An imposed strong magnetic field suppresses turbulence and profoundly changes the nature of the flow of an electrically conducting fluid. We consider this effect for the case of mixed convection flows in pipes and ducts, in which unique regimes characterized by extreme temperature gradients and high-amplitude fluctuations (the so-called magnetoconvective fluctuations) have been recently discovered. The configuration is directly relevant to the design of the liquid-metal components of future nuclear fusion reactors. This review presents the general picture of the flow transformation emerging from the recent studies, illustrates the key known facts, and outlines the remaining open questions. Implications for fusion reactor technology and novel experimental and numerical methods are also discussed.

Stably stratified wall-bounded turbulence is commonly encountered in many industrial and environmental processes. The interaction between turbulence and stratification induces remarkable modifications on the entire flow field, which in turn influence the overall transfer rates of mass, momentum, and heat. Although a vast proportion of the parameter range of wall-bounded stably stratified turbulence is still unexplored (in particular when stratification is strong), numerical simulations and experiments have recently developed a fairly robust picture of the flow structure, also providing essential ground for addressing more complex problems of paramount technological, environmental and geophysical importance. In this paper, we review models used to describe the influence of stratification on turbulence, as well as numerical and experimental methods and flow configurations for studying the resulting dynamics. Conclusions with a view on current open issues will be also provided.

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an “unphysical” pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.

The design and performance of liquid metal batteries (LMBs), a new technology for grid-scale energy storage, depend on fluid mechanics because the battery electrodes and electrolytes are entirely liquid. Here, we review prior and current research on the fluid mechanics of LMBs, pointing out opportunities for future studies. Because the technology in its present form is just a few years old, only a small number of publications have so far considered LMBs specifically. We hope to encourage collaboration and conversation by referencing as many of those publications as possible here. Much can also be learned by linking to extensive prior literature considering phenomena observed or expected in LMBs, including thermal convection, magnetoconvection, Marangoni flow, interface instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the LMB designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important.

The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses and supported by fluid-film bearings. The time-varying thermal bow, due to the asymmetric journal temperature distribution, may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. First discovered by Morton in the 1970s and theoretically analyzed by Keogh and Morton in the 1990s, the ME is still not fully understood by industry and academia experts. Traditional rotordynamic analysis generally fails to predict the potential existence of ME-induced instability in the design stage or troubleshooting process, and the induced excessive rotor vibrations cannot be effectively suppressed through conventional balancing, due to the continuous fluctuation of vibration amplitude and phase angle. In recent years, a fast growing number of case studies of ME have sparked academic interest in analyzing the causes and solutions of ME, and engineers have moved from an initial trial and error approach to more research inspired modification of the rotor and bearing. To facilitate the understanding of ME, the current review is intended to give the most comprehensive summary of ME in terms of symptoms, causes, prediction theories, and solutions. Published case studies in the past are also analyzed for ME diagnosis based on both the conventional view of critical speed, separation margin (SM), and the more recent view of the rotor thermal bow and instability speed band shifting. Although no universal solutions of ME are reported academically and industrially, recommendations to help avoid the ME are proposed based on both theoretical predictions and case studies.

Due to the restriction of lead-rich solder and the miniaturization of electronic packaging devices, lead-free solders have replaced lead-rich solders in the past decades; however, it also brings new technical problems. Reliability, fatigue, and drop resistance are of concern in the electronic industry. The paper provides a comprehensive survey of recent research on the methodologies to describe the mechanical behavior of lead-free solders. In order to understand the fundamental mechanical behavior of lead-free solders, the visco-plastic characteristics should be considered in the constitutive modeling. Under mechanical and thermal cycling, fatigue is related to the time to failure and can be predicted based on the analysis to strain, hysteresis energy, and damage accumulation. For electronic devices with potential drop impacts, drop resistance plays an essential role to assess the mechanical reliability of solder joints through experimental studies, establishing the rate-dependent material properties and proposing advanced numerical techniques to model the interconnect failure. The failure mechanisms of solder joints are complicated under coupled electrical-thermal-mechanical loadings, the increased current density can lead to electromigration around the current crowding zone. The induced void initiation and propagation have been investigated based on theoretical approaches to reveal the effects on the mechanical properties of solder joints. To elucidate the dominant mechanisms, the effects of current stressing and elevated temperature on mechanical behavior of lead-free solder have been reviewed. Potential directions for future research have been discussed.

A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid–solid boundary conditions has been ongoing for more than a century, starting from gas–solid interfaces and progressing to that of the more complex liquid–solid case. Breakthroughs have been made on the theoretical and experimental fronts but the mechanism behind the phenomena remains a puzzle. This paper provides a review of the theoretical models, and numerical and experimental investigations that have been carried out till date. Probable mechanisms and factors that affect the interfacial discontinuity are also documented.

