Non-equilibrium Heat Transfer Research Articles

Kinetic properties of a dendrite tip in a supercooled melt of pure metal.

High-speed dendritic growth of a crystal from a deeply supercooled pure metal melt is considered. The dendrite tip growth equation serves as the basis of the study, while local nonequilibrium heat transfer prop- erties have also been taken into account. The regularities of melt supercooling influence on the curvature of the apex behaviour and heat removal from the solid phase have been obtained. The interval limits of crystal- lization phase boundary aperiodic stability are calculated. A standing wave of perturbation of the dendrite tip has been studied: the periods of oscillations in coordinate and time have been determined, as well as the pat- terns of their behavior when the wave attenuation parameter changes have been indicated. The results of a comparative analysis of the dendrite tip kinetic properties for nickel and copper are presented

A novel identification method for the non-equilibrium heat transfer problem in porous material

A novel identification method for the non-equilibrium heat transfer problem in porous material

Lattice Boltzmann modeling of convective heat and solute transfer in additive manufacturing of multi-component alloys

Additive manufacturing (AM) is a remarkable breakthrough technology, allowing for the direct fabrication of three-dimensional components through the layer-by-layer stacking of materials. A novel free Surface lattice Boltzmann (LB) model is developed to simulate the heat and solute transfer in AM of multi-component alloys. The behavior liquid phase is described by using the free surface LB model, and the phase transitions between solid and liquid are modeled by using the LB-enthalpy method. A LB equation is directly constructed, which accounts for solute transfer in a certain multi-component alloys system. The thermodynamic information used in the calculation of phase transitions are determined by an extensive thermodynamic database. The model is validated via several benchmark examples of fluid flow and heat transfer. The characteristics of convective heat and solute transfer within various AM are investigated. Finally, the non-equilibrium convective heat transfer, phase transitions, and macroscopic segregation are discussed within the AM melt pools. The melt pool expands and convective heat transfer is enhanced by the Marangoni effect. Thus there is a consistent decrease in solute segregation. The solute segregation is more severe near the surface of the deposit layer. Additionally, the thermal convection experiences cyclic intensification attributed to the successive impact of multiple droplets in wire feeding and melting AM. This continuous impact serves to diminish the solute segregation. The results underscore the significant potential and advantages of LB method in accurately simulating the AM, which provides valuable insights for understanding the underlying mechanism of heat and solute transfer in materials and manufacturing.

Influence of boundary conditions on non-equilibrium heat transport under ultrafast laser action based on the lattice Boltzmann method

Based on the lattice Boltzmann method, this paper simulated the non-equilibrium heat transfer process in nano-silicon thin film under ultrafast laser irradiation. The influence of boundary conditions on heat transport was investigated. Results show that under rebound and diffuse boundary conditions, the energy distribution within the film is non-uniform due to interface effects. However, the specular boundary condition is equivalent to eliminating the interface, resulting in a smooth energy distribution. Under convective boundary conditions, the thermal wave phenomenon disappears owing to the open interface. When the energy tends to be stable, the energy density under convective boundary conditions is reduced to 50% of that under adiabatic boundary conditions. As the film size decreases, the differences between boundary conditions become more significant. Particularly when the film size is smaller than the phonon mean free path, the influence of boundary conditions cannot be neglected. Therefore, boundary conditions and size effects are important for the design of nanodevices. Furthermore, compared with the results obtained by the Cattaneo-Vernotte model, it is found that at smaller Knudsen numbers, the Cattaneo-Vernotte model has a better match with the lattice Boltzmann method.

Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions, which are linear to the nonlinear regime that prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities, a material energy density that is proportional to the radiation energy density, and a surface radiation temperature drive that obeys a temporal power law. The solutions are analyzed in detail, and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

Analysis of prediction methods for non-equilibrium internal flow condensation heat transfer

Due to the climate crisis, there is a need to improve the performance of energy conversion systems and increase the use of renewable energy sources. In this context, accurate performance prediction methods for heat exchangers, including condensers, are of crucial importance. In the heat transfer process in a condenser including desuperheating and subcooling, both sensible and latent heat transfer may occur simultaneously due to thermal non-equilibrium effects. Liquid condensate may form close to the vapor saturation point of the bulk flow in the desuperheating region, while superheated vapor may penetrate beyond the liquid saturation point far into the two-phase region, and gas bubbles and subcooled mixture may exist in the subcooled region. These are complex phenomena that to a large extent affect the performance of the condenser. This paper presents an analysis of the prediction methods for non-equilibrium condensation heat transfer. First, the heat transfer mechanisms of non-equilibrium condensation are discussed. Next, state-of-the-art prediction methods developed for the target heat transfer processes are analyzed. Moreover, a database containing all data available in the open literature is built to evaluate the predictive performance of the prediction methods. Finally, a new prediction method is proposed for the subcooled condensation based on the identified heat transfer mechanisms. The results suggest that the Jacob correlation has the best predictive performance, followed by the Kondou correlation. The mean absolute percentage errors of both the Jacob and Kondou prediction methods are lower than 15 %, and more than 85 % of the experimental data points are predicted with a deviation within ± 30 %. The new prediction method proposed for the subcooled condensation is in good agreement with the experimental data, with a mean absolute percentage error of 12 %.

New Analytical Solutions of Mathematical Models of Heat Shock of Local Non-Equilibrium Heat Transfer

The article is devoted to practically new model representations of locally nonequilibrium heat transfer in terms of nonstationary heat conduction for hyperbolic type equations (wave equations), as well as dynamic models of heat shock based on wave equations. The results presented in the article practically open up an independent scientific direction in analytical thermal physics and in the theory of thermal shock, namely: the study of the thermal response of solids of a canonical form of finite sizes to intense heating and cooling under conditions of a locally nonequilibrium heat transfer process. This direction required the development of a special apparatus of operational calculus due to the appearance in analytical solutions of model problems in the image space according to Laplace of non-standard operational images, the originals of which are unknown and are not available in reference books on operational calculus. The presented images are typical for operational solutions of a wide class of generalized boundary value problems for equations of hyperbolic type in the theory of heat conduction, diffusion, hydrodynamics, vibrations, propagation of electricity, thermomechanics and other areas of science and technology. Illustrative examples of analytical solutions of specific model problems of locally nonequilibrium heat transfer and the theory of thermal shock for a finite region are given in both classical and generalized formulations (the latter taking into account the finite rate of heat propagation). The characteristic features of functional structures as analytical solutions of the considered mathematical models are revealed.

New energy effect in non-cylindrical domains with a thermally insulated moving boundary

Objectives. To develop mathematical model representations of the energy effect in non-cylindrical domains having a thermally insulated moving boundary; to introduce a new boundary condition for thermal insulation of a moving boundary both for locally equilibrium heat transfer processes in the framework of classical Fourier phenomenology, as well as for more complex locally non-equilibrium processes in the framework of Maxwell–Cattaneo–Lykov–Vernott phenomenology, taking into account the finite rate of heat propagation into analytical thermophysics and applied thermomechanics; to consider an applied problem of analytical thermophysics according to the theory of thermal shock for a domain with a moving thermally insulated boundary free from external and internal influences; to obtain an exact analytical solution of the formulated mathematical models for hyperbolic type equations; to investigate the solutions obtained using a computational experiment at various values of the parameters included in it; to describe the wave nature of the kinetics of the processes under consideration.Methods. Methods and theorems of operational calculus, Riemann–Mellin contour integrals are used in calculating the originals of complex images with two branch points. A new mathematical apparatus for the equivalence of functional constructions for the originals of the obtained operational solutions, which considers the computational difficulties in finding analytical solutions to boundary value problems for equations of hyperbolic type in the domain with a moving boundary, is developed.Results. Developed mathematical models of locally nonequilibrium heat transfer and the theory of thermal shock for equations of hyperbolic type in a domain with a moving thermally insulated boundary are presented. It is shown that, despite the absence of external and internal sources of heat, the presence of a thermally insulated moving boundary leads to the appearance of a temperature gradient in the domain and, consequently, to the appearance of a temperature field and corresponding thermoelastic stresses in the domain, which have a wave character. A stochastic analysis of this energy effect forms the basis for a proposed transition of the kinetic energy of a moving thermally insulated boundary into the thermal energy of the domain. The presented model representations of the indicated effect confirmed the stated assumption.Conclusions. Mathematical models for locally nonequilibrium heat transfer processes and the theory of thermal stresses are developed and investigated on the basis of constitutive relations of the theory of thermal shock for equations of hyperbolic type in a domain with a thermally isolated moving boundary. A numerical experiment is presented to demonstrate the possibility of transiting from one form of analytical solution of a thermophysical problem to another equivalent form of a new type. The described energy effect manifests itself both for parabolic type equations based on the classical Fourier phenomenology, as well as for hyperbolic type equations based on the generalized Maxwell–Cattaneo–Lykov–Vernott phenomenology.

