Non-equilibrium Heat Transfer Research Articles

Physical study of the non-equilibrium development of a turbulent thermal boundary layer

The direct numerical simulation of a non-equilibrium turbulent heat transfer case is performed in a channel flow, where non-equilibrium is induced by a step change in surface temperature. The domain is thus made of two parts in the streamwise direction. Upstream, the flow is turbulent, homogeneous in temperature and the channel walls are adiabatic. The inflow conditions are extracted from a recycling plane located further downstream, so that a fully developed turbulent adiabatic flow reaches the second part. In the domain located downstream, isothermal boundary conditions are prescribed at the walls. The boundary layer, initially at equilibrium, is perturbed by the abrupt change of boundary conditions, and a non-equilibrium transient phase is observed until, further downstream, the flow reaches a new equilibrium state, presenting a fully developed thermal boundary layer. The work aims at identifying the non-equilibrium effects that are expected to be encountered in comparable flows, while providing the means to understand them. In particular, the study allows for the identification of an inner region of the developing boundary layer where several quantities are at equilibrium. Other quantities, instead, exhibit a behaviour of their own, especially in proximity to the leading edge. The analysis is supported by mean and root-mean-square profiles of temperature and velocity, as well as by budgets of first- and second-order moment balance equations for the enthalpy and momentum turbulent fields.

Обобщенные модельные представления теории теплового удара для локально-неравновесных процессов теплообмена

An open problem of the theory of thermal shock in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process was considered. The model simultaneously includes three coordinate systems: Cartesian coordinates - a massive body bounded by a flat surface; spherical coordinates - a massive body with an internal spherical cavity; cylindrical coordinates - a massive body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, medium. The task is set: to obtain an analytical solution, to carry out numerical experiments and to give their physical analysis. As a result, generalized model representations of thermal shock in terms of dynamic thermoelasticity have been developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of curvature of the boundary surface of the thermal shock area substantiates the initial statement of the dynamic problem in displacements using the proposed corresponding "compatibility" equation. The latter made it possible to propose a generalized dynamic model of the thermal reaction of massive bodies with internal cavities simultaneously in Cartesian, spherical and cylindrical coordinate systems under conditions of intense thermal heating and cooling, thermal heating and cooling, heating and cooling by the medium. The model is considered in displacements on the basis of local non-equilibrium heat transfer. An analytical solution for stresses is obtained, a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison with the classical solution is made without taking into account local non-equilibrium. On the basis of the operational solution of the problem, design engineering relations important in practical terms for the upper estimate of the maximum thermal stresses are proposed.

Spatial Control of Heat Flow at the Nanoscale Using Janus Particles

Janus nanoparticles (JNPs) feature heterogeneous compositions, bringing opportunities in technological and medical applications. We introduce a theoretical approach based on nonequilibrium molecular dynamics simulations and heat transfer continuum theory to investigate the temperature fields generated around heated spherical JNPs covering a wide range of particle sizes, from a few nm to 100 nm. We assess the performance of these nanoparticles to generate anisotropic heating at the nanoscale. We demonstrate that the contrasting interfacial thermal conductances of the fluid-material interfaces arising from the heterogeneous composition of the JNPs can be exploited to control the thermal fields around the nanoparticle, leading to a temperature difference between both sides of the nanoparticle (temperature contrast) that is significant for particles comprising regions with disparate hydrophilicity. We illustrate this idea using coarse-grained and atomistic models of gold nanoparticles with hydrophobic and hydrophilic coatings, in water. Furthermore, we introduce a continuum model to predict the temperature contrast as a function of the interfacial thermal conductance and nanoparticle size. We further show that, unlike homogeneous nanoparticles, the interfacial fluid temperature depends on the interfacial thermal conductance of Janus nanoparticles.

