Semi-infinite Body Research Articles

Finite-displacement elastic solution due to a triple contact line

At the line of triple contact of an elastic body with two immiscible fluids, the body is subjected to a force concentrated on this line, the fluid–fluid surface tension. In the simple case of a semi-infinite body, limited by a plane, a straight contact line on this plane, and a fluid–fluid surface tension normal to the plane, the classical elastic solution leads to an infinite displacement at the contact line and an infinite elastic energy. By taking into account the body–fluid surface tension (i.e., isotropic surface stress) and applying Kolosov’s approach of plane strain elasticity, we present a new and simple expression of the solution concerning the semi-infinite body, which gives a finite displacement and a ridge at the contact line, and finite elastic energy. A detailed description of the displacements, strains, and stresses in the neighborhood of the contact line is given. This solution also shows that Green’s formulae, in the volume and on the surfaces, are valid (these formulae play a central role in the theory).

Observation of Near-Field Thermal Radiation between Coplanar Nanodevices with Subwavelength Dimensions.

With the continuous advancement of nanotechnology, nanodevices have become crucial components in computing, sensing, and energy conversion applications. The structures of nanodevices typically possess subwavelength dimensions and separations, which pose significant challenges for understanding energy transport phenomena in nanodevices. Here, on the basis of a judiciously designed thermal photonic nanodevice, we report the first measurement of near-field energy transport between two coplanar subwavelength structures over temperature bias up to ∼190 K. Our experimental results demonstrate a 20-fold enhancement in energy transfer beyond blackbody radiation. In contrast with the well-established near-field interactions between two semi-infinite bodies, the subwavelength confinements in nanodevices lead to increased polariton scattering and reduction of supporting photonic modes and, therefore, a lower energy flow at a given separation. Our work unveils exciting opportunities for the rational design of nanodevices, particularly for coplanar near-field energy transport, with important implications for the development of efficient nanodevices for energy harvesting and thermal management.

Free-surface proximity induced bistability and semi-semicoherency in precipitation systems

In systems without a ‘high misfit’ and in the early stage of growth, the precipitates tend to remain coherent with the parent matrix. On further growth beyond a critical size (r*), the precipitates undergo a coherent to semi-coherent transition by formation of interfacial misfit dislocation loops to minimize the total strain energy of the system. The variation of r* with domain size has been studied and the concept of re-entrant interface transition to the coherent state was demonstrated in finite crystals. Dislocations can exist in a state of mechanical equilibrium; but are thermodynamically metastable. In the proximity of ‘interfaces’ dislocations experience a configurational force. The current work pertains to study the stability of an interfacial misfit dislocation loop in the proximity of a free-surface; wherein we evaluate configurational effects in a semi-infinite body. The Cu-2 wt%γFe alloy is used as a model system in this study. In this work we: (i) demonstrate the stabilization of the coherent state (divergence of r*), induced by the proximity of the free-surface; (ii) discover the existence of bistability in materials at the microstructural scale, resulting from the destabilization of the equatorial position of the dislocation loop and arising from symmetry breaking in climb of the interfacial loop due to the vicinity of a free-surface. (iii) identify regimes of ‘equi-bistablity’ and regions with asymmetry in energy wells, (iv) establish the existence of a ‘semi’-semicoherent state. Here, one specific system has been chosen to illustrate the effects; however, we expect the conclusions to have a broader applicability.

Surface–dislocation interaction by various models of surface elasticity

The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundary conditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed form for the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to the decrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.

Force impact of a flow of an infinitely deep liquid on a source under ice cover

A characteristic natural factor of the polar regions of the World Ocean and freezing sea areas is the presence of ice cover. The floating ice cover, which determines the dynamic interaction between the ocean and the atmosphere, affects the dynamics of not only the sea surface, but also subsurface waters, while both the ice cover and the entire mass of liquid beneath it participate in the general vertical movement. It is assumed that the ice cover is continuous, that is, its horizontal scales exceed the lengths of the excited waves and, under fairly natural conditions, is modeled by a thin elastic plate, the deformations of which are small and the plate is physically linear. The problem of calculating the force impact of a flow of an infinitely deep homogeneous liquid on a localized source under the ice cover is solved. The problem is solved for the two-dimensional case. Integral representation of the solution for wave drag and lift is obtained, which arise due to the presence of an ice cover and act on the source. The results of calculations of the force action acting on a localized source, simulating a blunt semi-infinite body of finite width, and a dipole, simulating a cylinder, are presented for various values of the oncoming flow velocity and their immersion depth. Numerical calculations show that as the depth of the source immersion increases, the force effect of the fluid flow, which occurs due to the presence of an ice cover, decreases. The dependences of the wave resistance and lift force on the velocity of the incoming fluid flow demonstrate a qualitatively different behavior. The obtained results with different values of the physical parameters included in them make it possible to evaluate the characteristics of ice cover disturbances and its impact on various sources of natural and anthropogenic disturbances observed in real marine conditions.