Investigating effects of pore-scale variables and pore geometries on the thermal behaviors of porous concretes

Thermal behaviors play significant roles in the design of porous concretes. However, the effects of pore geometries on microscopic thermal behaviors are not still well understood. This work aims to propose a microscopic analysis framework to construct different microstructure models and to study the effects of pore geometries on the thermal behaviors of porous concretes. The microstructures with pore and cement phases are generated using the random generation algorithm (RGA) and compared with realistic microstructures. Digital numerous simulations are conducted to investigate the temperate distribution and heat transfer properties in the pixelated microstructures. Pore-scale variables, such as pore fractal dimension, pore size and porosity, are defined to understand their effects on the thermal behaviors of concretes. Results show that the transient temperature variation behaviors occur in the microstructures, which may be caused by the non-equilibrium heat transfer in the transient time scale. The effective thermal conductivity (ETC) decreases with increasing the pore radius, circularity, porosity and pore number, and it increases as pore fractal dimension increases. The microstructures with square pores have the largest ETC than those microstructures with pentagon, hexagon, and circle pore geometries. Totally, the numerical ETC agrees well with the analytical ETC, showing the accuracy of the proposed microscopic analysis framework. The proposed microscopic concrete analysis framework can provide effective tools to the fire resistance design of concrete constructions used for the green buildings and deep projects such as the deep bury of nuclear wastes.

Numerical analysis on the energy efficiency improvement of thermo-injection method of masonry walls drying by applying the variable temperature profiles of drying air

The influence of the drying air temperature profile on the effectiveness of the thermo-injection masonry wall drying method was investigated by applying numerical modeling. The in-house non-equilibrium heat and moisture transfer model was used to perform simulations. A two weeks drying process was simulated. Four drying strategies characterized by constant, jump, stepwise, and periodic drying air temperature profiles were studied and compared. Three different heating intervals (i.e., 12, 24, and 48 h), which referred to drying air temperature profile changes, were examined. The drying air temperature varied between 20 and 60 °C. Moreover, the relative humidity of the drying air corresponded to the three seasons in Poland, i.e., winter, spring, and summer, and ranging between 70 and 90% at ambient conditions. It was found that drying strategies with the jump and stepwise temperature profiles may decrease the energy consumption required for masonry wall drying by up to 5.9% during the season with a low drying air relative humidity (i.e., during winter). However, energy savings were insufficient during the highly humid season (i.e., summer). The heating interval of 48 h was the best for the jump strategy and may be the best for the stepwise approach in a longer than two weeks drying process. The stepwise strategy removed significantly more water from the wall to reach the same level of moisture mass fraction in the drying zone as the constant and jump strategies. The slower wall heating process and the continuous action of capillary water uptake were responsible for this behavior. The same phenomena caused the periodic strategy to be ineffective.

Developing generalized model representations of thermal shock for local non-equilibrium heat transfer processes

