Thermal Non-equilibrium Conditions Research Articles

Dissociation rate constants for oxygen at temperatures up to 11000 K

Measurements of the absorption and vibrational temperature evolution of molecular oxygen behind the shock wave front in regimes with temperatures near the front varying over the range 4000–11 000 K made it possible to determine the dissociation rate constant for O2 molecules under both thermal equilibrium and nonequilibrium conditions. The dependence of the dissociation rate constant on the ratio Tv/T, that is, on the deviation from the thermal equilibrium conditions, is demonstrated experimentally. The corresponding expression for the two-temperature dissociation rate constant is proposed.

Effects of superheat on characteristics of flashing spray and snow particles produced by expanding liquid carbon dioxide

This research experimentally investigates influences of superheat on flashing spray characteristics and on the snow formation of liquid CO2. Results show that liquid, two-phase flow or even three-phase flow can be found upon the release of liquid CO2 from high pressure to atmospheric pressure. This is due to complicated phase transition processes that involve hydrodynamic instabilities and thermal non-equilibrium conditions. Results also show that the spray pattern transfers from jet spray to cone spray, and then to a bowl spray configuration with the increase of superheat. The drastic changes in spray angle and mass flow rate indicate onset conditions from external-flashing to internal-flashing atomization mode. This is due to bursts of bubbles inside the nozzle chamber that result in the choking of the two-phase flow. Moreover, a few microns of CO2 snow size are measured in this research, which is consistent with records from literature on this topic. The narrower size distribution of snow particles and a critical spray angle resulting from two competing phenomena under internal-flashing atomization mode are also discussed in this research.

Entropy generation analysis of an adsorption cooling cycle

This paper discusses the analysis of an adsorption (AD) chiller using system entropy generation as a thermodynamic framework for evaluating total dissipative losses that occurred in a batch-operated AD cycle. The study focuses on an adsorption cycle operating at heat source temperatures ranging from 60 to 85°C, whilst the chilled water inlet temperature is fixed at 12.5°C, – a temperature of chilled water deemed useful for dehumidification and cooling. The total entropy generation model examines the processes of key components of the AD chiller such as the heat and mass transfer, flushing and de-superheating of liquid refrigerant. The following key findings are observed: (i) The cycle entropy generation increases with the increase in the heat source temperature (10.8 to 46.2W/K) and the largest share of entropy generation or rate of energy dissipation occurs at the adsorption process, (ii) the second highest energy rate dissipation is the desorption process, (iii) the remaining energy dissipation rates are the evaporation and condensation processes, respectively. Some of the noteworthy highlights from the study are the inevitable but significant dissipative losses found in switching processes of adsorption-desorption and vice versa, as well as the de-superheating of warm condensate that is refluxed at non-thermal equilibrium conditions from the condenser to the evaporator for the completion of the refrigeration cycle.

Exploring Chemical and Thermal Non-equilibrium in Nitrogen Arcs

Plasma torches operating with nitrogen are of special importance as they can operate with usual tungsten based refractory electrodes and offer radical rich non-oxidizing high temperature environment for plasma chemistry. Strong gradients in temperature as well as species densities and huge convective fluxes lead to varying degrees of chemical non-equilibrium in associated regions. An axi-symmetric two-temperature chemical non-equilibrium model of a nitrogen plasma torch has been developed to understand the effects of thermal and chemical non-equilibrium in arcs. A 2-D finite volume CFD code in association with a non-equilibrium property routine enabled extraction of steady state self-consistent distributions of various plasma quantities inside the torch under various thermal and chemical non-equilibrium conditions. Chemical non-equilibrium has been incorporated through computation of diffusive and convective fluxes in each finite volume cell in every iteration and associating corresponding thermodynamic and transport properties through the scheme of ‘chemical non-equilibrium parameter’ introduced by Ghorui et. al. Recombination coefficient data from Nahar et. al. and radiation data from Krey and Morris have been used in the simulation. Results are presented for distributions of temperature, pressure, velocity, current density, electric potential, species densities and chemical non-equilibrium effects. Obtained results are compared with similar results under LTE.

