Non-equilibrium Heat Transfer Research Articles

An investigation of non-equilibrium heat transport in a gas system under external force field

The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale governing equations, such as the Boltzmann and Navier-Stokes equations, are valid in their respective modeling scales. Without identifying a physical scale between the above two limits for the modeling of the flow motion, it is challenging to develop a multiple scale method to capture non-equilibrium flow physics seamlessly across all regimes. Based on the modeling scale of cell size and implementing conservation laws directly in a discretized space, a well-balanced unified gas-kinetic scheme (UGKS) for multiscale gaseous flow has been constructed and used in the study of non-equilibrium flow and heat transport under external force field. In this paper, static heat conduction problems under external force field in different flow regimes are quantitatively investigated. In the lid-driven cavity case, the stratified flow is observed under external force field. With the increment of external force, the flow topological structure changes dramatically, and the temperature gradient, shearing stress, and external force play different roles in the determination of the total heat flux in different layers corresponding to different flow regimes. As a typical non-Fourier’s heat conduction phenomena in the transition regime, the external force enhances the heat flux significantly along the forcing direction, with the relationship q→force∝ϕ→, where q→force is the force-induced heat flux and ϕ→ is the external force acceleration. This relationship is valid in all flow regimes with non-vanishing viscosity coefficient or the limited length of particle mean free path. Both theoretical analysis and numerical experiments are used to show the important role of external force on non-equilibrium heat transfer.

Fluctuations of radiative heat exchange between two bodies

We present a theory to describe the fluctuations of nonequilibrium radiative heat transfer between two bodies both in far and near-field regime. As predicted by the blackbody theory, in far field, we show that the variance of radiative heat flux is of the same order of magnitude as its mean value. However, in near-field regime we demonstrate that the presence of surface polaritons makes this variance more than one order of magnitude larger than the mean flux. We further show that the correlation time of heat flux in this regime is comparable to the relaxation time of heat carriers in each medium. This theory could open the way to an experimental investigation of heat exchanges far from the thermal equilibrium condition.

Heat Transfer in Nonequilibrium Flows with Homogeneous and Heterogeneous Recombination Reactions

The aeroheating performance of hypersonic vehicles is usually significantly influenced by the chemical reaction processes. For the new-generation hypersonic cruise vehicles, the boundary-layer flow is shown to be in chemical nonequilibrium due to rarefied gas effects. As a result, there will be a competition between the homogeneous recombination of atoms in the near-wall flowfield and the heterogeneous recombination on the catalytic wall surface, which, leading to a coupling of the heat diffusion and conduction, is beyond the application scope of the classical theories developed originally for the traditional blunt reentry vehicles. In this paper, the theoretical modeling and the direct simulation Monte Carlo method are employed to study the corresponding rarefied nonequilibrium flow and heat transfer phenomena near the sharp leading edges. A generalized model is proposed to evaluate the deviation of the actual aeroheating performance from the classical description. Based on this model, an integrated nonequilibrium criterion and a simple but effective bridging function are introduced to predict the stagnation-point heat transfer under the competitive effects between the homogeneous and heterogeneous recombination of atoms. The analytical formula is validated by the numerical results under various flow conditions.

A thermodynamic and heat transfer model for LNG ageing during ship transportation. Towards an efficient boil-off gas management

A non-equilibrium thermodynamic and heat transfer model for LNG ageing during ship transportation has been developed based on experimental data. The measurements reveal that the liquid temperature remains nearly constant, whereas significant variations are observed for the gas temperature. The measurement of the liquid temperature along the tank height suggests that a small scale rollover phenomenon may have taken place in one cargo tank. A time dependent heat transfer mechanism has been considered by taking into account the temperature variations of the atmospheric air, the seawater and the cofferdam environment which affect the cargo tanks. An important finding is that the evaporation rate (boil-of rate) is forced to follow the fuel flow consumption profile imposed by the vessel’s propulsion system in order to match the tank pressure and volume constraints. The theoretical model is favorably compared to a comprehensive set on per hour basis of on board measurements of cargo temperatures and pressures, recorded during laden voyages, providing a better understanding of the underlying processes involved. The dominant role of the fuel consumption on the evaporation rate may be utilized in order to devise an efficient cargo management strategy during the laden voyage.

Surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow

This paper deals with the surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow. An interface condition with finite-rate thermochemistry was established to balance the three-dimensional Navier-Stokes solver and TPS thermal response solver, and a series of coupled simulations of chemical non-equilibrium aerothermodynamics and structure heat transfer with various surface catalycities were performed for hypersonic Mars entries. The analysis of surface thermochemistry reveals that the surface chemical reactions have great contribution to aerodynamic heating, and the temperature-dependence of finite-rate catalysis highly influences the evolution of the coupling aerodynamic heating in the coupling process. For fixed free stream parameters with proper catalytic excitation energy, a “leap” phenomenon of the TPS-coupled heat flux with the coupling time appears in the initial stage of the coupling process, due to the strong thermochemical effects on the TPS surface.

Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady state heat flux and noise power at moderate coupling regimes, below which we find those two transport quantities are enhanced by the finite qubit energy bias. With external modulations, the geometric-phase-induced heat flux shows monotonic decrease as increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under finite qubit energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes, and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.

Multiscale processes of the flow and non-equilibrium interphase heat and mass transfer self-organization in multiphase systems

Multiscale processes of self-organization of the flow and non-equilibrium heat and mass transfer during the separation of a binary mixture in a multiphase system formed by a structural packing and a counter-flow vapor-liquid flow are considered. The conditions for the appearance of large-scale convective flow during separation of the binary mixture of refrigerants R21-R114 in a distillation column with Koch 1Y structure packing are obtained. The physical properties of this mixture are similar to the properties of air component at cryogenic temperatures.

Approach to the Assessment of Size-Dependent Thermal Properties of Disperse Solutions: Time-Resolved Photothermal Lensing of Aqueous Pristine Fullerenes C60 and C70

An approach is proposed for assessment of the thermal properties of aqueous pristine fullerene C60 and C70 dispersions (AFDs) at the level of 10–7–10–5 mol L–1 by photothermal (thermal-lens) spectroscopy for their application in medicine and technology. Along with relevant size-characterization techniques—differential scanning calorimetry (DSC) with the Gibbs–Kelvin equation and dynamic light scattering (DLS) techniques—this approach provides an estimation of the size-dependent thermal properties of disperse solutions—thermal diffusivity, thermal effusivity [thermal inertia], and thermal conductivity. The values for AFDs under the conditions of the attained thermal equilibrium show good precision, and the cluster size estimations agree with the reference methods. The reconstruction of the thermal-lens characteristic time over the course of the blooming of the thermal-lens effect reveals a short increase in the apparent thermal diffusivity. This is accounted for by nonequilibrium heat transfer within fulle...

Thermal Non-equilibrium Heat Transfer and Entropy Generation due to Natural Convection in a Cylindrical Enclosure with a Truncated Conical, Heat-Generating Porous Bed

Natural convection in enclosures driven by heat-generating porous media has diverse applications in fields like geothermal, chemical, thermal and nuclear energy. The present article focuses on heat transfer and entropy generation characteristics of a heat-generating porous bed, placed centrally within a fluid-filled cylindrical enclosure. Pressure drop and heat transfer in the porous bed are modelled using the Darcy–Brinkmann–Forchheimer approximation and the local thermal non-equilibrium model, respectively. Energy flux vectors have been utilised for visualising convective energy transfer within the enclosure. The study of a wide range of Rayleigh number (\(10^{7}\)–\(10^{11}\)) and Darcy number (\(10^{-6}\)–\(10^{-10}\)) reveals that heat transfer in the porous region can be classified into conduction-dominated and convection-dominated regimes. This is supplemented with an entropy generation analysis in order to identify and characterise the irreversibilities associated with the phenomenon. It is observed that entropy generation characteristics of the enclosure closely follow the above-mentioned regime demarcation. Numerical computations for the present study have been conducted using ANSYS FLUENT 14.5. The solid energy equation is solved as a user-defined scalar equation, while data related to energy flux vectors and entropy generation are obtained using user-defined functions.

Closure of a macroscopic turbulence and non-equilibrium turbulent heat and mass transfer model for a porous media comprised of randomly packed spheres

Turbulent heat and mass transfer in packed beds of spheres is widely encountered in industrial and food storage applications and, as such, modeling of such cases is of interest in design and development. Herein, we propose a closure of the volume- and time-averaged (macroscopic) turbulence, and non-equilibrium turbulent heat and mass transfer equations for randomly packed spheres, based on computational results of flow and heat transfer for a unique geometric model. In this respect, the closure results are derived from pore-level (microscopic) information obtained from numerical simulations of turbulent heat and fluid flow. Turbulence is incorporated at both levels using the k–ɛ model, and the dispersive effects of turbulence are also considered. For the momentum equation, the closure is sought for the Darcy and Forchheimer terms. For the non-equilibrium heat and mass transport equations, we obtain closures for the dispersion, turbulent flux, turbulent dispersion, and interfacial heat and mass transfer terms. The closure results are found to be dependent upon the porosity and Reynolds number. However, the mean sphere diameter and its local variation inside the representative elemental volumes only weakly affect the results. The closure results are presented as power law-based correlations, such that they can be easily implemented in a volume-time-averaged framework.

