects on the onset, respectively. The influence of mechanical anisotropy, thermal anisotropy of fluid, thermal relaxation time parameters and the Darcy number is to broaden the size of convection cells whereas thermal anisotropy of the solid and the Darcy-Prandtl number demonstrate a mixed behaviour. A first order amplitude equation is derived separately for steady and overstable modes by performing a weak nonlinear stability analysis using a modified multiscale method. Depending on the values of governing parameters, it is seen that the stationary mode bifurcates subcritically and supercritically, while the oscillatory mode always bifurcates supercritically.

Linear Stability on the Local Thermal Nonequilibrium Model of Mixed Convection Boundary Layer Flow over a Moving Wedge in a Porous Medium: Viscous Dissipation and Radiation Effects

Abstract This paper studies the local thermal nonequilibrium (LTNE) model for two-dimensional mixed convection boundary-layer flow over a wedge, which is embedded in a porous medium in the presence of radiation and viscous dissipation. It is considered that the temperature of the fluid and solid phases is not identical; hence, we require two energy equations: one for each phase. The motion of the mainstream and wedge is approximated by the power of distance from the leading boundary layer. The flow and heat transfer in the LTNE phase is governed by the coupled partial differential equations, which are then reduced to nonlinear ordinary differential equations via suitable similarity transformations. Numerical simulations show that when the interphase rate of heat transfer is large, the system attains the local thermal equilibrium (LTE) state and so is for porosity scaled conductivity. When LTNE is strong, the fluid phase reacts faster to the mainstream temperature than the corresponding solid phase. The state of LTE rather depends on radiation and viscous dissipation of the model. Further, numerical solutions successfully predicted the upper and lower branch solutions when the velocity ratio is varied. To assess which of these solutions is practically realizable, an asymptotic analysis on unsteady perturbations for a large time leading to linear stability needs to be performed. This shows that the upper branch solutions are always stable and practically realizable. The physical dynamics behind these results are discussed in detail.

An improved analytical model for heat flow in cancerous tumours to avoid thermal injuries during hyperthermia.

The present study highlights an analytical hybrid scheme consisted of a shift of variables and finite integral transform for analysing a local thermal non-equilibrium (LTNE) bioheat model. This model can have utilised to be a betterment of prediction of the temperature field in the localised hyperthermia therapy (LHT) for the treatment of cancer patients. As the hyperthermia treatment is only the application in living tissues, an appropriate initial condition for the therapeutic thermal response is proposed instead of a constant temperature taken in the previous studies based on the 1-D heat flow. The present analysis suggests the therapeutic exposure time of 7776.8s (2.16 h) with constant heat flux and the exposure time of 10969.9s (3.06 h) with a sinusoidal heat flux within the usual temperature range of the hyperthermia (in a combination of thermal ablation and medium temperature hyperthermia) to be more effective in the treatment protocol. The presented results show that fatal injuries (tissue trauma, thermal burn, etc.) of internal organs might be possible to avoid by the current therapeutic condition. Therefore, this study may nullify the adverse effect of the existing model with the constant heating and consequently, the repercussion of the several therapeutic variables is to estimate with the development of a thermal profile for the suitability of a therapeutic condition. On the other hand, the present study well matches with the published analysis in case of both the theoretical and experimental (live tissues of the pig due to unavailability of real-time data on the human body) studies and it found the maximum deviation of the thermal response as 2.26% and 2.66%, respectively.

Turbulent flow and heat transfer in a partially filled ventilated cavity using the local thermal non-equilibrium method

In this study, a thermal energy storage system is modeled as an axisymmetric ventilated cavity partially filled with a porous medium that is subject to turbulent flow. Local thermal non-equilibrium is considered to analyze the heat transport and the turbulent k−ε model is used to account for the high inlet flow velocities. Finite volume method is employed for discretization of the equations that are relaxed with the SIMPLE method. The investigation is concerned with the turbulence field, heat fluxes and pressure drop in the system relative to variations in Reynolds number (from 8.3 × 103 to 5 × 104), porosity (ϕ from 0.6 to 0.8) and Da number (from 4x10−5 to 4x10−7). Results indicate that porosity effects slight changes in the turbulence field while the temperatures increase significantly faster for higher porosity cases. Turbulence in higher porosity cases was lower, accompanying the increase in thermal efficiencies. Variations in Da number with fixed porosity showed that, for lower Da number, recirculation in the clear region increased while for higher Da number porous region turbulence increased. Also, higher Da decreased heat exchange between fluid and solid phases. Finally, an increase in thermal efficiency for lower Da number flows was followed by increased average turbulent kinetic energy and relative pressure drop.

