Normal Heat Transport Research Articles

Anomalous thermal conductivity of alkaline-earth-metal-substituted EuTiO3 induced by resonant scattering

We have investigated thermal conductivities (κ) of polycrystalline Eu1–xAxTiO3 (A = Ca, Sr, Ba, 0 ≤ x ≤ 0.8) bulk materials in the temperature range of ∼ 2 K <T < 1173 K. The EuTiO3 demonstrates anomalous glass-like κ(T) behavior at low temperatures. Partial substitutions with Sr2+ and Ba2+ do not cause a significant change in the κ(T) behavior, while a κ(T) peak, which looks like a manifestation of a typical crystalline solid, appears only in the Ca-substituted samples with an orthorhombic structure when x ≥ 0.4. After excluding the magnetic effects on κ and discussing the possible phonon scattering mechanisms in depth, together with heat capacity Cp measurements and high-resolution X-Ray diffraction characterization, we find that the unusual low κ at low temperatures is attributed to resonant scattering induced by the intrinsic disordered local structure and lattice instability in EuTiO3. Due to the different lattice dynamics of ATiO3, the lattice structure of Eu1–xCaxTiO3 can be regarded as formed by a part-soft (from EuTiO3) part-rigid (from CaTiO3) sublattice. The anomalous κ(T) behavior of Eu1–xCaxTiO3 results from the combined effect of phonon transport between the normal phononic heat transport in the rigid sublattice and the strong damping of heat conduction in the soft sublattice.

Modeling and Simulations of Deteriorated Turbulent Heat Transfer in Wall-Heated Cylindrical Tube

Abstract This paper discusses the modeling and simulations of deteriorated turbulent heat transfer (DTHT) for a wall-heated fluid flows, which can be observed in gas-cooled nuclear power reactors during pressurized conduction cooldown (PCC) event due to loss of force circulation flow. The DTHT regime is defined as the deterioration of normal turbulent heat transport due to increase of acceleration and buoyancy forces. The computational fluid dynamics (CFD) tools such as Nek5000 and STAR-CCM+ can help to analyze the DTHT phenomena in reactors for efficient thermal-fluid designs. Three-dimensional (3D) CFD nonisothermal modeling and simulations were performed in a wall-heated circular tube. The simulation results were validated with two different CFD tools, Nek5000 and STAR-CCM+, and validated with an experimental data. The predicted bulk temperatures were identical in both CFD tools, as expected. Good agreement between simulated results and measured data were obtained for wall temperatures along the tube axis using Nek5000. In STAR-CCM+, the under-predicted wall temperatures were mainly due to higher turbulence in the wall region. In STAR-CCM+, the predicted DTHT was over 48% at outlet when compared to inlet heat transfer values.

Generalized self-consistent reservoir model for normal and anomalous heat transport in quantum harmonic chains.

Fictitious stochastic reservoirs incorporate scattering and dephasing mechanisms into the system in contact with these reservoirs. The reservoir-system coupling is described by the related self-energy in terms of the nonequilibrium Green's function formalism or equivalently the quantum Langevin equation formalism. In this study, we investigate thermal transport in a finite segment of an infinitely extended quantum harmonic chain with an equal self-energy at each site by using the self-consistent reservoir approach. In this setup, the entire system is lattice translation invariant so that mismatched boundaries are excluded from the model. Solving the Landauer-Büttiker equations under the self-consistent adiabatic condition, we quantitatively elucidate a thermally induced crossover of ballistic-to-diffusive transport and its scaling relation prescribed by a temperature-dependent mean free path. It is also shown that normal transport emerges in the diffusive limit for a linear self-energy, while nonlinear higher-order ones generically lead to anomalous transport. Physical implications of these observations are discussed in terms of the persistence of a massless Goldstone mode as well as the conservation of total linear momentum.

Crossover from ballistic to normal heat transport in the ϕ^{4} lattice: If nonconservation of momentum is the reason, what is the mechanism?

Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ϕ^{4} model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.

Heat conduction in diatomic chains with correlated disorder

The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter – the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then – to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard–Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard–Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.

Diverging Fluctuations of the Lyapunov Exponents.

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of suitably correlated background noise.

Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction

Previous studies have suggested a crossover from superdiffusive to normal heat transport in one-dimensional (1D) anharmonic oscillator systems with a double-well type interatomic interaction like , when the system temperature is varied. In order to better understand this unusual manner of thermal transport, here we perform a direct dynamics simulation to examine how the spreading processes of the three physical quantities, i.e. the heat, the total energy and the momentum, would depend on temperature. We find three main points that are worth noting. (i) The crossover from superdiffusive to normal heat transport is well verified from a new perspective of heat spread. (ii) The spreading of the total energy is found to be very distinct from heat diffusion, especially under some temperature regimes, energy is strongly localized, while heat can be superdiffusive. So one should take care to derive a general connection between the heat conduction and energy diffusion. (iii) In a narrow range of temperatures, the spreading of momentum implies clear unusual non-ballistic behaviors; however, such unusual transport of momentum cannot be directly related to the normal transport of heat. An analysis of phonon spectra suggests that one should also take the effects of phonon softening into account. All of these results may provide insights into establishing the connection between the macroscopic heat transport and the underlying dynamics in 1D systems.