Under nanoconfinement, fluid molecules and ions exhibit radically different configurations, properties, and energetics from those of their bulk counterparts. These unique characteristics of nanoconfined fluids, along with the unconventional interactions with solids at the nanoscale, have provided many opportunities for engineering innovation. With properly designed nanoconfinement, several nanofluidic systems have been devised in our group in the past several years to achieve energy conversion functions with high efficiencies. This review is dedicated to elucidating the unique characteristics of nanofluidics, introducing several novel nanofluidic systems combining nanoporous materials with functional fluids, and to unveiling their working mechanisms. In all these systems, the ultra-large surface area available in nanoporous materials provides an ideal platform for seamlessly interfacing with nanoconfined fluids, and efficiently converting energy between the mechanical, thermal, and electrical forms. These systems have been demonstrated to have great potentials for applications including energy dissipation/absorption, energy trapping, actuation, and energy harvesting. Their efficiencies can be further enhanced by designing efforts based upon improved understanding of nanofluidics, which represents an important addition to classical fluid mechanics. Through the few systems exemplified in this review, the emerging research field of nanoscale fluid mechanics may promote more exciting nanofluidic phenomena and mechanisms, with increasing applications by encompassing aspects of mechanics, materials, physics, chemistry, biology, etc.

Thermal pain arising from the teeth is unlike that arising from anywhere else in the body. The source of this peculiarity is a long-standing mystery that has begun to unravel with recent experimental measurements and, somewhat surprisingly, new thermomechanical models. Pain from excessive heating and cooling is typically sensed throughout the body through the action of specific, heat sensitive ion channels that reside on sensory neurons known as nociceptors. These ion channels are found on tooth nociceptors, but only in teeth does the pain of heating differ starkly from the pain of cooling, with cold stimuli producing more rapid and sharper pain. Here, we review the range of hypotheses and models for these phenomena, and focus on what is emerging as the most promising hypothesis: pain transduced by fluid flowing through the hierarchical structure of teeth. We summarize experimental evidence, and critically review the range of heat transfer, solid mechanics, fluid dynamics, and electrophysiological models that have been combined to support this hypothesis. While the results reviewed here are specific to teeth, this class of coupled thermomechanical and neurophysiological models has potential for informing design of a broad range of thermal therapies and understanding of a range of biophysical phenomena.

Thermal dispersion is an important topic in the convective heat transfer in porous media. In order to determine the heat transfer in a packed bed, the effective thermal conductivity including both stagnant and dispersion thermal conductivities should be known. Several theoretical and experimental studies have been performed on the determination of the effective thermal conductivity. The aim of this study is to review the experimental studies done on the determination of the effective thermal conductivity of the packed beds. In this study, firstly brief information on the definition of the thermal dispersion is presented and then the reported experimental studies on the determination of the effective thermal conductivity are summarized and compared. The reported experimental methods are classified into three groups: (1) heat addition/removal at the lateral boundaries, (2) heat addition at the inlet/outlet boundary, (3) heat addition inside the bed. For each performed study, the experimental details, methods, obtained results, and suggested correlations for the determination of the effective thermal conductivity are presented. The similarities and differences between experimental methods and reported studies are shown by tables. Comparison of the correlations for the effective thermal conductivity is made by using figures and the results of the studies are discussed.

This work serves a two-fold purpose of briefly reviewing the currently existing literature on the scaling of thermal turbulent fields and, in addition, proposing a new scaling framework and testing its applicability. An extensive set of turbulent scalar transport data for turbulent flow in infinitely long channels is obtained using a Lagrangian scalar tracking approach combined with direct numerical simulation of turbulent flow. Two cases of Poiseuille channel flow, with friction Reynolds numbers 150 and 300, and different types of fluids with Prandtl number ranging from 0.7 to 50,000 are studied. Based on analysis of this database, it is argued that the value and the location of the maximum normal turbulent heat flux are important scaling parameters in turbulent heat transfer. Implementing such scaling on the mean temperature profile for different fluids and Reynolds number cases shows a collapse of the mean temperature profiles onto a single universal profile in the near wall region of the channel. In addition, the profiles of normal turbulent heat flux and the root mean square of the temperature fluctuations appear to collapse on one profile, respectively. The maximum normal turbulent heat flux is thus established as a turbulence thermal scaling parameter for both mean and fluctuating temperature statistics.