Natural convection in a triangular cavity filled with a nanofluid-saturated porous medium using three heat equation model

The present study aims to examine the local thermal non-equilibrium natural convection heat and mass transfer of nanofluids in a triangular enclosure filled with a porous medium. The effect of the presence of nanoparticles and the thermal interaction between phases on the flow, temperature distribution of phases, the concentration distribution of nanoparticles as well as the Nusselt number of phases is theoretically studied. The interaction between the phases of nanoparticles and the base is taken into account by using a three thermal energy equation model while the concentration distribution of nanoparticles is modeled by Buongiorno’s model. A hot flush element is mounted at the vertical wall of the triangle enclosure to provide a constant temperature of Th while the inclined wall is at a constant temperature of Tc. A three heat equation model by considering the local thermal non-equilibrium model of nanoparticles, the porous medium, and the base fluid is developed and utilized for natural convection of nanofluids in an enclosure. The drift-flux of nanoparticles due to the nano-scale effects of thermophoresis and Brownian motion effects is addressed. The governing equations are represented in a non-dimensional form and solved by employing the finite element method. The results indicate that the increase of Rayleigh number shows a significant increase in the average Nusselt number for the base fluid phase, a less significant increase in the average Nusselt number for the solid matrix phase, and almost an insignificant effect in the average Nusselt number of the nanoparticle phase. Increasing the buoyancy ratio parameter (the ratio of mass transfer buoyancy forces to the thermal buoyancy forces) tends to reduce and increase the average Nusselt number in fluid and porous phases, respectively. An optimum value of buoyancy ratio parameter for the average Nusselt number of the nanoparticle phase is observed.

Analytical solution of forced convective heat transfer in parallel-plate channel partially filled with metallic foams

The forced convection flow and heat transfer characteristics in parallel-plate channel partially filled with metallic foams have been studied analytically. To predict fluid and thermal transport in the bottom heated partially filled channel, the Brinkman-extended Darcy momentum model and Non-equilibrium heat transfer model for porous media were employed for the foam filled region coupling with the momentum and energy conservation equations for foam free region. The interface between foam filled region and foam free region are subject to continuous temperature and energy balance to derive the analytical solutions for fully developed flow and convection heat transfer in entire plate channel including foam filled region and non-foam region. Then, the velocity and temperature distributions were predicted for the whole region of the parallel-plate channel based on the analytical solutions. The effects of key parameters on flow resistance and heat transfer performance has been investigated. Unlike the completely filled channel, the influences of pore density and porosity on flow and heat transport are dependent on the height of the foam.

Nonequilibrium Gas Flow and Heat Transfer in a Heated Square Microcavity

The flow of a rarefied gas in a square enclosure with one wall at high temperature and the other three walls at the same low temperature is investigated. The flow, characterized by the reference Knudsen number and ratio of the cold over the hot temperatures, is simulated both deterministically, using the nonlinear Shakhov kinetic model, and stochastically, using the DSMC method. Excellent agreement between the two approaches is obtained. It is found that along the side walls the gas velocity, depending on the flow parameters, may be either from cold to hot or from hot to cold regions. Furthermore, it is confirmed that the average heat flux departing from the hot plate exhibits a nonmonotonic behavior with regard to the temperature ratio, deducing a maximum heat flux at a temperature ratio of about 0.3. The flow and heat transfer characteristics are explained by computing the ballistic and collision parts of the total bulk quantities and by investigating the contribution of each part to the overall solution.

Evaluation of recoverable energy potential from enhanced geothermal systems: a sensitivity analysis in a poro‐thermo‐elastic framework

AbstractThis study presents application of an efficient approach to simulate fluid flow and heat transfer in naturally fractured geothermal reservoirs. Fluid flow is simulated by combining single continuum and discrete fracture approaches. The local thermal nonequilibrium approach is used to simulate heat transfer by conduction in the rock matrix and convection (including conduction) in the fluid. Fluid flow and heat transfer models are integrated within a coupled poro‐thermo‐elastic framework. The developed model is used to evaluate the long‐term response of a geothermal reservoir with specific boundary conditions and injection/production schedule. A comparative study and a sensitivity analysis are carried out to evaluate the capability of the integrated approach and understand the degree by which different reservoir parameters affect thermal depletion of Soultz geothermal reservoir, respectively. Also observed, there exists an optimum fracture permeability after which the reservoir stimulation does not change the recovery factor significantly. Estimation of fluid temperature by the assumption of local thermal nonequilibrium heat transfer between the fracture fluid and the rock matrix gives fluid temperature of about 3°C less than that of estimated by thermal equilibrium heat transfer at early stage of hot water production.

