Non-equilibrium Heat Transfer Research Articles

Optimized Piston Motion for an Alpha-Type Stirling Engine.

The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of dissipative processes. In order to ensure the possibility of a technical implementation and the simplicity of the optimization, we restrict the possible piston movements to a parametrized class of smooth piston motions. In this theoretical study the engine model is based on endoreversible thermodynamics, which allows us to incorporate non-equilibrium heat and mass transfer as well as the friction of the piston motion. The regenerator of the Stirling engine is modeled as ideal. An investigation of the impact of the individual loss mechanisms on the resulting optimized motion is carried out for a wide range of parameter values. We find that an optimization within our restricted piston motion class leads to a power gain of about 50% on average.

Numerical analysis of local non-equilibrium heat transfer in layered spherical tissue during magnetic hyperthermia

A solid multi-layered concentric sphere with Gaussian space source is considered as the tissue model for magnetic hyperthermia treatment. The generalized dual-phase-lag model of bioheat transfer is used to describe the behavior of heat transport in tissue in the hyperthermia treatment process for accounting the local non-equilibrium effect. The effects of blood perfusion with the transient temperature are included in the tissue model. The hybrid numerical scheme based on Laplace transform, change of variables, and the modified discretization technique is extended to solve the present problem. The analytical solution for constant heat generation in the inner sphere is presented and evidences the accuracy and rationality of the present numerical results. In an ideal hyperthermia treatment, all the diseased tissues should be selectively heated without affecting any healthy tissue. Attempting to achieve the ideal temperature distribution, the thermal dose is estimated at the specified condition. The corresponding thermal efficacy of tumor damage has also been assessed based on the Arrenius equation.

Локалізація ексергетичних втрат в утилізаторі теплоти відхідних газів газоспоживальних теплових установок

The problem of increasing the thermodynamic efficiency of power plants can be solved only by using a complex approach using methods based on modern methods of exergy analysis in combination with methods of heat transfer theory, theory of linear systems, structural-variant methods, multi-level optimization methods, etc. The analysis of the possibility of applying the discrete-modular principle and the corresponding complex method for analyzing the efficiency of the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine is performed in the paper. The aim of the work is to analyze the localization of exergy losses, their differentiation, and the establishment of the relative contribution of various types of losses to the general exergy losses in the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine. The structural features of the heat-recovery exchanger and the exergy properties that reflect the essence of exergy methods: universality and additivity, made it possible to use the discrete-modular principle and a complex method based on exergy-dissipative functions for efficiency analysis. The advantage of this method is the ability to analyze the localization of exergy losses in separate modules of the heat-recovery exchanger and to differentiate the exergy losses associated with nonequilibrium heat transfer between the heat-transfer agents and the wall, heat conduction and the movement of heat-transfer agents. Using the chosen complex method, the analysis of the localization of exergy losses in the heat-recovery exchanger was carried out and the exergy-dissipative functions of each of the eight modules of the heat-recovery exchanger were calculated. Differentiation of exergy losses was carried out and the relative contribution of exergy losses associated with the processes of heat transfer from flue gases to the wall, from wall to water, in heat conduction processes, as well as exergy losses associated with the movement of heat-transfer agents, in the general exergy losses was analyzed. To determine the exergy losses due to nonequilibrium heat transfer between the heat-transfer agents and the motion of the heat-transfer agents, the differential exergy equations, the equations for the heat flow densities between the heat-transfer agents and the wall, the equation for the heat flow density due to heat conduction through the wall and the equations of motion are used. It has been established that the localization of maximum exergy losses in all modules of the heat-recovery exchanger is associated with losses due to heat transfer from flue gases to the wall.