Objectives. Processes of energy transfer in solids and resultant thermal loads are widespread in nature and technology. This explains the scientific and practical significance of constructing a theory of these processes, as well as developing effective methods for studying the modeled concepts developed on this basis. The purpose of such studies is to determine basic flux patterns of complex processes occurring especially under conditions of powerful energy impacts in various technological operations. These include plasma-chemical processing of materials, their processing in infrared furnaces and solar plants, intense heating of materials carried out by laser or electron beams, and the use of powerful radiation emitters for thermal hardening and hardening of the surface of products. In these cases, the phenomenon of thermal shock arises, forming one of the central topics in thermomechanics and strength physics of solids. The present work considers an open theoretical problem of thermal shock in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process. Depending on the type and curvature of the boundary surface of the considered massive body, the model can be used to study the problem in 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 are considered: temperature heating, thermal heating, and heating by medium. Following the development of an analytical solution, the results of conducted numerical experiments are presented along with their physical analysis.Methods. The study applies methods and theorems of operational calculus according to the theory of special functions.Results. Generalized model representations of thermal shock are developed in terms of dynamic thermoelasticity 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.Conclusions. 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 temperature heating, thermal heating, and heating by medium is proposed. The model is considered in terms of displacements based on local nonequilibrium heat transfer. A numerical experiment carried out according to the obtained analytical solution for stresses forms a basis for a description of the wave nature of the propagation of a thermoelastic wave. A comparison with the classical solution is made without taking into account local nonequilibrium. The calculation of engineering relations carried out on the basis of the operational solution of the problem is important in practical terms for the upper estimate of the maximum thermal stresses.

Experimental analysis of heat transfer characteristics of static water pool under low pressure vaporization

Low pressure vaporization (LPV) is considered a promising method for rapid cooling and a significant rate of water vaporization. This article presents an experimental investigation for the detailed heat and mass characterization of a static water pool exposed to low pressure conditions. An LPV experimental setup has been fabricated in the lab to investigate the effect of process parameters like initial temperature (Tw,0), initial vacuum tank pressure (Pv,0), and the water pool height (Hw,0) on the non-equilibrium fraction (NEF) and heat transfer coefficient (hv). Results shows that NEF initially increased to a high value and then tediously dropped. The final value of NEF decreased with decreasing the initial vacuum tank pressure and initial water pool height inside the flash chamber. A maximum value of the hv existed with the rise of the degree of superheat (ΔT) of liquid. It is found that with an increase of the degree of superheat by 13.44 °C, the value of hv is enhanced by 67%, and the NEF decreased by 46.7%, respectively.

THREE TEMPERATURE MODEL FOR HEAT AND MASS TRANSFER IN NON-NEWTONIAN Cu-EG NANOFLUIDS EMBEDDED WITH PERMEABLE MEDIUM

In the current study, the impacts of local thermal non-equilibrium model and Cu-EG Oldroyd-B nanofluid layer on natural convective heat and mass transfer in a permeable medium are investigated. The transport equations are framed using modified Buongiorno two-phase Darcy model with different temperature profiles for fluid, particle, and porous-matrix phases. The thermophysical properties of the considered nanofluid are calculated using available experimental data. In the current situation, weak, non-linear analysis has been performed to find the Nusselt number and Sherwood number by solving finite amplitude equations using NDSolve in Mathematica 12.0. Influence of different parameters including viscoelastic parameters, LTNE parameters, thermal Rayleigh number, and nanoparticle volume fraction on heat and mass transfer mechanisms are explained graphically. An increase in the Nusselt number with the rising values of volume fraction of nanoparticles is registered and reach its maximum value at φ = 0.05 due to enhanced thermal conductivity. The significant findings for Oldroyd-B nanofluids are that the stress relaxation parameter declines heat transfer while strain retardation parameter promotes it. This study improves the theoretical understanding of heat transfer in porous media and facilitates the use of such theoretical models in practical applications.

Research on heat transfer properties of graphene composites

Abstract Graphene is a new type of two-dimensional carbon material with excellent mechanical strength, high thermal conductivity, high light transmittance and high specific surface area. Its excellent performance makes it suitable for high-performance electronic devices, composite materials, gas sensors and energy storage and other fields, and has broad application prospects, especially its ultra-high thermal conductivity has attracted great interest of scholars at home and abroad. In this study, the heat transfer theory and the heat transfer mechanism of graphene are firstly cited, and three commonly used composite heat transfer fitting models are proposed. Advantages and disadvantages of measurement methods are described. According to the aforementioned theoretical basis, the equilibrium molecular dynamics and non-equilibrium molecular dynamics heat transfer models were used to fit graphene and its composites, and the thermal conductivity of graphene composites was analysed. Finally, the future research directions of graphene thermal conductivity are prospected.