Laminated glass elements are sandwich structures where the glass presents linear-elastic behavior, whereas the polymer interlayer is, in general, a linear-viscoelastic material. Several analytical models have been proposed since the 1950s to determine the response of laminated glass elements to both frequency and thermal conditions. In this paper, it is proved that Ross, Kerwin, and Ungar's model can be considered as a particular case of the Mead and Markus model when the exponential decay rate per unit length is neglected. The predictions of these models are compared with those obtained from operational modal tests carried out on a laminated glass beam at different temperatures. Finally, a new effective thickness for the dynamic behavior of laminated glass beams, which allows the determination of the dynamic response using a simple monolithic elastic model, is proposed.

A generalization of the quasi-continuum (QC) method to finite temperature is presented. The resulting “hot-QC” formulation is a partitioned domain multiscale method in which atomistic regions modeled via molecular dynamics coexist with surrounding continuum regions. Hot-QC can be used to study equilibrium properties of systems under constant or quasistatic loading conditions. Two variants of the method are presented which differ in how continuum regions are evolved. In “hot-QC-static” the free energy of the continuum is minimized at each step as the atomistic region evolves dynamically. In “hot-QC-dynamic” both the atomistic and continuum regions evolve dynamically in tandem. The latter approach is computationally more efficient, but introduces an anomalous “mesh entropy” which must be corrected. Following a brief review of related finite-temperature methods, this review article provides the theoretical background for hot-QC (including new results), discusses the implementational details, and demonstrates the utility of the method via example test cases including nanoindentation at finite temperature.

Natural convection in triangular enclosures is an important problem. It displays well the generic attributes of this class of convection, with its dependence on enclosure geometry, orientation and thermal boundary conditions. It is particularly rich in its variety of flow regimes and thermal fields as well as having significant practical application. In this paper, a comprehensive view of the research area is sought by critically examining the experimental and numerical approaches adopted in studies of this problem in the literature. Different thermal boundary conditions for the evolution of the flow regimes and thermal fields are considered. Effects of changes in pitch angle and the Rayleigh number on the flow and thermal fields are examined in detail. Although most of the past studies are in the laminar regime, the review extends up to the recent studies of the low turbulent regime. Finally, areas of further research are highlighted.

The exact mathematical analogy exists between Newton’s law of cooling and Proposition II, Book II (The motion of bodies in resisting mediums) of the Principia. Several approaches for the proof of Proposition II are presented based on the expositions available in the historical literature. The relationships among Napier’s logarithms (1614), Euclid’s geometric progression (300 B.C. ), and Newton’s law of cooling (1701) are explored. Newton’s legacy in the thermofluid sciences is discussed in the light of current knowledge. His characteristic parameter for the temperature fall ratio, Δ T / ( T − T ∞ ) , is noted. The relationships and connections among Newton’s cooling law (1701), Fourier’s heat conduction theory (1822), and Carnot’s theorem (1824)based on temperature difference ( Δ T ) as a driving force are noted. After tracing the historical origins of Newton’s law of cooling, this article discusses some aspects of the historical development of the heat transfer subject from Newton to the time of Nusselt and Prandtl. Newton’s legacy in heat transfer remains in the form of the concept of heat transfer coefficient for conduction, convection, and radiation problems. One may conclude that Newton was apparently aware of the analogy of his cooling law to the low Reynolds number motion of a body in a viscous fluid otherwise at rest, i.e., its drag is approximately proportional to its velocity.

Advances in laser, microwave, and similar technologies have led to recent developments of thermal treatments for disease and injury involving skin tissue. In spite of the widespread use of heating therapies in dermatology, they do not draw upon the detailed understanding of the biothermomechanics of behavior, for none exists to date, even though each behavioral facet is well established and understood. It is proposed that a detailed understanding of the coupled biological-mechanical response under thermal agitation will contribute to the design, characterization, and optimization of strategies for delivering better treatment. For a comprehensive understanding on the underlying mechanisms of thermomechanical behavior of skin tissue, recent progress on bioheat transfer, thermal damage, thermomechanics, and thermal pain should be systematically reviewed. This article focuses on the transfer of heat through skin tissue. Experimental study, theoretical analysis, and numerical modeling of skin thermal behavior are reviewed, with theoretical analysis carried out and closed-form solutions obtained for simple one-layer Fourier theory based model. Non-Fourier bioheat transfer models for skin tissue are discussed, and various skin cooling technologies summarized. Finally, the predictive capacity of various heat transfer models is demonstrated with selected case studies.