Numerical simulation of the transient process of monopropellant rocket engines

Liquid monopropellant rocket engines are widely used in space propulsion and are developing in the direction of non-toxic and pollution-free propellants. The use of non-toxic monopropellants with a low decomposition rate makes the start-up and shutdown processes of the engines longer, and the gas inlet assumptions that were applicable to the calculation of hydrazine monopropellant engines cannot be used. Based on the steady-state calculation model of hydroxyl ammonium nitrate (HAN)-based monopropellant engine, we propose a combined model that considers decomposition of liquid monopropellant and non-equilibrium heat transfer between fluid and solid catalyst bed, and uses this model and the gas inlet hypothesis to calculate the working process of an HAN-based monopropellant rocket engine of 60 N thrust. The calculated results are compared with the test curve, and the results show that the decomposition of liquid monopropellant plays a key role in the starting and stopping processes. When the gas inlet assumption is adopted without considering the decomposition of the liquid monopropellant, the calculated start-up time is much shorter than the hot-firing test, and there is no tail-off section when shutting down. The pressure-rise and pressure-decay curve calculated by the combined model agree well with the test curve, and the maximum deviation during the steady state is less than 10%. For HAN-based monopropellant engines, the pressure rises slowly at the first start because the temperature of catalyst bed is lower, which results in a lower rate of decomposition. When restarted shortly after a shutdown, the pressure rises rapidly due to the high temperature of the catalyst bed and the high rate of decomposition. The HAN-based monopropellant can penetrate a few millimeters downstream of the injector, and there is a significant tail when the engine is shut down, which is caused by the continued decomposition of the remaining propellant after the shutdown.

Testing of a new non-equilibrium heat and moisture transfer model in porous building materials

In this paper the new non-equilibrium model of heat and moisture transfer in heterogenous building materials is presented and tested. The new hygro-thermal model differs from the other approaches which are based on the classical assumption of instantaneous local mechanical, thermal and hygric equilibrium between vapour and water in the pores in building materials. Instead of this assumption the model uses the finite rate of transition of moisture from the liquid to the vapour state and vice versa while still keeping mechanical and thermal equilibrium between components of the medium. The linear kinetics of this transition is applied. The assessment of the model correctness is also performed in the paper. In the first step of the testing the model predictions were successfully verified with the reference data obtained numerically. Then the model was validated using reference data obtained experimentally. Finally, the influence of volumetric mass transfer coefficient between vapour and water as well as water and vapour in pores is investigated, i.e., kinetics of the vapour-water/water-vapour transition is analysed. During the model testing traditional building material were considered (i.e., ceramic brick). However, the model may be used for investigation of hygro-thermal behaviour of bio-based materials.

Numerical investigation of influence of the temperature and relative humidity of air on the drying process of porous building

The impact of the relative humidity and temperature of air on drying rates of the porous building material was investigated by the non-equilibrium heat and moisture transfer model implemented in the ANSYS Fluent software. Simulations of 24 hours drying process of a brick initially saturated in 97% by water were conducted for two drying air temperature, i.e., 23.8°C and 40°C and relative humidity in the range from 10% to 50%. The relative moisture content at the end of simulations and times needed to reach the relative moisture content bellow 0.3 were determined. Not only the temperature but also the relative humidity of drying air had impact on the drying rate during the first drying period when water evaporated from the sample surface. The temperature of drying medium was more important than the relative humidity during the second drying period when water evaporated inside the brick. The drying process was faster in the higher temperature than in the lower one, even for the high relative humidity.

Simulation of Nonequilibrium Heat Transfer in an Anisotropic Semispace Under the Action of a Point Heat Source

Based on a novel analytical solution of the problem of wave heat transfer in an anisotropic semispace under the action of a nonstationary point source of thermal energy, a study was made of a nonequilibrium thermal state of this space originating as a result of its delay (for the time of heat flux density relaxation) from the temperature gradient on the semispace surface. Based on the extended Vernotte–Cattaneo–Luikov hypothesis, a new law of wave heat transfer has been formulated having the form of the Fourier law, and a wave equation has been derived for heat transfer of parabolic type with a lagging argument in time equal to the relaxation time derived.

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

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

Influence of the Liquid Pressure on Collapse of a Vapor Bubble in Hot Acetone

Compression of the content of a vapor cavitation bubble during its collapse in hot acetone is studied. The temperature of liquid is 419 K, its pressure is varied in the range from 15 to 150 bar. A realistic model is used, in which the dynamics of vapor in the bubble and of the surrounding liquid is governed by the gas dynamics equations. The nonstationary heat conductivity of vapor and liquid, and the non-equilibrium heat and mass transfer across the bubble surface are taken into account. Wide-range equations of state are applied. It is shown that as the liquid pressure increases, three scenarios of the bubble content compression are successively realized. In the first scenario, the compression is nearly uniform. In the second and third scenarios, the bubble content is compressed by radially convergent isentropic and shock waves, respectively. The shock wave scenario, which arises starting with a pressure of about 90 bar, is realized in three versions.