Thermodynamic and transport properties of two-temperature SF6 plasmas

This paper deals with thermodynamic and transport properties of SF6 plasmas in a two-temperature model for both thermal equilibrium and non-equilibrium conditions. The species composition and thermodynamic properties are numerically determined using the two-temperature Saha equation and Guldberg-Waage equation according to deviation of van de Sanden et al. Transport properties including diffusion coefficient, viscosity, thermal conductivity, and electrical conductivity are calculated with most recent collision interaction potentials by adopting Devoto’s electron and heavy particle decoupling approach but expanded to the third-order approximation (second-order for viscosity) in the frame of Chapman–Enskog method. The results are computed for various values of pressures from 0.1 atm to 10 atm and ratios of the electron temperature to the heavy particle temperature from 1 to 20 with electron temperature range from 300 to 40 000 K. In the local thermodynamic equilibrium regime, results are compared with available results of previously published studies.

Comparison of the Mollification and Wavelet Prefiltering of Temperature Data in an Ill-Posed Inverse Heat Conduction Problem, Application: Nonthermal Equilibrium Porous Medium

The mollification and wavelet prefiltering methods are employed in the ill-posed inverse heat conduction problem of heat flux estimation in a porous medium. The estimation of transient heat flux using the conjugate gradients method along with the adjoint differential equations has been carried out under a nonthermal equilibrium condition. The temperature sensor is located on the inactive surface of porous medium and the effects of the two already-mentioned prefiltering methods on the estimation of heat flux are studied for different noise levels. By smoothing the temperature data, the degree of difficulty of the estimation is reduced considerably. Comparison of the two filtering methods shows that a comparable improvement in performance can be achieved when using both filtering methods via mitigating the ill-posed nature of the problem. The performance of wavelet filter is somewhat superior to the mollification filter; however, the later can be implemented much more conveniently in a computer program.

The Reactive Thermal Conductivity of Thermal Equilibrium and Nonequilibrium Plasmas: Application to Nitrogen

The accuracy of numerical simulation on plasma behavior depends strongly on the reliability of thermophysical property data. Large number of studies for thermal plasma properties in the local thermodynamic equilibrium (LTE) exist; however, the database for thermal nonequilibrium plasmas is still far from completeness. This paper derives a general expression of total reactive thermal conductivity (TRTC) with great applicability to monatomic, diatomic, and polyatomic gases in terms of a two-temperature model. The derived formula is applied to nitrogen plasmas under thermal equilibrium and nonequilibrium conditions, considering its wide use in plasma systems and switching devices. Typical calculated results of TRTC with two different Saha equations and Guldberg-Waage equations in the temperature range of 300 K-40 000 K under different degrees of nonequilibrium are given and compared with those computed according to Brokaw and Butler's derivation for the special case of LTE plasmas, which shows excellent agreement. The influence of different expressions for Saha equations and Guldberg-Waage equations, together with different pressures of 0.1, 1, 3, 5, and 10 atm, on the TRTC evaluated by this newly developed expression is presented as well. These provide reliable reference data for use in the simulation of plasmas.

A Comparison of Thermal Dispersion Behaviour in High-Conductivity Porous Media of Various Pore Geometries

The effect of pore geometry on the axial thermal dispersion conductivity for high-conductivity porous media under general thermal non-equilibrium conditions is studied numerically. Pore geometries including arrays of inline square and circular cylinders, staggered circular cylinders, and a three-dimensional idealization of a graphite foam pore geometry are used to study the effects of the solid constituent shape and arrangement, as well as the effect of a relatively complex three-dimensional pore structure. Results indicate that in general, the dispersion conductivity cannot be considered a simple function of the Péclet number due to the effects of inertia, which cause the dispersion behaviour to depend on both the Reynolds and Prandtl numbers. On the basis of the current results, it is recommended that the influences of the Reynolds and Prandtl numbers be considered separately when generating models for the dispersion conductivity.