Thermal performance evaluation of latent heat storage systems with plate fin-metal foam hybrid structure

The thermal performance of phase change materials (PCM) embedded with fins and metal foam is investigated. Plate fins are attached to the enclosure, and metal foam is embedded between adjacent fins to enhance heat transfer. To predict the melting behavior, a numerical model is established based on the enthalpy-porosity method, considering natural convection, flow resistance induced by metal foam, and non-equilibrium heat transfer. Nine cases considering various geometric parameters, heat transfer enhancement designs, and heated wall temperature are studied. Furthermore, a dimensionless theoretical model is derived to conclude the effect of combined parameters. It shows that the melting time reduces by 24.8 % as the fin height decreases from 80 mm to 50 mm, and the melting time becomes shorter with the decrease of fin thickness. However, the heat flux gets higher for higher fin height and thinner fin thickness. Moreover, the melting rate and heat flux become higher for higher fin volume fraction, lower metal foam porosity, and higher heated wall temperature. Furthermore, the theoretical model reveals that as Stefan number, fin efficiency, and the ratio of thermal diffusivity to the squared fin height become larger, the melting rate becomes higher.

Condensation heat and mass transfer characteristics of low GWP zeotropic refrigerant mixture R1234yf/R32 inside a horizontal smooth tube: An experimental study and non-equilibrium film model development

Condensation heat and mass transfer characteristics of low GWP zeotropic refrigerant mixtures R1234yf/R32 (mass fractions of 0.52:0.48 and 0.77:0.23, respectively) inside a horizontal smooth tube (inner diameter 4 mm) were studied experimentally. Moreover, a non-equilibrium film heat and mass transfer model was also developed by considering the mass transfer resistance on the vapor and the liquid side. Effects of mass flux, vapor quality, thermophysical properties and mass fraction on the heat transfer coefficients (HTCs) were analyzed. The heat transfer characteristics, especially the heat transfer deterioration caused by the mass transfer difference of the zeotropic refrigerant mixture, were evaluated. The experiment data show the HTCs of R1234yf/R32 (0.48:0.52) are lower than that of R1234yf at the inlet nearby of the condenser, then that becomes higher gradually than R1234yf due to mass transfer resistance decreasing. The non-equilibrium film model shows good agreement with the experimental results with the mean deviation in HTC of 22.9% at a mass fraction of 0.77:0.23 and 17.8% at a mass fraction of 0.48:0.52. Furthermore, the heat transfer degradation coefficient, interface temperature, diffusion flux of R32 and mass transfer Nusselt number were also reasonably determined with the non-equilibrium film model.

A fast synthetic iterative scheme for the stationary phonon Boltzmann transport equation

The heat transfer in solid materials at the micro- and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier’s heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find steady-state solutions to the BTE for highly non-equilibrium heat transfer problems, but converges extremely slowly in the near-diffusive regime. In this paper, a fast synthetic iterative scheme is developed to expedite convergence for the implicit DOM. The key innovative point of the present scheme is the introduction of a macroscopic diffusion-type equation for the temperature variation, which is exactly derived from the phonon BTE and valid for all Knudsen numbers. The synthetic equation, which is asymptomatically preserving to Fourier’s heat conduction equation in the diffusive regime, contains a term related to Fourier’s law and a term determined by the second-order moment of the distribution function that reflects the non-Fourier heat transfer. The mesoscopic kinetic equation and macroscopic diffusion-type equations are tightly coupled, because the macroscopic equation provides the temperature for the BTE, while the BTE provides a high-order moment to the diffusion-type equation. This synthetic iterative scheme strengthens the coupling of phonons with different wave vectors in the phase space to facilitate fast convergence from the diffusive to ballistic regimes. Typical numerical tests in one-, two-, and three-dimensional problems demonstrate that our scheme can describe the multiscale heat transfer problems accurately and efficiently. For all test cases, the present convergence is one to three orders of magnitude faster than the traditional implicit DOM in the near-diffusive regime.

Control of non-equilibrium Casimir force

We introduce the concepts of the control theory into the study of non-equilibrium Casimir forces and radiative heat transfer. As an illustration, we consider the plate-plate system for non-equilibrium Casimir forces, where two dielectric plates having different temperatures are separated by a vacuum gap. Previous works have indicated that this system only supports an unstable mechanical equilibrium. Here, we prove analytically and confirm numerically that the equilibrium can be made stable through a feedback control process involving temperature measurement and modulation. Our results show that it should be fruitful to explore the concepts from control theory in the study of the Casimir force and radiative heat transfer.