Ексергетичні втрати в повітронагрівачі теплоутилізаційної системи котельної установки

Однією з причин зниження ефективності теплоутилізаційних систем та їх окремих елементів є втрати ексергетичної потужності. Такі втрати пов'язані з гідродинамічним опором при русі теплоносіїв, з незворотними процесами при теплообміні між теплоносіями, з процесами теплопровідності. Зниження втрат ексергетичної потужності дає змогу підвищити ефективність теплоутилізаційних систем. Це визначає актуальність робіт, присвячених вирішенню зазначеної проблеми. Для розрахунку втрат ексергетичної потужності в теплоутилізаційних системах та їх окремих елементах розроблено комплексну методику, яка поєднує ексергетичні методи з методами, побудованими на розрахунку дисипаторів ексергії. Розроблена методика дає змогу розділити втрати ексергетичної потужності згідно з причинами та зонами їх локалізації і виявити умови, за яких ці втрати будуть мінімальними. Основні етапи методики включають розробку математичної моделі досліджуваних процесів на основі рівняння ексергії, рівнянь балансів ентропії і ексергії, рівняння нерозривності, рівняння для внутрішньої енергії. У межах розробленої математичної моделі отримано диференціальні рівняння ентропії та ексергії і формули для розрахунку дисипаторів ексергії, що характеризують гідродинамічні втрати і втрати ексергетичної потужності внаслідок нерівноважного теплообміну між теплоносіями. Визначено значення дисипаторів ексергії для пластинчастого повітронагрівача теплоутилізаційної системи котельної установки за різних режимів роботи котла. Встановлено внесок кожного виду втрат у сумарні втрати ексергетичної потужності у повітронагрівачі і визначено область максимальних втрат цієї потужності.

Numerical Simulations of Flow-Assisted Mixed Convection in a Vertical Channel Filled with High Porosity Metal Foams

In this work, two-dimensional numerical simulations of flow-assisted mixed convection in a vertical channel filled with high porosity metal foams have been carried out by using the commercial ANSYS FLUENT. In order to enhance heat transfer, the vertical channel is filled with aluminum metal foams of different pores per inch (PPI). Four different metal foams PPI 10, 20, 30, and 45, with porosity values varying from 0.90 to 0.95 are considered in this study. The geometry under consideration consists of metal foam attached to the aluminum plate in the vertical channel and the resulting problem becomes conjugate heat transfer. The metal foam region is considered as a homogeneous porous medium with the Darcy Extended Forchheirmer model to evaluate the flow characteristics while the local thermal non-equilibrium heat transfer model is considered for the heat transfer analysis. Initially, numerical results are compared with the experimental results available in literature and the agreement was found to be good. Parametric studies show that as the metal foam PPI increases, the pressure drop increases, while the heat transfer is seen to increase with an increase in the pore density of the metal foam.

Thermal Non-Equilibrium Heat Transfer Modeling of Hybrid Nanofluids in a Structure Composed of the Layers of Solid and Porous Media and Free Nanofluids

The free convection heat transfer of hybrid nanofluids in a cavity space composed of a clear flow, porous medium and a solid part is addressed. The cavity is heated from the bottom and cooled from the top. The side walls are well insulated. The upper part of the cavity is a clear space with no porous or solid materials and is filled with hybrid nanofluid. The bottom part is divided into two parts of a porous space saturated with the hybrid nanofluid and a solid thermal conductive block. There are conjugate heat transfer mechanisms between the solid block and the porous medium filled with the hybrid nanofluid as well as the hybrid nanofluid in the clear space. For the porous medium model, the local thermal non-equilibrium effects are considered. The hybrid nanofluids contain copper (20 nm) and alumina nanoparticles (40 nm) hybrid nanoparticles. The governing equations for the flow and heat transfer of the hybrid nanofluid in the clear space and the porous medium are introduced. Considering the conjugate heat transfer between the solid block and the hybrid nanofluid fluid in the pores and the porous matrix, appropriate boundary conditions for heat channeling are utilized. The governing equations are transformed into non-dimensional form to generalize the model. The finite element method is employed to solve the equations. The grid check and validation procedure are performed. Subsequently streamlines, isotherms, and Nusselt number are studied as important aspects of flow and heat transfer in the cavity. The increase in the portion of the clear flow part in the cavity enhances heat transfer due to better hybrid nanofluid circulation.