B123 中性子ラジオグラフィによる管内沸騰二相流のボイド率定量評価(OS9 熱・流動)

The void fraction in a forced convective flow boiling is very important information for understanding the characteristics of the boiling two-phase flow. Consequently, many experimental investigations have been carried out to obtain the local void fraction so far, but the detail data among the whole of the test-section has not been enough. Especially, the data under subcooled condition are quite limited. In this study, the void fraction distribution in a forced convective boiling was quantitatively measured by using the thermal neutron radiography. These results were compared with several existing void fraction correlations. Although these correlations show a good agreements with experimental results under low heat flux condition, there is no suitable correlation to estimate the void fraction under non-thermal equilibrium condition.

Analysis of forced convection heat transfer from a circular cylinder embedded in a porous medium

Time-dependent forced convection heat transfer from a single circular cylinder embedded in a horizontal packed bed of spherical particles under local thermal non-equilibrium condition is investigated numerically using the spectral-element method. The non-Darcian effects, i.e. inclusion of the effect of solid boundaries and inertia forces, and the effect of thermal dispersion, are taken into account. The influences of the presence of the porous material and its thermal properties: solid-to-fluid thermal conductivity ratio k r ∈ [ 0.01 , 1000 ] and Biot number B i ∈ [ 0.01 , 100 ] , on the rates of heat transfer and the hydrodynamic and thermal responses, are examined for the Reynolds number range R e D ∈ [ 1 , 250 ] . These effects are quantified. Perhaps not surprisingly, the results show that the presence of the porous particles suppresses significantly the wakes behind the cylinder and enhances considerably the heat transfer. A comparison that is made between the one- and two-equation energy model predictions shows that the former model predicts a continuous increase in Nu f against k r ; however, the trend of Nu f with k r , for k r > 10, is governed entirely by Bi when the latter model is used. Also, the increase in Bi decreases Nu f and increases Nu s , and high values of k r or Bi lead to establishing a thermal equilibrium status in the porous bed.

Restrictions on the Validity of the Thermal Conditions at the Porous-Fluid Interface—An Exact Solution

Thermal conditions at the porous-fluid interface under local thermal nonequilibrium (LTNE) conditions are analyzed in this work. Exact solutions are derived for both the fluid and solid temperature distributions for five of the most fundamental forms of thermal conditions at the interface between a porous medium and a fluid under LTNE conditions and the relationships between these solutions are discussed. This work concentrates on restrictions, based on the physical attributes of the system, which must be placed for validity of the thermal interface conditions. The analytical results clearly point out the range of validity for each model for the first time in the literature. Furthermore, the range of validity of the local thermal equilibrium (LTE) condition is discussed based on the introduction of a critical parameter. The Nusselt number for the fluid at the wall of a channel that contains the fluid and porous medium is also obtained. The effects of the pertinent parameters such as Darcy number, Biot number, Bi, Interface Biot number, Biint, and fluid to solid thermal conductivity ratio are discussed.

Analysis of heat flux bifurcation inside porous media incorporating inertial and dispersion effects – An exact solution

The phenomenon of heat flux bifurcation inside a porous medium is analyzed by studying the convective heat transfer process within a channel partially filled with a porous medium under Local Thermal Non-Equilibrium (LTNE) conditions. Either the thermal dispersion effect or the inertial effect is considered in the physical model. Exact solutions are derived for both the fluid and solid temperature distributions for three interface thermal models at the porous-fluid interface. The required conditions for validity of each interface thermal model are obtained, and the equivalence correlations between different interface thermal models are developed. The range of validity of the Local Thermal Equilibrium (LTE) condition is established, and the phenomenon of heat flux bifurcation inside a porous medium is established and demonstrated for the first time in the literature. Furthermore, the Nusselt number is obtained and investigated for pertinent parameters. The ranges of physical parameters in which the thermal dispersion effect and the inertia effect are important are established.

Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition

Forced convection through a channel partially filled with a porous medium is investigated analytically in the present work. Thermally developed condition is considered and the local thermal non-equilibrium model is utilized to obtain the exact solutions of both fluid and solid temperature fields for flow inside the porous material as well as for flow in the clear region. Nusselt number is obtained in terms of the porous insert thickness ( S), porosity ( ɛ) as well as pertinent parameters such as thermal conductivity ratio ( k), Biot number ( Bi), and Darcy number ( Da). The values of S by which the temperature difference between the two phases approach to zero, for different values of Bi, k, and Da number are obtained. It is found that three mechanisms affect the Nu number i: clear fluid conduction ii: internal heat exchange in the porous medium iii: channeling effect in the clear flow. The value of S, which yields the highest Nu number is found to vary linearly from 0.8 to 0.97 as the value of Da decreases from 10 −3 to 10 −7. At the expense of reasonable pressure drop the optimum thickness of porous material in order to enhance the heat transfer rate is found S = 0.8.

Closure of non-equilibrium volume-averaged energy equations in high-conductivity porous media

A formulation for closure of the volume-averaged energy equations under local thermal non-equilibrium conditions has been proposed, providing a general method for obtaining the relevant effective properties for high-conductivity porous materials. The method requires numerical solution of the flow field, as well as closure problems, over a representative volume of porous media. This study considers an array of highly conductive circular cylinders for which all relevant effective properties are obtained. Comparisons are made to results in literature for low Reynolds numbers, while results at higher Reynolds numbers are presented to provide insight into the effects of inertia on the effective properties.

Homogeneous amorphous FexGe1−xmagnetic semiconductor films with high Curie temperature and high magnetization

Homogeneous amorphous Fe${}_{x}$Ge${}_{1\ensuremath{-}x}$ (0.3 \ensuremath{\leqslant} $x$ \ensuremath{\leqslant} 0.5) FMS films with a high Fe concentration were synthesized under thermal nonequilibrium condition by magnetron cosputtering. The microstructure, magnetism, electrical transport, and ferromagnetic resonance were systematically studied. The results indicate that Fe${}_{x}$Ge${}_{1\ensuremath{-}x}$ films have intrinsic ferromagnetism with a high Curie temperature and magnetization. The saturation magnetization can be well fitted by Bloch's spin-wave formula in a wide temperature range. Quantitative analysis of electrical transport reveals that Fe${}_{x}$Ge${}_{1\ensuremath{-}x}$ FMS films show conductivity of weakly localized carriers (holes) on the metallic side. Moreover, the anomalous Hall resistivity is proportional to the magnetization for all samples, indicating the carriers are spin polarized and the ferromagnetism is intrinsic. The ferromagnetic resonance further reveals that the Fe${}_{0.5}$Ge${}_{0.5}$ thin films have uniform collective ferromagnetism. Therefore, Fe${}_{x}$Ge${}_{1\ensuremath{-}x}$ ferromagnetic semiconductors with a high Curie temperature and magnetization have potential application in spintronic devices as a highly efficient spin injection source.

Assessment of Thermal Non-Equilibrium Condition on Heat Transfer through a Channel Lined with Porous Media – Constant Wall Temperature

In this paper, forced convection in a channel lined with a porous layer is investigated. The main goal is to assess the effect of local thermal non-equilibrium condition on overall heat transfer in the channel. The effects of thermal conductivity of solid and thickness of porous layer are also studied. Flow assumed to be laminar and fully developed. The Brinkman-Forchheimer model for flow as well as the two equation energy model is used. The results showed that when the problem tends to local thermal equilibrium condition, heat transfer is enhanced due to heat conduction through solid phase. Another factor, which can facilitate the heat transfer, is the increase of the thermal conductivity of solid material. This trend is sensitive to the thickness of porous layer and modified Biot number, which is a measure (criterion) of local fluid to solid heat transfer. As thickness and modified Biot number increase, the Nusselt number becomes more sensitive to the thermal conductivity ratio.

Effect of hydrogenation on transport and magnetic properties in homogeneous amorphous MnxGe1−x:H films

Homogeneous amorphous MnxGe1−x:H films were synthesized under thermal nonequilibrium condition by magnetron co-sputtering technology with hydrogen in Ar atmosphere. Compared to the MnxGe1−x films without hydrogen, the MnxGe1−x:H films with hydrogen show higher concentration of hole carriers, larger conductivity, and higher saturation magnetization. Moreover, it was found that the anomalous Hall resistivity is proportional to the perpendicular magnetization. These electrical and magnetic properties indicate that the ferromagnetism of the MnxGe1−x:H films is intrinsic ferromagnetism mediated by the spin-polarized hole carriers.