Three-dimensional numerical investigation on melting performance of phase change material composited with copper foam in local thermal non-equilibrium containing an internal heater

This work aims to numerically study the 3D melting heat transfer of latent heat thermal energy storage (LHTES) systems with phase change material (PCM) embedded in copper foam inside an internal heated cubic cavity. The enthalpy-porosity method to model the phase change process is employed and the Darcy-Forchheimer law and local thermal non-equilibrium (LTNE) model are assumed for the metal foam. The numerical code of proposed model shows good agreement for copper foam composited PCM melting with carefully designed experiments. Special attentions are given to detect the effects of Rayleigh number (Ra), porosity (ε), Darcy number (Da) and heater size on evolvement of solid-liquid interface, temperature stratification and full melting. The results show that increasing Ra enhances convective heat transfer in the upper part of the porous cavity; though the completely melting time remains almost unchanged. For a fixed porosity, decrease of Da reduces the melting rate in the medium melting stage, and the temperature distribution of low Da is dominated by the heat conduction in porous media at the later stage, but Da shows a negligible effect on the complete melting time. For a fixed Da, increase of porosity decelerates the complete melting time. Apart from that, the heater size also plays an important role in the melting performance of composited PCM.

Heat transfer enhancement of laminar impinging slot jets by nanofluids and metal foams

A study on impinging slot jets in a confined channel filled with metal foam, saturated with nanofluids, and lower wall partially heated is numerically accomplished. The partially heated wall is at an assigned temperature and buoyancy effects are taken into consideration. A two-dimensional domain is analyzed considering the local thermal non-equilibrium for the metal foam and the single-phase model is assumed to simulate the nanofluids at assigned Rayleigh number for several Peclet numbers. The governing equation solutions are accomplished using the Ansys-Fluent code and simulations are carried out for aluminum foams with nanofluids, Al2O3/water based, as working fluids. Several porosity values, from 0.90 to about 0.97, for different pore density, pore per inches (PPI), from 5, to 40 PPI, are used. The volumetric concentrations change from 0% to 5% with a particle diameter of 30 nm. The distance between the slot jet outlet section and the lower heated surface is five times the slot jet width. The presented results point out that the dimensionless convective heat transfer coefficients increase with increase in values of Peclet number, and decrease with the volumetric concentration. It is noted that the surface heat transfer coefficient shows different behavior varying porosity for assigned Peclet and Rayleigh numbers. Some correlations for the average total Nusselt number in terms of porosity and volumetric concentration are proposed in quadratic forms for assigned pore density and Peclet number.

Local Thermal Nonequilibrium Natural Convection in a Cavity with Heat-Generating Porous Layer

Natural convection in a partially porous cavity with a heat generating source in the solid phase is studied numerically under a local thermal nonequilibrium condition. The right and left walls of the cavity are maintained at hot and cold temperatures, respectively. The horizontal walls are thermally insulated. The finite volume method and the semi-implicit method for pressure-linked equations (SIMPLER) algorithm are used to solve the conservation equations. The effects of relevant parameters, such as internal and external Rayleigh numbers , , interphase heat transfer coefficient , modified thermal conductivity ratio , and dimensionless porous layer thickness are discussed. The results revealed that at high values of the interphase heat transfer coefficient, the impact of an internal Rayleigh number on the dynamic and thermal fields decreases with an increase in the modified thermal conductivity ratio.