Effect of thickness and thermal conductivity of metal foams filled in a vertical channel – a numerical study

PurposeThis paper aims to discuss about the two-dimensional numerical simulations of fluid flow and heat transfer through high thermal conductivity metal foams filled in a vertical channel using the commercial software ANSYS FLUENT.Design/methodology/approachThe Darcy Extended Forchheirmer model is considered for the metal foam region to evaluate the flow characteristics and the local thermal non-equilibrium heat transfer model is considered for the heat transfer analysis; thus the resulting problem becomes conjugate heat transfer.FindingsResults obtained based on the present simulations are validated with the experimental results available in literature and the agreement was found to be good. Parametric studies reveal that the Nusselt number increases in the presence of porous medium with increasing thickness but the effect because of the change in thermal conductivity was found to be insignificant. The results of heat transfer for the metal foams filled in the vertical channel are compared with the clear channel in terms of Colburn j factor and performance factor.Practical implicationsThis paper serves as the current relevance in electronic cooling so as to open up more parametric and optimization studies to develop new class of materials for the enhancement of heat transfer.Originality/valueThe novelty of the present study is to quantify the effect of metal foam thermal conductivity and thickness on the performance of heat transfer and hydrodynamics of the vertical channel for an inlet velocity range of 0.03-3 m/s.

A hyperbolic lattice Boltzmann method for simulating non-Fourier heat conduction

Classical lattice Boltzmann method (LBM) can recover Fourier's law. Since Fourier's law results in a parabolic heat conduction equation, the classical LBM is called the parabolic Boltzmann method (PLBM). But the Fourier’s law is based on the absurd assumption that the heat transfer rate is infinite, so whether the classical LBM can be used to observe the non-Fourier heat transfer problem remains controversial. In this paper, a hyperbolic lattice Boltzmann method (HLBM), which can be used to analyze the non-Fourier effect, was derived based on the Cattaneo-Vernotte (CV) model. To verify the accuracy of the HLBM, the process of a gold film irradiated by the laser was simulated using the HLBM and the PLBM and the results were compared with the experimental data. Because of the non-equilibrium heat transfer between electron and lattice during the laser irradiation, the two-step HLBM/PLBM models were proposed according to the two-temperature model. The results show that the electron temperatures simulated by the two models are not much different from each other, and both of them coincide with the experimental values. However, the thresholds obtained by the two models are different, and the results of HLBM are closer to the experimental values.

Two-Temperature Model and Simulation of Induced Electric Field During Combustion Synthesis of Zinc Sulfide in Argon

A two-temperature (2T) model is employed to analyze an electric field induced during the combustion synthesis of zinc sulfide under the two opposite gravitational conditions of the ascending and descending temperature combustion front motion. This model undertakes situations when the gas is always in a massive abundance, and therefore, the temperatures of the solid and gas phases do not have sufficient time to equilibrate thermally each other during the combustion front motion and generate conditions under which the assumption of one-temperature model of thermal quasi-equilibrium between the phases is no longer valid. The numerical study conducted in a comparison with the experimental results and 1T model shows that 2T model predicts more accurately quantitative values of electric charge density, gas pressure as well as generated voltage during the combustion at both descending and ascending directions of thermal front motions. This demonstrates the key role of non-equilibrium heat transfer for the combustion synthesis, while the temperatures of gas and solid are not equal. The predicted results of characteristic features of induced electric field are in a good agreement with the experimental data.