Highly Thermally Conductive Bimorph Structures for Low-Grade Heat Energy Harvester and Energy-Efficient Actuators.

Low-power electronics are urgently needed for various emerging technologies, e.g., actuators as signal transducers and executors. Collecting energy from ubiquitous low-grade heat sources (T < 100 °C) as an uninterrupted power supply for low-power electronics is highly desirable. However, the majority of energy-harvesting systems are not capable of collecting low-grade heat energy in an efficient and constant manner. Limited by materials and driving mode, fabrications of low-power and energy-efficient actuators are still challenging. Here, highly thermally conductive bimorph structures based on graphene/poly(dimethylsiloxane) (PDMS) structures have been fabricated as low-grade heat energy harvesters and energy-efficient actuators. Regular temperature fluctuations on bimorph structures can be controlled by nonequilibrium heat transfer, leading to stable and self-sustained thermomechanical cycles. By coupling ferroelectric poly(vinylidene fluoride) with bimorph structures, uninterrupted thermomechanoelectrical energy conversion has been achieved from the low-grade heat source. Utilizing the rapid thermal transport capability, multifinger soft grippers are assembled with bimorph actuators, demonstrating fast response, large displacement, and adaptive grip when driven by low-temperature heaters.

Numerical investigation on melting behaviour of phase change materials/metal foam composites under hypergravity conditions

The integration of electronic devices in aerospace vehicles leads to a significant increase in the heat dissipation, which makes thermal management a severe challenge. Due to the high thermal energy storage capacity and the excellent thermal diffusivity, phase change materials (PCM)/metal foam composite is a potential thermal management material. In order to deepen the understanding of melting behaviour of PCM/metal foam under hypergravity, the numerical model considering natural convection, flow resistance of metal foam, and non-equilibrium heat transfer is proposed, and the effects of inclination angle, hypergravity value, metal foam porosity, and pore density on the melting are analyzed. It shows that the inclination angle has a great influence on the morphology of the melting interface, while has limited influence on the variation of PCM liquid fraction. As the inclination angle changes from 0° to 180°, the heated wall temperature first decreases, and then increases after reaching the lowest value at 45°, which is the optimal inclination angle. With the rise of hypergravity value, natural convection is enhanced, the heated wall temperature is reduced, while the hypergravity value has limited effect on the PCM liquid fraction. Furthermore, with the increase of metal foam porosity, natural convection is enhanced, while the heated wall temperature and the melting time become larger. When the porosity is larger than 0.95, the effect of metal foam on natural convection suppression is greater than that of heat conductivity enhancement, leading to that the performance of PCM/metal foam is worse than that of the pure PCM. Besides, with the decrease of pore density, natural convection is enhanced, the heated wall temperature becomes lower. Therefore, metal foam with lower pore density is preferred. This paper provides guidance to the optimal design of PCM-based heat sink for aerospace applications.

Effects of chemical energy accommodation on nonequilibrium flow and heat transfer to a catalytic wall

The accurate prediction of the aeroheating performance of hypersonic vehicles requires more detailed modeling of the catalysis process, rather than merely employing a catalytic coefficient. In this paper, the theoretical modeling, as well as the direct simulation Monte Carlo method, is used to preliminarily study the incomplete chemical energy accommodation effects, that is, only a part of the potential energy released in the heterogenous recombination reaction is transferred to the surface, while the remaining is retained as the vibrational energy of the desorbed molecule. An integrated model is proposed to describe the contribution of each energy mode in the rarefied nonequilibrium heat and mass transfer process. Based on the model and several Damköhler numbers, an analytical formula is derived, and is also shown to compare well with the numerical results. On account of the incomplete accommodations of the chemical and vibrational energy on the wall, a variation up to 20% is observed in predicting the stagnation point heat flux under typical nonequilibrium flow conditions. This study could enrich our understanding of the nonequilibrium heat transfer phenomenon and also shows a potential practical value.