A study of Darcy–Bénard regular and chaotic convection using a new local thermal non-equilibrium formulation

The onset of Darcy–Bénard regular and chaotic convection in a porous medium is studied by considering phase-lag effects that naturally arise in the thermal non-equilibrium heat transfer problem between the fluid and solid phases. A new type of heat equation is derived for both the phases. Using a double Fourier series and a novel decomposition, an extended Vadasz–Lorenz model with three phase-lag effects is derived. New parameters arise due to the phase-lag effects between local acceleration, convective acceleration, and thermal diffusion. The principle of exchange of stabilities is found to be valid and the subcritical instability is discounted. The new perspective supports the finding of an analytical expression for the critical Darcy–Rayleigh numbers representing, respectively, the onset of regular and chaotic convection. The understanding of the transition from the local thermal non-equilibrium situation to the local thermal equilibrium one is also best explained through the new perspective. In its present elegant form, the extended Vadasz–Lorenz system with three phase-lag effects is analyzed using the largest Lyapunov exponent and the bifurcation diagram. It is found that the lag effects not only give rise to a quantitative difference in the above two metrics concerning chaos, but also present a qualitative difference as well in the form of the very nature of chaos.

Heat losses in applied smouldering systems: Sensitivity analysis via analytical modelling

As applied smouldering systems gain popularity for a variety of energy conversion purposes, there is a strong interest in optimizing the reactor design to support robust smouldering. Heat losses play a critical role in the energy balance of smouldering systems, and therefore have strong implications toward understanding propagation limits and reactor design. Heat losses in an applied smouldering system were approximated by adapting the analytical model from Kuznetsov (1996), originally developed for unsteady local thermal non-equilibrium heat transfer in a porous cylinder, to simulate the cooling zone trailing the smouldering front. The analytical model was adapted to a smouldering system by solving on a domain that lengthens as the cooling zone expands at the rate of the smouldering velocity. The results are incorporated into a global energy balance on the smouldering system, thereby providing an inexpensive and rapid method to estimate the system energy efficiency. Confidence in the analytical model was provided by demonstrating its predictions compare well with existing experimental and numerical estimates of heat losses from similar smouldering systems. The model was then used to quantify the sensitivity of the heat losses to two key reactor design parameters: radius and insulation quality. The system energy efficiency was shown to be highly sensitive to improved insulation and increased radius up to ~0.1 m (i.e., laboratory-sized reactors). However, this sensitivity diminished with size. Beyond 0.4 m radius, the predicted system energy efficiency was high (~85-95%) and relatively insensitive to reactor radius and insulation quality. Therefore, commercial, batch treatment smouldering reactors do not need to be larger than 0.4 m in radius to protect against heat losses and maximize their energy efficiency. This threshold design radius is considerably less than used in current reactors and therefore can provide valuable cost savings.

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.

Analytical Solutions to Models of Local Nonequilibrium Heat Transfer

Analytical Solutions to Models of Local Nonequilibrium Heat Transfer

Numerical simulation of gap length influence on energy deposition in spark discharge

The aim of the work is to study the influence of the length of the spark gap on energy input into the discharge channel during its gas-dynamic expansion. Methodology. The research is carried out by numerical modeling of the process of spark discharge development at variable values of the discharge gap length and at invariable other discharge conditions. The length of the gap was set in the range from 1 mm to 20 mm. The study was conducted using a numerical model of spark development, which takes into account the processes of nonstationary gas-dynamic expansion of the spark channel, the transient process in the electric circuit, nonequilibrium chemical processes, gas ionization, heat transfer and electrons thermal conductivity. The simulation was performed in atmospheric pressure nitrogen. The calculation was performed for various parameters of the RLC circuit, such as capacitance, inductance, resistance and voltage across the capacitor. Results. The study evaluates the influence of the spark length on the discharge current, the resistance of the spark channel, the energy deposited in the spark channel, and the distribution of thermodynamic parameters of the gas during the development of the spark discharge. It is confirmed that increasing the length of the gap increases the resistance of the spark. The deviation from the linear relationship between the deposited energy or the radiated energy and the length of the spark gap is estimated. Scientific novelty. A linear relationship between the gap length and the deposited energy is revealed when the total energy is above tens of Joules. Deviations from the linear dependence were detected in the discharge circuit when the total energy is below one of Joules. Practical value. The research results allow predicting the effect of the spark gap length on the energy input into the discharge channel under conditions of a slight change in the discharge current. In the conditions of essential change of amplitude of discharge current it is expedient to apply numerical researches for specification of changes in the energy deposited into a spark discharge.