The role of thermal effusivity on the incipient growth of the surface temperature in a semi-infinite region absorbing heat flux at the surface

Heat conduction theory stipulates that two thermo-physical properties of materials: the thermal conductivity “k” and the thermal diffusivity “ ” influence the temperature evolution in regular and irregular bodies as a response to various cooling/heating conditions. The traditional statement involving the two thermo-physical properties is examined at length in the present study for the case of a semi-infinite region. The primary objective of the present study is to investigate the influence of the less known thermo-physical property called the thermal effusivity “e” on the incipient surface temperature raise in a semi-infinite body affected by uniform surface heat flux. The secondary objective of the study is to identify a key figure-of-merit named the dimensionless threshold time that separates the incipient temperature elevation in a semi-infinite region from the incipient temperature elevation in a large wall of finite thickness under the same uniform surface heat flux. The outcome of the methodical analysis suggests that the accurate estimate for the dimensionless threshold time in the semi-infinite region should be 0.10.

Temperature Field Modelas a Factor to Improve a Horizontal Ground Heat Exchanger of a Heat Pump System: Review of Scientific Approaches and the Content of the Analytical Model

The article is devoted to the research of issues related to the organization of control systems for heat pump installations (HPS). HPS is used to use low-potential energy of the environment in the heat supply of buildings. HPS with horizontal ground heat exchangers (HGHE) are of great importance for improving energy efficiency. The efficiency and reliability of HPS with HGHE strongly depends on the state of the soil temperature field. A large number of scientific publications are devoted to modeling soil temperature fields forHGHEparameterdetermination; a significant part of them is devoted to the study of vertical ground heat exchangers. Scientific developments presented in foreign publications on modeling the temperature field of the HGHE location environment are focused on the use of HPS in the cold supply mode and/or in the heat supply mode under conditions of a slight decrease in temperature, which excludes soil freezing. The aim of the study was to apply the existing methods of the analytical theory of thermal conductivity to develop a soil-environment TP model for the placement of a HGHE HPS; the developed model is intended for engineering calculations of the main design HGHEparameters; the model is also applicable to determine the annual specific heat flow as an important parameter in the optimal control system of the HPI. The development of the model is based on the condition of a two-element structure of the soil massif: under the HGHE and above the HGHE; the target parameter is the temperature of the soil mass, depending on the coordinate and time, disclosed through the indicator 'relative temperature rise'; in accordance with the provisions of the thermal conductivitytheory, the relative excess temperature is given for the cases of a semi-infinite body (soil mass under the HGHE) and a slab (soil mass above the HGHE). The proposed model is implemented on the example of two constituent entities of the Russian Federation. The results obtained made it possible to determine the minimum guaranteed possibility of using HPS for heat supply in these climatic conditions. The model presented in the article can be used as a context for further studies of the main parameters of HGHE HPS operation and optimization of HPS operation modes.

(Invited) Multiscale Diffusion-Reaction Heat Transfer Analysis for Predicting Thermal Runaway in Li-Ion Cells and Battery Packs

Thermal runaway in Li-ion cells and battery packs remains a topic of much importance for ensuring the safety of electrochemical energy conversion and storage systems. Thermal runaway also indirectly affects performance, as conservative overdesign to reduce the risk of thermal runaway affects system-level performance metrics such as energy storage density. Given the considerable challenges in experimental investigation of thermal runaway, theoretical models to predict thermal runaway characteristics of a cell or battery pack are critically needed. Such models can help guide the design of experiments, and ensure that practical systems are reasonably safe without being needlessly overdesigned.This talk will summarize ongoing work on theoretical analysis of multilayer diffusion-reaction heat transfer problems for predicting thermal runaway in Li-ion cells and battery packs. Following a linearization of heat generation terms, the governing energy conservation equation is solved in a multilayer geometry representative of a Li-ion cell comprising multiple electrode and separator layers, or of a battery pack containing several cells. It is mathematically shown that under certain conditions, this problem may admit a finite number of imaginary eigenvalues, which are shown to cause thermal runaway. It is shown that the occurrence of imaginary eigenvalues is governed by a delicate balance between heat generation, thermal conduction within the multilayer body and heat removal from the boundaries, based on which, an explicit threshold condition for thermal runaway is derived. This threshold condition is interpreted in the context of parameter values relevant to Li-ion cells. For example, it is shown that boundary cooling is severely limited in its role to prevent thermal runaway, whereas improving thermal transport within the cell is likely to be a lot more effective. This theoretical model is also extended to a two-layer problem comprising a finite layer adjoined by a semi-infinite body that may model immersion cooling of a Li-ion cell or battery pack. It is shown that while this diffusion-reaction problem is, in principle, unconditionally unstable, the finite time period of any discharge process may allow the temperature field to still remain within a safe envelope, if designed appropriately. Based on this mathematical model, scenarios related to immersion cooling of pouch cells are investigated.The theoretical work described in this talk is broadly relevant to several diffusion-reaction systems. In the particular context of Li-ion cells, these results may form the foundation of techniques to proactively predict and prevent thermal runaway in Li-ion cells and battery packs.