Thermal management of power electronics with liquid cooled metal foam heat sink

In this paper, a combined experimental and numerical study of liquid cooled aluminum foam (AF) heat sink applicable for high power electronics cooling was conducted. AF heat sinks with porosity (0.88) and pore densities (10 PPI and 20 PPI) are fabricated and the empty channel is employed for comparison. Experimental measurements were conducted subjected to non-Darcy flow regime. Numerical analysis was based on the Brinkman-Forchheimer extended Darcy momentum model, together with the energy equations of local thermal non-equilibrium (LTNE) and local thermal equilibrium (LTE) models. The permeability and inertia coefficient of the AF samples were correlated based on the measured pressure drop. New correlations of interfacial heat transfer coefficient between water and AF solid matrix were also determined. Numerically predicted local surface temperature and temperature field distributions were presented and validated with the experimental measurements. The results reveal that the permeability decreases and the inertial coefficient increases with increasing pore density. The thermal performance of AF heat sinks is appreciably superior to the empty channel, under a given flow rate, the Num of the AF heat sink can be 1.40–1.76 times of the empty channel. Heat transfer enhancement by 20 PPI foam is inappreciable, approximately 5%, compared to that of 10 PPI. The LTNE model demonstrates more accurate for predicting the spatial temperature distributions than the LTE model. The results also indicate that the non-equilibrium heat transfer phenomenon in water-cooled AF heat sink is not pronounced, and the non-equilibrium effect is declined with increasing velocity.

Metal foam/PCM melting evolution analysis: Orientation and morphology effects

Phase Change Materials (PCM) are promising materials for thermal energy storage systems. Since they present a relatively low thermal conductivity, they are often embedded in an open cell a metallic foam to enhance the overall thermal conductivity. In this paper, both experimental and numerical results on PCMs coupled with aluminum foams under different heat fluxes, porosities, number of Pores Per Inch (PPIs) and orientation are presented. The test cell is equipped with a Zincum Selenide window that allows to capture the whole temperature distribution by means of a IR camera. The melting front position in time is tracked by means of a MATLAB® algorithm based on IR camera images that are useful for a more robust tracking of melting front. Numerical simulations are performed with references to the porous media volume-averaged approach, under the assumption of local thermal non-equilibrium between the two phases. The most updated correlations for the porous media closing coefficients are taken from the literature. All the experiments are compared with numerical simulations, showing a very good agreement. After showing the effects of the different input parameters on melting front evolution, an analysis in terms of different convective heat losses to the environment and melting temperature range is presented to appreciate how these two variables affect the melting front position. Finally, total melting front evolution has been compared between experiments and simulations, showing a good agreement. This has been evaluated for different conditions, showing that a decrease in the porosity drastically reduces the melting time, while PPI has no relevant effect and small effects can be observed from orientation.

Analytical and Numerical Study on Thermally Developing Forced Convective Flow in a Channel Filled with a Highly Porous Medium Under Local Thermal Non-Equilibrium

An analytical and numerical study was made on thermally developing forced convective flow in a channel filled with a fluid-saturated porous medium, subject to constant heat flux, under local thermal non-equilibrium. The Brinkman-extended Darcy model was employed to investigate the combined effects of the Darcy number, Biot number, effective thermal conductivity ratio and Graetz number on the longitudinal thermal development in a channel filled with a highly porous medium. 3D convective regime maps were constructed for wide ranges of the parameters, using a 3D coordinate system based on the Biot, Darcy and Graetz number coordinates. The 3D convective regime maps proposed in this study enable one to identify the three distinctive thermal regions possible along the longitudinal coordinate in a channel, namely the entrance developing region, transition region and fully developed region, depending on the relative thicknesses of the fluid and solid thermal boundary layers. It has been found that the Darcy number strongly influences the heat transfer rate in the developing region, yielding a higher Nusselt number for a lower Darcy number, whereas both Biot number and the effective thermal conductivity ratio markedly influence the level of the fully developed Nusselt number. The heat transfer performance evaluation carried out under equal pumping power for the aluminum foam embedded channel saturated with air reveals that a substantial heat transfer argumentation is possible by filling the channel with an aluminum foam.

LTNE effects on binary nanofluid convection: A modified model

Double-diffusive convection problem for nanofluids is investigated under the effect of local thermal non-equilibrium (LTNE). A more realistic and effective modified model has been applied to consider the problem where volume fraction of nanoparticles is assumed to be invariable in primary state. Importance of the modified method lies in the fact that it considers both physical properties of nanoparticles i.e. density as well as conductivity for consideration of nanoparticle effects as compared to earlier models which were insensitive to the effects of conductivity of the nanoparticles. Three additional LTNE parameters have been introduced in the eigen value equation which play a remarkable role in the onset of nanofluid convection. To consider the impact of various parameters one term Gelerkin method is employed along with the use of Mathematica software for numerical computations. The LTNE parameters in the presence of solute significantly influence the critical wave number which was not true for LTE model.