Efficacy evaluation and treatment parameter optimization for laser surgery of Ota's nevus based on an advanced non-equilibrium bio-tissue heat transfer model.

This study was performed to better understand the laser-tissue interaction mechanism and optimize the laser wavelength and pulse duration for the laser treatment of Ota's nevus, thereby providing the precise theoretical guidance for clinician to improve the therapeutic effect. A non-equilibrium bio-tissue heat transfer model coupled with thermo-mechanical effect for the explosive vaporization of melanin granule induced by laser heating was developed to investigate the temperature and thermal damage distribution using alexandrite (755 nm) and Nd:YAG (1064 nm) lasers with the pulse width of 10-120 ns. Cryogen spray cooling (CSC) was introduced to prevent the epidermal thermal damage due to competitive laser absorption between epidermal and dermal melanin. Thermal injury of the epidermis with temperature in the melanin zone reaching 132.3 °C was induced by alexandrite laser. The optimal pulse durations were 50 and 30 ns, and the corresponding incident laser fluence thresholds were 6.45 and 19.5 J·cm-2 for alexandrite and Nd:YAG laser, respectively, with the pre-cooling of R32 spray. Using R32 spray cooling, the 1064-nm laser fluence threshold of melanin can be increased by 56.0%, resulting in an indirect increase (80.4%) of injury thickness. Nd:YAG laser (1064 nm) was highly suitable for the removal of melanin in the deep tissue owing to its deep penetration. Too short pulse duration should be avoided to prevent the epidermal thermal damage. The improvement of therapeutic effect by CSC demonstrates its high clinical application potential.

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.

A LOCAL THERMAL NONEQUILIBRIUM MODEL FOR COUPLED HEAT AND MASS TRANSFER WITH DISPERSION AND THERMAL DIFFUSION IN POROUS MEDIA

A theoretical model is proposed to predict Darcy-scale mass transport in porous media coupled with nonequilibrium heat transfer and taking into account the thermal diffusion process. A volume-averaging technique was used with approximations leading to a two-equation or two-temperature model for the macroscale energy balance equations. Because of the Soret effect, the concentration deviation with respect to the averaged value is a function of concentration and temperature gradients in the fluid phase, the temperature gradient in the solid phase, and the difference between the two averaged temperatures. The mapping between deviations and averages involves four closure problems for the mass transport equations: problems were solved numerically over a two-dimensional periodic-unit cell for evaluation purposes. The results show that the effective coefficients depend strongly on the thermophysical properties of the medium and the Peclet number. In particular, the effective-Soret coefficient in porous media changes with the Peclet number and the phases' thermal conductivity ratios.

Simulation of walnut drying under hot air heating using a nonequilibrium multiphase transfer model

A nonequilibrium multiphase moisture and heat transfer model was developed to simulate the drying of a single walnut under hot air heating. The walnut was modeled as a 3-layer sphere by differentiating the shell, kernel, and an air gap between them. Drying characteristics of walnuts at 43, 55, 65, and 75 °C under 1.4 m/s air velocity were simulated using finite element method. The simulation results agreed well with experimental data, and the model showed good predictability for drying of walnuts with different initial moisture contents and dimension characteristics (R adj 3 > 0.996 for moisture and R adj 3 > 0.983 for temperature). The spatial distributions of liquid moisture, water vapor, and temperature in the walnut were determined through model simulation, which provided important information for understanding the mechanisms of heat and moisture transfer during walnut drying process. Findings from this study established theoretical basis for improving the walnut drying process and determining the suitable drying conditions.