Water displacement drag decomposition of aircraft elastic tires rolling on contaminated runways

During the taxiing of an aircraft on a water-contaminated runway, the rolling tires impact water film resulting in a considerable water displacement drag and a large amount of spray, which will affect the safety of take-off and landing. The characteristics and flow mechanism of the water displacement drag generated by an elastic tire are numerically studied based on the coupling method of Smoothed Particle Hydrodynamics and Finite Element Method. The water displacement drag is divided into wave-generated drag and film-generated drag based on flow mechanism for the first time, and the former is much larger than the latter. The water displacement drag satisfies the Gaussian distribution along the rotation axis. The longitudinal grooves cause a significant increase in the wave-generated drag and a reduction in the film-generated drag. A simple potential flow model around a semi-infinite bluff body is proposed to reveal the flow physics of film-generated drag. Two drag formulas are proposed to quickly predict the wave-generated drag and film-generated drag.

Magneto-thermoelastic problem of semi-infinite body considering non-local and memory effects under hydrostatic pressure

Magneto-thermoelastic problem of semi-infinite body considering non-local and memory effects under hydrostatic pressure

Simultaneous estimation of reference temperature and heat transfer coefficient in transient film cooling problems

This paper aims to simultaneously estimate the reference temperature and heat transfer coefficient in film cooling situations from transient temperature measurements. The exist-ing steady-state technique is a tedious process and employs distinct boundary conditions to evaluate each parameters of the film cooling. Applying different boundary conditions may lead to errors in the estimated parameters due to differences in aerodynamic condi-tions. On the other hand, a transient technique can estimate both parameters in a single test by utilizing short-duration transient temperature data. Hence, the present study uses a novel approach for solving transient film cooling problems based on the inverse heat con-duction approach, which can simultaneously estimate heat transfer coefficient and refer-ence temperature. The present method employs an optimization technique known as the Levenberg-Marquardt Algorithm. The objective function for the inverse algorithm is con-structed using the analytical solution of a transient one-dimensional semi-infinite body. The transient surface temperature data required for the present analysis is obtained through a numerical simulation of film cooling arrangement over a flat surface. Laterally averaged effectiveness and heat transfer coefficient for blowing ratios of 0.5, 0.8, and 1.0 are analyzed using the present technique and compared against the steady-state simulation results to demonstrate the methodology. An average deviation of around 7% for the estimated effec-tiveness and 4% for the heat transfer coefficient values are observed between the present IHCP method and the steady state simulation results. The deviation in heat transfer coeffi-cient predominately occurred near the film hole exit of x/d < 5, which might have occurred due to the conjugate solution employed in the present work.

Simultaneous estimation of reference temperature and heat transfer coefficient in transient film cooling problems

This paper aims to simultaneously estimate the reference temperature and heat transfer coefficient in film cooling situations from transient temperature measurements. The exist-ing steady-state technique is a tedious process and employs distinct boundary conditions to evaluate each parameters of the film cooling. Applying different boundary conditions may lead to errors in the estimated parameters due to differences in aerodynamic condi-tions. On the other hand, a transient technique can estimate both parameters in a single test by utilizing short-duration transient temperature data. Hence, the present study uses a novel approach for solving transient film cooling problems based on the inverse heat con-duction approach, which can simultaneously estimate heat transfer coefficient and refer-ence temperature. The present method employs an optimization technique known as the Levenberg-Marquardt Algorithm. The objective function for the inverse algorithm is con-structed using the analytical solution of a transient one-dimensional semi-infinite body. The transient surface temperature data required for the present analysis is obtained through a numerical simulation of film cooling arrangement over a flat surface. Laterally averaged effectiveness and heat transfer coefficient for blowing ratios of 0.5, 0.8, and 1.0 are analyzed using the present technique and compared against the steady-state simulation results to demonstrate the methodology. An average deviation of around 7% for the estimated effec-tiveness and 4% for the heat transfer coefficient values are observed between the present IHCP method and the steady state simulation results. The deviation in heat transfer coeffi-cient predominately occurred near the film hole exit of x/d < 5, which might have occurred due to the conjugate solution employed in the present work.