Two-temperature thermodynamic and transport properties of carbon–oxygen plasmas

Thermodynamic and transport properties of different carbon–oxygen plasmas mixtures are presented for both thermal equilibrium and non-equilibrium conditions: to the knowledge of the authors, the latter data have not been reported in the literature. The calculations of transport properties are carried out using the Chapman–Enskog method up to the third order; properties for plasmas out of equilibrium have been obtained using both the two-temperature theory developed by Rat et al and a simplified theory by Devoto, that neglects the coupling between electrons and heavy particles; it is shown that for carbon–oxygen mixtures no differences between results obtained using these two theories can be appreciated for thermal and electrical conductivities; some discrepancies have been found for ordinary diffusion coefficients of the type electron-heavy particle. Moreover, local thermodynamic equilibrium results for transport properties obtained using Lennard-Jones potentials have been compared with results obtained using more recent potential data and with available results reported in the literature. Results for composition, mass density, specific heat, thermal conductivity, electrical conductivity and viscosity of atmospheric pressure plasmas in the electron temperature range 300–30 000 K are reported.

The Effect of Thermal Contact Resistance at Porous-Solid Interfaces in Finned Metal Foam Heat Sinks

A numerical study on the effect of thermal contact resistance and its impact on the performance of finned aluminum foam heat sinks has been conducted. Calculations are based on the solution of the volume-averaged mass, momentum, and energy equations under conditions of local thermal nonequilibrium using a finite-volume-based computational fluid dynamics code for conjugate fluid/porous/solid domains. Numerical results have been obtained for a wide range of contact resistances at the porous-solid interfaces, up to the limit of an effectively infinite resistance. As the contact resistance is increased to such high levels, the heat transfer is found to asymptote as conduction into the solid constituent of the foam is completely blocked. Even without conduction into the solid, a convective enhancement is obtained due to the presence of the foam material. It is reasoned that this is due to the thinning of the momentum boundary layers as a result of the presence of the porous material, which acts as a momentum sink. As a result of the thinner boundary layers, the flow speed near the finned surfaces and base is increased, which serves to increase the rate of convection from these surfaces. It is also found that for most reasonable interface materials, such as thermal epoxies, the impact of thermal contact resistance on the heat transfer performance in comparison to that for an ideal bond is small.

Effect of isothermal aging on the mechanical performance of brazed ceramic/metal joints for planar SOFC-stacks

One of the key requirements for the application of planar solid oxide fuel cells is the hermetical sealing of ceramic and metallic stack-components. Gas tightness and associated mechanical integrity of the sealants are therefore key prerequisites for reliable operation over the lifetime of the stack. To withstand mechanical stresses generated by the differences in thermal expansion of the involved materials as well as non-equilibrium thermal conditions upon heating and cooling, joining with metals rather than brittle glass-ceramics is considered to be advantageous. Hence, as one of the joining possibilities for SOFCs of planar design reactive air brazing of the ceramic cell into a metallic frame has gained increasing interest and proofed its suitability in several mid term full scale stack experiments at Forschungszentrum Jülich. Fracture experiments were carried out to characterize the fracture energy and associated failure mechanisms of silver-based reactive air brazes, used for joining the zirconia electrolyte of an anode supported planar cell with a metallic Crofer22APU frame. The specimens were mechanically tested in notched beam bending geometry at room temperature. Mechanical testing was accompanied by in-situ observation with optical and SEM resolution. Discussion of the results focuses on the influence of isothermal aging and associated interfacial reactions on crack path location and mechanical characteristics. State of the art CuO-containing brazes turned out to be outbalanced by a newly conceived CuO-free braze. The new braze did not only display superior delamination resistance in the as-brazed state, combined with an additional pre-oxidation treatment of the steel but also showed improved degradation resistance against isothermal aging.