Microencapsulated phase change material (MEPCM) saturated in metal foam as an efficient hybrid PCM for passive thermal management: A numerical and experimental study

This article reported an efficient hybrid phase change material (PCM) for passive thermal management that integrated micro-encapsulated phase change material (MEPCM) and metal foam. This PCM composite was aimed to enhance the heat transfer of MEPCM, while avoid the leakage of molten phase change material (PCM). We proposed a two-energy equation model and experiment demonstration to investigate phase change heat transfer inside MEPCM/foam composite. The surface/internal temperatures, interface evolution and non-equilibrium heat transfer in the composite were discussed. Results showed that the pure MEPCM was not suitable for thermal management due to the low thermal conductivity. The wall temperature of the MEPCM/foam composite was only half of the pure MEPCM attributed to the latent heat absorption of MEPCM and thermal enhancement of metal foam. The higher porosity composite obtained higher surface temperature, and also consumed less time to start phase change due to the lower effective thermal conductivity. Besides, better thermal control was achieved by the MEPCM/foam composite with higher pore density attributed to its larger volumetric area. The employment of metal matrix made the internal temperature distribution more homogeneous and reduced the inside temperature gradient.

Heat transfer performance evaluation based on local thermal non-equilibrium for air forced convection in channels filled with metal foam and spherical particles

A local thermal non-equilibrium heat transfer analysis was conducted for air forced convection in channels filled with metal foam and particles. A general analytical expression was obtained for evaluating Nusselt numbers for the hydro-dynamically and thermal fully developed channel flows subject to constant heat flux, which can be used to investigate heat transfer performances of various porous media under equal pumping power. Such performance evaluations were made for aluminum metal foams of the porosity ranging from 0.85 to 0.95 and the pore diameter to channel half height ratio ranging from 0.01 to 0.20, and also for various packed aluminum particles of the diameter to channel half height ranging from 0.01 to 0.20. It has been found that the conventional local thermal equilibrium model leads to substantial overestimation of Nusselt number in the range of moderate pumping power, especially when the metal foam with large pore diameter is used to fill the channel. The analysis also revealed that in the moderate range of pumping power, the metal foam of comparatively low porosity performs better, while, in the high range of pumping power, the packed bed with large particle diameter gives higher heat transfer performance due to enhanced thermal dispersion.

Локально-неравновесный теплоперенос в анизотропном полупространстве под действием нестационарного точечного источника тепловой энергии

Локально-неравновесный теплоперенос в анизотропном полупространстве под действием нестационарного точечного источника тепловой энергии

Сollapse of weakly-nonspherical cavitation bubble in acetone and tetradecane

Collapse of a weakly-spherical cavitation bubble in acetone and tetradecane is studied. The bubble radius is 500 μm, the temperature and pressure of the liquid are 293 K and 15 bar in the case of acetone and 663 K and 50 bar in the case of tetradecane. A hydrodynamic model is used in which the compressibility of the liquid, the nonstationary thermal conduction of the vapor and the liquid, and nonequilibrium heat and mass transfer on the bubble surface, as well as imperfection of the vapor, are considered. Realistic wide-range equations of state are used. It has been found that converging shock waves appear in the bubbles during its collapses in acetone and tetradecane. The maximum values of the thermodynamic parameters are comparable. A comparison of the evolution of the bubble sphericity perturbation and motion of the shock wave in the bubble allows suggesting that tetradecane is a more favorable medium for the realization of a near-spherical cumulation in a bubble than acetone.

Non-isothermal slip flow over micro spherical particle at low Reynolds numbers

In present work, a numerical study was carried out to investigate the non-isothermal slip flow over a micro spherical particle at low Reynolds numbers. The slip boundary conditions (non-equilibrium momentum exchange and heat transfer) were adopted in the numerical model to predict the discontinuity phenomena at the gas-particle interface. It shows that the drag force acting on the particle and the average Nusselt number on the particle surface both decrease as the Knudsen number increases, which are caused by the effects of velocity slip and temperature jump on the gas-particle interface, respectively. As the particle temperature increases, the drag coefficient increases due to the increasing gas viscosity and the average Nusselt number decreases as the heat conduction becomes dominant at low Reynolds numbers. The influence of gas compressibility on the flow and heat transfer processes were studied based on the numerical predictions, which should be considered for the non-isothermal gaseous flow in the slip regime even if the Mach number is smaller than 0.3. And the effect of gas variable properties cannot be neglected as the temperature difference exists between the particle and gaseous fluid.