An alternative post-processing of transient liquid crystal experiments using the wall temperature gradient time response

An alternative method for the fast evaluation of transient liquid crystal experiments is presented in this study. The calibration of liquid crystals has been considered essential to obtain accurate heat transfer measurements. Nevertheless, liquid crystal aging, illumination, and ex situ calibration effects remain a difficult and might influence the heat transfer level. Proposed here is to bypass liquid crystal calibration by utilizing the evolution of the wall temperature gradients. This necessitates the use of the detection times of the maximum red and green intensities of narrow bandwidth liquid crystals, e.g., less than 1 K, whose temperature span is on the order of 0.3 K. The calculation of the heat transfer coefficients can be thus feasible by differentiating the wall temperature from the solution of the semi-infinite body approach with respect to time. This approach is examined over different experiments with varying geometries and liquid crystal detection times. The in-advance possession of the calibration curves of the liquid crystals allows for the method’s cross-evaluation. The results indicate that the proposed method is in sufficiently good agreement with the values obtained using the calibrated liquid crystal signals. In particular, the average heat transfer coefficient of a surface is within 8% from the traditional method which is sufficient for industrial applications and preliminary thermal designs.

Mathematical Model of Heat Conduction for a Semi-Infinite Body, Taking into Account Memory Effects and Spatial Correlations

One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to an ordinary continuous medium, a randomly wandering particle moves away from the reference point more slowly since not all directions of motion become available to it. The slowdown of the diffusion process in fractal media is so significant that physical quantities begin to change more slowly than in ordinary media.This effect can only be taken into account with the help of integral and differential equations containing a fractional derivative with respect to time. Here, the problem of heat and mass transfer in media with a fractal structure was posed and analytically solved when a heat flux was specified on one of the boundaries. The second initial boundary value problem for the heat equation with a fractional Caputo derivative with respect to time and the Riesz derivative with respect to the spatial variable was studied. A theorem on the semigroup property of the fractional Riesz derivative was proved. To find a solution, the problem was reduced to a boundary value problem with boundary conditions of the first kind. The solution to the problem was found by applying the Fourier transform in the spatial variable and the Laplace transform in time. A computational experiment was carried out to analyze the obtained solutions. Graphs of the temperature distribution dependent on the coordinate and time were constructed.

Heat flux during a drop train impact in the drop rebound regime

The focus of this study is on the heat flux during cooling of a hot substrate by an impacting monodisperse drop train. Such a drop train is used for achieving high heat flux densities over small surfaces. The temperature inside the substrate is measured with high temporal and spatial resolution using thermocouples. Furthermore, a new analytical model has been developed to describe and predict the transient cooling and temperature of a semi-infinite body by the impacting drop train, assuming a single point heat sink on the surface. The experimental data agree very well with the theoretical predictions for various drop train frequencies.

Analytical solution of three-dimensional particle transport in porous media considering a dual deposition mode

Based on the classical one-dimensional particle transport model, a three-dimensional particle transport model with a dual deposition mode considering sieving and adsorption effects was established. Through Laplace and Fourier transforms, general solutions for particle transport in saturated semi-infinite porous media under one-dimensional seepage and three-dimensional dispersion conditions were derived. According to the basic solution in the case of a point source injection on the surface of a semi-infinite body, the analytical expression in the case of a circular surface source injection was obtained by the integration method. The analytical solution is verified using two well-established numerical simulation solvers. The influence of parameters such as the hydrodynamic dispersion coefficient, sieving coefficient, adsorption coefficient, and desorption coefficient, on the mechanism of the particle transport process was analyzed under the conditions of constant concentration and circulating concentration injection of the circular surface source. The results showed that the hydrodynamic dispersion effect accelerated the transport of particles, shortened the breakthrough time, and increased the peak concentration. Moreover, a larger sieving coefficient and particle adsorption coefficient meant a smaller particle release coefficient, and more particles deposited on the solid matrix with a smaller peak particle concentration in the pores.