New operational relations for mathematical models of local nonequilibrium heat transfer

Objectives . Recently, interest in studying local nonequilibrium processes has increased in the context of the development of laser technologies, the possibility of reaching ultrahigh temperatures and pressures, and the need for a mathematical description of various physical processes under extreme conditions. In simulating local nonequilibrium processes, it becomes necessary to take into account the internal structure of investigation subjects, which significantly complicates the classical transport models. An important stage here is to construct mathematical models of various physical fields in which their spatiotemporal nonlocality should be taken into account. For these purposes, hyperbolic equations are used for a wide class of phenomena and, first of all, for unsteady-state heat conduction processes based on the generalized Maxwell–Cattaneo–Luikov–Vernotte phenomenology. Mathematical models in the form of boundary value problems for hyperbolic equations are called generalized boundary value problems. These problems differ significantly in solving difficulty from the classical ones based on Fourier phenomenology. The specificity of these problems is the relative simplicity of the initial mathematical models, together with the difficulty of solving them in an analytically closed form. Hence, very little success has been achieved in finding exact analytical solutions to problems of this kind. The most acceptable approach to solving them is operational calculus. However, it gives analytical solutions in the Laplace transform space as complex functional structures, the inverse transforms of which are not available in well-known reference books on operational calculus. On this path, serious computational difficulties arise. The study aimed to analyze a set of nonstandard transforms arising from the operational solution of mathematical models of local nonequilibrium heat transfer and to obtain their inverse transforms. Methods . Methods and theorems of operational calculus, methods of contour integration of complex transforms, and the theory of special functions were used. Results . Operational calculus was developed for mathematical models of local nonequilibrium heat transfer in terms of the theory of unsteady-state heat conduction for hyperbolic equations (wave equations). Nonstandard operational transforms, the inverse transforms of which are unavailable in the literature, were considered. It was shown that the presented transforms are common to operational solutions of a wide class of generalized boundary value problems for hyperbolic equations in the theory of heat conduction, diffusion, hydrodynamics, vibrations, propagation of electricity, thermomechanics, and other areas of science and technology. Partially bounded and finite domains were explored. Illustrative examples were given, namely, the results of numerical experimental studies of a local nonequilibrium heat transfer process that took into account the finiteness of the heat transfer rate, which had a wave character. The latter was expressed by the presence of the Heaviside step function in the analytical solution of the problem. The physical meaning of the finiteness of the heat transfer rate was substantiated. The isochron was constructed for the temperature function in a partially bounded domain. It was shown that the temperature profile has a discontinuity on the surface of the propagating wave front. This leads to the retention of heat outflow beyond the discontinuity boundary. This is a characteristic feature of the analytical solutions of the wave equations, along with the possibility to describe the analytical solution of the problem as equivalent integral relations, which noticeably simplify numerical calculations. Conclusions . The inverse transforms of nonstandard operational (Laplace) transforms were presented, which are contained in the operational solutions of a wide class of problems of local nonequilibrium (heat, mass, momentum) transfer processes, electrical circuits, hydrodynamics, oscillation theory, thermomechanics, and others. Illustrative examples were given, and the possibility of transition from one form of an analytical solution to another equivalent form was shown. The presented analytical solutions of hyperbolic heat transfer models in canonical domains are new in classical thermal physics.

Generalized Bio-Heat Transfer Model Combining With the Relaxation Mechanism and Nonequilibrium Heat Transfer

Abstract The heat transport within living biological tissue is a complicated process coupled with various physiological activities. The nonhomogeneous inner anatomical structure leads to an essential difference from classical heat transfer. The generalized model of bioheat transfer involving the relaxation mechanism as well as nonequilibrium heat transfer is first proposed to explore the heat transport properties within living biological tissues. Due to the volume averaging theory, the new local instantaneous energy equations of blood and tissue are constructed separately by introducing the phase lags, in which the delay effect between the heat flux and temperature gradient absent in existing generalized models is considered. The effective phase lags covering the delay effect and nonequilibrium effect are obtained on this basis. A detailed parametric study has been conducted to estimate the values of these effective phase lags and evaluate their contributions on heat transport within living biological tissues. The results state that the effective phase lags depend on the anatomical structure of tissues and its physical properties. The delay effect is dominated in general and has a higher temperature elevation than that induced by nonequilibrium effect only.

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.