We discuss the role and the attributes of, as well as the state-of-the-art and some major findings in, the area of predictive analytical (“mathematical”) thermal stress modeling in electronic, opto-electronic, and photonic engineering. The emphasis is on packaging assemblies and structures and on simple meaningful practical models that can be (and actually have been) used in the mechanical (“physical”) design and reliability evaluations of electronic, opto-electronic, and photonic assemblies, structures, and systems. We indicate the role, objectives, attributes, merits, and shortcomings of analytical modeling and discuss its interaction with finite-element analysis (FEA) simulations and experimental techniques. Significant attention is devoted to the physics of the addressed problems and the rationale behind the described models. The addressed topics include (1) the pioneering Timoshenko’s analysis of bimetal thermostats and its extension for bimaterial assemblies of finite size and with consideration of the role of the bonding layer of finite compliance; this situation is typical for assemblies employed in electronics and photonics; (2) thermal stresses and strains in solder joints and interconnections; (3) attributes of the “global” and “local” thermal expansion (contraction) mismatch and the interaction of the induced stresses; (4) thermal stress in assemblies adhesively bonded at the ends and in assemblies (structural elements) with a low-modulus bonding layer at the ends (for lower interfacial stresses); (5) thin film systems; (6) thermal stress induced bow and bow-free assemblies subjected to the change in temperature; (7) predicted thermal stresses in, and the bow of, plastic packages of integrated circuit devices, with an emphasis on moisture-sensitive packages; (8) thermal stress in coated optical fibers and some other photonic structures; and (9) mechanical behavior of assemblies with thermally matched components (adherends). We formulate some general design recommendations for adhesively bonded or soldered assemblies subjected to thermal loading and indicate an incentive for a wider use of probabilistic methods in physical design for reliability of “high-technology” assemblies, including those subjected to thermal loading. Finally, we briefly address the role of thermal stress modeling in composite nanomaterials and nanostructures. It is concluded that analytical modeling should be used, whenever possible, along with computer-aided simulations (FEA) and accelerated life testing, in any significant engineering effort, when there is a need to analyze and design, in a fast, inexpensive, and insightful way, a viable, reliable, and cost-effective electronic, opto-electronic, or photonic assembly, package, or system.

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.

Three-dimensional (3D) constitutive equations of piezoelectric (PZ) plates and shells are considered for inverse linear and electrostrictive (quadratic) piezoeffects. Prestressed multilayer PZ shells reinforced with metal including the case of uneven thickness polarization are studied. Asymptotic and variational methods to solve the governing differential equations of PZ shells are considered. Concentrations of electrical and mechanical fields near structure imperfections and external local loading are investigated. The electrothermoviscoelastic heating of PZ shells is considered at harmonic excitation. From numerical analysis and the experimental data of energy dissipation and the temperature behavior of PZ shell the conditions of optimal transformation of electric energy into mechanical deformations are defined. Thus, the geometrical parameters and working frequencies are determined with due account of dielectric relaxation processes. The following nonlinear phenomena are studied: acoustoelectronic wave amplification; electron injection into metalized polar dielectric; resonance growth by 5–20 times of internal electrical field strength in the PZ shells and plates; and autothermostabilization of ferroelectric resonators. For a better understanding of R.D. Mindlin’s gradient theory of polarization in view of electron processes in thin metal-dielectric-metal structures, use was made of solid state physics interpretations as well as experimental data. High concentration of mechanical stresses and temperature and electrical fields near structure defects (first of all, near boundary between various materials) defines the main properties of polar dielectrics. An unknown domain of electrode rough surface influence was estimated, and as result an uneven polarization distribution was found. A theory of nonlinear autowave systems with energy dissipation was used in a physical model of the electrothermal fracture of dielectrics (contacting with metal electrodes), and as a result a nondestructive testing method to study the microstructure defect formation has been suggested.

This review article gives an overview of some topics related to classical and modern problems in the theory of heat, its meaning for various branches, and thermal management of equipment. The specific requirements for new technologies involved in the thermal operation of miniaturized instruments, components of equipment, devices, units operating in fast-response regimes, improvement of heat resistance, reliability, and endurance are considered. Special requirements have been put forward for nanotechnologies, where engineering parts, elements of devices, and technological equipment have microscopic and submicroscopic dimensions. Also, the stringent requirements of thermal modes of modern large-scale technologies in such branches of industry as nuclear power engineering and rocket-space engineering have become more important and determining. The thermal modes of these technologies call for new approaches to the design of the thermodynamic state of micro- and macrosystems, high-temperature plasma, and cryogenic temperatures. New results of the study of the mechanism of heat transfer in phase transitions, principally in new approaches to the problem of enhancement of heat transfer in one- and two-phase flows are presented. The importance of studies of thermal processes providing reliable thermal modes of new power plants, microsystems, and nanotechnologies is shown. The significance of advances in the study of thermal processes for developing the theory of heat is discussed. Especially considered are achievements in the theory of heat for its role in the decisions of actual problems of biology, medicine, and environment. This review article cites 105 references, most of them in Russian.