Analysis of face stability at the launch stage of shield or TBM tunnelling using a concrete box in complex urban environments

An emerging construction method using a concrete box can effectively reduce the risks such as face collapse and extrusion at the launch stage of shield or tunnel boring machine (TBM) tunnelling. It occupies a small construction plant and can be applied to complex urban environments, especially in mountainous cities. However, the failure mechanisms of the tunnel face at the launch stage of the novel method are still not properly understood. Based on the upper-bound theorem of the limit analysis (LA), two multi-block failure models are proposed in this work for tunnelling launch in semi-infinite body and in areas with slope overburden. The limit equilibrium (LE) method is used to obtain the vertical earth pressure of upper finite soil mass considering the soil arching effect. The comparisons of the support pressure, failure zone and dip angle of the slip surface obtained from the proposed models with the results of numerical simulations and previous studies indicate that the proposed approach provides realistic and satisfactory predictions. The effects of soil cohesion, internal friction angle, slope dip angle, reduction coefficient and the ratio of tunnel diameter to overburden width are further assessed. The proposed models were applied to two practical engineering cases to determine reinforcement measures using grouting and pipe-roof methods required during the tunnelling launch, and were demonstrated to be able to provide useful guidance for the practical operations.

Method of analyzing coating structure under conical concave contact

The evaluation of mechanical performance for a coating structure is important in the fields of mechanics and materials. The exact solutions of the contact mechanics for transversely isotropic elasticity coating structures under conical concave contact are presented in this paper. Based on the Green's function of semi-infinite bodies, the Green's function of coating structure is obtained with mirror image method. The exact solutions obtained indicates the displacement and stress at any position of the coating, substrate, and interface, which provide the code basis for the analysis of interface failure and determination of material parameters in numerical analysis software. This paper presents exact solutions in the elastic stage, and there are stress singularities in the contact center and contact boundary, which provide a reference for future research on the relationships between stress singularities and plastic mechanical behavior.

Viscoelastic analysis of surface deformation above salt caverns for gas storage based on semi-infinite space

The construction of salt caverns for energy storage is of strategic significance, but the operation of underground gas storages in salt formations will cause surface deformation. The research and analysis of surface deformation is an important part of the stability evaluation of salt caverns for gas storage. From the perspective of classical mechanics theory, the analytical solution of surface deformation above salt caverns for gas storage is deduced. The surface displacement caused by the contraction of a salt cavern is regarded as the boundary displacement caused by the surface force acting on a spherical cavern in a semi-infinite space. The equivalent conversion of load form is carried out based on the mirror principle. The vertical subsidence and horizontal displacement of the surface of the elastic semi-infinite space is obtained. According to the elastic-viscoelastic correspondence principle, the viscoelastic solution of the surface displacement of the semi-infinite body, regarded as Maxwell body, can be obtained. A numerical model of a salt cavern for gas storage is established based on the engineering practice. The results of the analytical solution and the numerical simulation are compared and analyzed to verify the accuracy of the analytical solution. The analytical solution was applied to predict the surface displacement above a group of caverns, and the influence of the layout of salt caverns and cavern center spacing on the surface displacement is analyzed. The research results show that the regular triangular layout is slightly better than the square layout. The larger the cavern center spacing, the smaller the maximum surface subsidence. The proposed theoretical prediction model can provide a theoretical basis for controlling surface deformation for the construction of gas storage caverns.

The role of thermal effusivity in heat exchange between finite-sized bodies

Thermal effusivity is a thermophysical property of materials that combines thermal conductivity and volumetric heat capacity. Thermal effusivity is often interpreted in terms of a body's ability to exchange heat when brought in contact with another body at a different temperature, and is relevant in thermal property measurements, such as the transient plane source method as well as in energy harvesting and thermal management. Well-known theoretical models show that thermal effusivity is the only thermophysical property that governs heat exchange between two semi-infinite bodies. In contrast, there is a lack of work on heat exchange between bodies of finite thickness, which may be a relevant consideration in several practical scenarios. This work presents an analytical solution for heat exchange between two finite bodies initially at different temperatures. The effect of thermal contact resistance is accounted for. Results from this work are shown to approach semi-infinite results when the layer thickness becomes large. It is shown that while the heat flux for finite thickness in general depends on both thermal effusivity and thermal diffusivity, exclusive dependence on effusivity may occur under certain conditions, particularly for poorly conducting materials. The sensitivity of interfacial heat flux on these thermal properties is examined in the regimes in which most materials of interest lie. The limits in which the semi-infinite approximation is reasonable are determined. A practical problem is solved as an illustration. This work improves the fundamental understanding of thermal effusivity and thermal interaction between finite-sized bodies, and may find applications in a variety of engineering problems such as thermal property measurement, energy harvesting and thermal management.