A review on latest development in heat transfer through porous media in combination with nanofluids and wavy walls

Heat flow through porous media and different phenomenon in these media are studied widely in recent years due to their extraordinary applications in different fields of engineering, bio-engineering and energy systems etc. In this report, recent advances in the numerical investigation of completely or partial filled porous media alone or in combination with wavy walls and nanofluids/nanoparticles have been reviewed. The main emphasis of this is to review the theoretical and numerical aspects of the effect of position of porous insert, nanoparticle volume concentration and the amplitude of the waves associated with wavy channels on the Nusselt number, pressure drop, entropy generation and efficiency of heat transfer. The conditions which define the boundary for the use of LTE (Local thermal equilibrium) and LTNE (Local thermal nonequilibrium) equations for evaluation of the porous media have also been reviewed. The LTE equations were found to be appropriate for the systems in which the temperature different between the solid and fluid phase is very small whereas, if the temperature difference between the two is large, then only LTNE can be employed. The porous media along with wavy walls and nanofluid combinations was found to exhibit better results in terms of Nusselt number and heat transfer efficiency but to obtain bets results, minimum amplitude in case of wavy walls and volume concentration of nanoparticle concentration should be optimized.

Numerical investigation on latent thermal energy storage in shell and corrugated internal tube with PCM and metal foam

A numerical investigation on Latent Heat Thermal Energy Storage System (LHTESS) based on an aluminum foam totally filled with phase change material (PCM) is accomplished. The PCM used is a pure paraffin wax with melting over a range of temperature and a high latent heat of fusion. The LHTESS geometry under investigation is a vertical shell and tube. The corrugated internal surface of the hollow cylinder is assumed at a constant temperature above the PCM melting temperature. The other external surfaces are assumed adiabatic. The paraffin wax phase change process is modelled with the enthalpy-porosity theory, while the metal foam is considered as a porous media obeying to the Darcy-Forchheimer law. Local thermal non-equilibrium (LTNE) model is assumed to analyze the heat transfer in the metal foam. The governing equations are solved employing the Ansys-Fluent code. The numerical simulations results, reported as a function of time, and concerning the LHTESS charging phase, are compared in terms of melting time, average temperature and energy storage rate. The corrugated internal surface effect is analyzed with respect to the wavelength and wave amplitude of the corrugation.

Advanced thermal lattice Boltzmann method for the simulation of latent heat thermal energy in a porous storage unit

The current research expounds numerical investigation of key parameters effects, namely porosity ( ε= 0.4, 0.6, 0.7 and 0.8), Reynolds number (Re = 100, 200, 400 and 600) and Eckert number (Ec= 0, 1, 5 and 10) on the forced convective laminar flow and heat transfer through a horizontal porous channel filled with a metal foam structure impregnated with paraffin as a phase change material (PCM). The Darcy-Brinkman-Forchheimer model under the local thermal non-equilibrium (LTNE) condition is deemed at the representative elementary volume (REV) scale. The fully coupled equations of Navier-Stokes, Poisson’s equation, energy equations, and continuity equation were handled numerically via a thermal single relaxation time lattice Boltzmann method (TSRT-LBM). To facilitate implementation, all LB equations are based on the same speed discretization scheme (D2Q9). Three-population distribution functions were applied to simulate the fluid flow, and temperatures of the fluid and solid phases. Previously, the numerical model was validated by available cases. Then, a comprehensive investigation has been performed to investigate the influence of the aforementioned dimensionless numbers. All LBM results are found to be highly consistent with other numerical works. The outcomes reported that at lower porosities, the energy and exergy efficiencies increased with increasing Re and Ec. However, for large porosity values, the efficiencies were optimum for a critical Re ~ 400. To sum up, it can be stated that the implemented thermal lattice Boltzmann method has been demonstrated as a suitable approach study the thermal sensible energy storage.