Non-equilibrium kinetics, diffusion and heat transfer in shock heated flows of N2/N and O2/O mixtures

In this paper, the influence of vibrational and dissociation kinetics on heat transfer and diffusion in non-equilibrium flows of N2/N and O2/O mixtures in the relaxation zone behind shock waves is studied on the basis of the state-to-state and one-temperature kinetic theory approaches. The results of calculations of vibrational level populations ni, gas temperature T, total energy flux q, diffusion velocities of molecules at different vibrational states Vi and atoms Va in the relaxation zone behind a shock front are presented for the free stream Mach numbers M=18, 15, 10. The contribution of different dissipative processes to the total energy flux is evaluated for various flow conditions. Characteristic features of non-equilibrium kinetics, diffusion and energy transfer in two considered mixtures are discussed. The impact of vibrational excitation of N2 and O2 molecules in the free stream on a relaxation zone structure and transport properties behind a shock is shown.

Comparison and Analysis of Heat Transfer in Aluminum Foam Using Local Thermal Equilibrium or Nonequilibrium Model

Aluminum foams are favorable in modern thermal engineering applications because of the high thermal conductivity and the large specific surface area. The present study aims to investigate an application of porous aluminum foam by using the local thermal equilibrium (LTE) and local thermal nonequilibrium (LTNE) heat transfer models. Three-dimensional simulations of laminar flow (porous foam zone), turbulent flow (open zone), and heat transfer are performed by a computational fluid dynamics approach. In addition, the Forchheimer extended Darcy's law is employed to evaluate the fluid characteristics. By comparing and analyzing the average and local Nusselt numbers, it is found that the LTNE and LTE models can reach the same Nusselt numbers inside the aluminum foam when the air velocity is high, meaning that the aluminum foam is in a thermal equilibrium state. Besides, a high interfacial heat transfer coefficient is required for the aluminum foam to reach a thermal equilibrium state as the height of the aluminum foam is reduced. This study suggests that the LTE model can be applied to predict the thermal performance at high fluid velocities or for the case with a large height.

The measurement and analysis of the nonequilibrium heat transport time of the electrons in the Co, Cr and Ag three kinds of metal films based on the transient reflection

Co, Cr and Ag three kinds of metal films are deposited by the magnetron sputtering technique. The electron nonequilibrium heat transfer process is studied and the nonequilibrium heat transport time of the electrons of the three kinds of metal films is measured using the femtosecond transient thermal reflection technique, which plays a positive role in solving the problem that the devices are damaged in the processing of the laser heating the metals. The results show that: in the condition of the same pump power of the femtosecond laser, the nonequilibrium heat transport time of the electrons is Ag>Co>Cr. And for the same kind of the thin films, the nonequilibrium heat transport time of the electrons is proportional to the thickness of the films, and is inversely proportional to the power density of the femtosecond laser on the films.

Nonequilibrium thermal effects during pulsed action on conducting medium

The two-temperature model for a medium with free electrons subject to nonequilibrium heat transfer is considered. The possibility is shown for tailing of heating area boundaries and the existence of undamped heat waves due to the small duration of temperature pulses acting on the material. A quantitative estimate is made for parameters of the temperature mode when the tailing of heating area boundaries appears according to heat conduction models.

Mathematical Simulation of the Locally Nonequilibrium Heat Transfer in a Body with Account for its Nonlocality in Space and Time

Differential equations for the locally nonequilibrium heat transfer in an infinite plate, in which the nonlocality of this plate in space and time is taken into account, have been derived. Exact analytical solutions of these equations were obtained and analyzed in detail. This analysis has shown that, in the case where the nonlocality of the plate in space and time is taken into account in the indicated equations, they do not give abrupt changes in the temperature of the plate and negative temperatures for it. It was established that, in locally nonequilibrium processes, the first-kind boundary conditions (a heat shock) cannot be realized instantaneously at any conditions of heat exchange between a body and the environment and that, consequently, in the process of this exchange, the coefficient of heat transfer cannot exceed any limiting values determined by the physical properties (including the relaxation ones) of the body.

Bioheat transfer analysis of biological tissues induced by laser irradiation

This paper develops an analytical solution for a generalized dual phase lag (DPL) model based on the nonequilibrium heat transfer in biological tissues during laser irradiation achieved by performing volume average to the local instantaneous energy equation for blood and tissue. The obtained energy equation is solved by employing the separation of variables and Duhamel's integral method for both absorbing and scattering tissues. The generalized DPL model anticipates different results than that of the predicted by the classical DPL and Pennes bioheat transfer (parabolic) models. It is found that the generalized DPL model calculates lower temperature than that of obtained by the classical DPL model due to considering heat convection between blood vessels and tissue. The obtained analytical results are also compared with existing numerical and experimental data to verify the accuracy of the analytical solution. The results indicate that the generalized DPL model reduces to Pennes bioheat transfer model when both thermal lag times are zero. It is shown that effects of blood perfusion rate, coupling factor and the lag time τT on the temperature response of tissue are similar. Furthermore, the comparison between the analytical results and existed experimental data shows that the present mathematical model is an efficient tool for evaluation of bioheat transfer in biological tissues.