Heat transfer enhancement of nano-encapsulated phase change material (NEPCM) using metal foam for thermal energy storage

This study provides a new shape-stabilized phase change material (PCM) composite for enhanced thermal energy storage with nano-encapsulated phase change material (NEPCM) embedded in copper metal foam since it combines the characteristics of high latent heat of core PCM(octadecane), shape stable from encapsulation (polystyrene) and high thermal conductivity and high area/volume ratio of copper metal foam. We experimentally investigate phase change heat transfer of Foam/NEPCM composite with the consideration of foam porosity effect and foam/NEPCM thermal non-equilibrium heat transfer. Compared with pure NEPCM, foam/NEPCM composite provides maximum wall temperature reduction of 47 °C and more uniform internal temperature due to thermal enhancement of metal foam and latent heat absorption of NEPCM. The molten PCM convection is fully constrained in NEPCM shell, which makes heat conduction the solitary heat transfer mechanism in foam/NEPCM composite during phase change. Attributed to its higher thermal conductivity and area/volume ratio, the lower porosity foam/NEPCM composite obtains lower heated wall temperature and internal temperature near the heated wall than the higher porosity composite does. Moreover, the thermal non-equilibrium is more obvious at the location near the heated wall inside foam/NEPCM composite than that farther away.

Structure of a Temperature Front in a Fractured Porous Medium

We investigate the structure of a temperature front in a nonisothermal single-phase flow through a fractured-porous medium taking into account the nonequilibrium effects stipulated by the differences in the temperature between the fractures and the low-permeable matrix of the medium in which they are embedded. Using the dual-porosity model, we estimate the front thickness and constrain the similarity parameter domains, in which it is determined by either heat conduction or nonequilibrium heat transfer in the medium. Three asymptotic cases are considered for the temperature distribution in the front structure for different spatial scales of the nonisothermal flow. In these cases, the temperature distribution is described by finite relations.

Microstructure-based non-Fourier heat transfer modeling of HIFU treatment for thyroid cancer

Background and objectivesHigh intensity focused ultrasound is an emerging non-invasive technique for the thermal ablation of cancer. Modeling of high intensity focused ultrasound as a method to induce hyperthermia, by considering non-equilibrium convective heat transfer has been under-represented in the previous studies. Therefore, in the present study, we aimed to study the effect of blood vessels during high intensity focused ultrasound ablation of thyroid cancer. In addition, high intensity focused ultrasound modeling was greatly improved by considering non-Fourier heat transfer. MethodsThe modified dual-phase-lag model was used for the modeling of heat transfer in thyroid cancer during the ultrasound irradiation. The model parameters were linked with the tissue's microstructure parameters. Meanwhile, an interfacial convective heat transfer was considered between the blood vessels and the extravascular matrix. The extent of the vascular region was determined using the field emission scanning electron microscopy images. The non-linear Westervelt equation was solved for the sound wave to determine the heat source for the induced hyperthermia treatment. ResultsReferring to the acoustic results, sharp-wave ripples were observed due to the inclusion of notable amplitudes of excited harmonics. The thermal results showed a maximum temperature rise of 25.08°C and 51.47°C at the powers of 5 W and 10 W using the modified dual-phase-lag model, while the Pennes model predicted a temperature rise of 28.77°C and 55.5°C at the same powers. It was also concluded that a constant blood temperature, overestimates the dissipated energy and the temperature reduction during the cooling period, as a 15% deviation in the tumor temperature was observed from the non-equilibrium state at 10.65 s exposure and 10 W power. Eventually, the calculation of the ablated volumes indicated that the volumes were up to 4.5 times larger by the Pennes model compared to the modified dual-phase-lag model. ConclusionsIt can be concluded from the results that there should be a serious concern on the high intensity focused ultrasound modeling based on the parameters of blood vessels. Based on the thermal maps, the cancerous tissue should be exposed to a higher energy level of ultrasound waves in order to cause the desired damage against the estimated energy level predicted by the Pennes model.

A novel fixed-grid interface-tracking algorithm for rapid solidification of supercooled liquid metal

In this study, we present a novel fixed-grid interface-tracking method using finite volume method to simulate multidimensional rapid solidification (RS) of under-cooled pure metal. The discretized advection equation for solid fraction function is solved using the THINC/WLIC method, which is a VOF method. The governing equations for fluid flow are solved numerically using pressure-velocity coupling SIMPLE algorithm in a 2-D model with incompressible Newtonian fluid. The energy equation is modeled using an enthalpy-based formulation. The nonequilibrium solidification kinetics, interface tracking, undercooling, nucleation, heat transfer, and movement of liquid are included in the presented RS model.