1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

Transport and the spread of heat in Hamiltonian one dimensional momentum conserving nonlinear systems is commonly thought to proceed anomalously. Notable exceptions, however, do exist of which the coupled rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous energy and momentum transport in those low dimensional systems. We develop the theory for both, the statistical densities for momentum- and energy-spread and particularly its momentum-/heat-diffusion behavior, as well as its corresponding momentum/heat transport features. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. Subtracting the part which corresponds to a ballistic momentum spread relates (via this integrated, subleading momentum flux correlation) to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We next put forward the intriguing hypothesis: normal spread of this so adjusted excess momentum density causes normal energy spread and alike normal heat transport (Fourier Law). Its corollary being that an anomalous, superdiffusive broadening of this adjusted excess momentum density in turn implies an anomalous energy spread and correspondingly anomalous, superdiffusive heat transport. This hypothesis is successfully corroborated within extensive molecular dynamics simulations over large extended time scales. Our numerical validation of the hypothesis involves four distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted coupled rotator model), (ii) unbounded interactions acting at large distances (the coupled rotator model amended with harmonic pair interactions), (iii) the case of a hard point gas with unbounded square-well interactions and (iv) a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard–Jones model). We compare our findings with recent predictions obtained from nonlinear fluctuating hydrodynamics theory.

Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths

Guided by a stylized experiment we develop a self-consistent anharmonic phonon concept for nonlinear lattices which allows for explicit ``visualization.'' The idea uses a small external driving force which excites the front particles in a nonlinear lattice slab and subsequently one monitors the excited wave evolution using molecular dynamics simulations. This allows for a simultaneous, direct determination of the existence of the phonon mean-free path with its corresponding anharmonic phonon wave number as a function of temperature. The concept for the mean-free path is very distinct from known prior approaches: the latter evaluate the mean-free path only indirectly, via using both a scale for for the phonon relaxation time and yet another one for the phonon velocity. Notably, the concept here is neither limited to small lattice nonlinearities nor to small frequencies. The scheme is tested for three strongly nonlinear lattices of timely current interest which either exhibit normal or anomalous heat transport.

Experimental evaluation of safety grade decay heat removal in prototype fast breeder reactor

After the reactor shutdown, decay heat in prototype fast breeder reactor (PFBR) will be removed through normal heat transport path (OGDHR) and separate dedicated passive safety grade decay heat removal (SGDHR) system. If normal heat transport path is not available for decay heat removal due to various reasons, the highly reliable passive SGDHR system is the only means of decay heat removal. To study the performance of SGDHR system of PFBR, an experimental set up in sodium, SADHANA was designed, constructed and commissioned. The scaled down model of 1:22 in power was modelled with Richardson number and Euler number similitude. Sodium to sodium decay heat exchanger and sodium to air heat exchanger in SADHANA is similar to the corresponding heat exchangers of the prototype reactor system. Steady state experiments were carried out in SADHANA facility to evaluate the heat transport characteristics of the system under various conditions. From the steady state experiments it is concluded that the SGDHR system in PFBR is capable of removing the intended amount of decay heat from the hot sodium pool of the reactor. This paper gives the details of the steady state experiments conducted to characterise the heat transport behaviour of the SGDHR system and the results of the experiments.

Quality Management during Manufacturing of High Tempertaure Thin Walled Austenitic Stainless Steel Sodium Tanks of Prototype Fast Breeder Reactor

Austenitic stainless steels are the major material of construction for the fast breeder reactors in view of their adequate high temperature mechanical properties, compatibility with liquid sodium coolant, good weldability, availability of design data and above all the fairly vast and satisfactory experience in the use of these steels for high temperature service. All the Nuclear Steam Supply System (NSSS) components of FBR are thin walled structure and require manufacture to very close tolerances under nuclear clean conditions. As a result of high temperature operation and thin wall construction, the acceptance criteria are stringent as compared to ASME Section III. The material of construction is Austenitic stainless steel 316 LN and 304 LN with controlled Chemistry and calls for additional tests and requirements as compared to ASTM standards. Prototype Fast Breeder Reactor (PFBR) is sodium cooled, pool type, 500 MWe reactor which is at advanced stage of construction at Kalpakkam, Tamilnadu, India. In PFBR, the normal heat transport is mainly through two secondary loops and in their absence; the decay heat removal is through four passive and independent safety grade decay heat removal loops (SGDHR). The secondary sodium circuit and the SGHDR circuit consist of sodium tanks for various applications such as storage, transfer, pressure mitigation and to take care of volumetric expansion. The sodium tanks are thin walled cylindrical vertical vessels with predominantly torispherical dished heads at the top and bottom. These tanks are provided with pull-out nozzles which were successfully made by cold forming. Surface thermocouples and heaters, wire type leak detectors are provided on these tanks. These tanks are insulated with bonded mineral wool and with aluminum cladding. All the butt welds in pressure parts were subjected to 100% Radiographic examination. These tanks were subjected to hydrotest, pneumatic test and helium leak test under vacuum. The principal material of construction being stainless steel for the sodium tanks shall be handled with care following best engineering practices coupled with stringent QA requirements to avoid stress corrosion cracking in the highly brackish environment. Intergranular stress corrosion cracking and hot cracking are additional factors to be addressed for the welding of stainless steel components. Pickling and passivation, Testing with chemistry controlled demineralised water are salient steps in manufacturing. Corrosion protection and preservation during fabrication, erection and post erection is a mandatory stipulation in the QA programme. Enhanced reliability of welded components can be achieved mainly through quality control and quality assurance procedures in addition to design and metallurgy. The diverse and redundant inspections in terms of both operator and technique are required for components where zero failure is desired &amp; claimed. This paper highlights the step by step quality management methodologies adopted during the manufacturing of high temperature thin walled austenitic stainless steel sodium tanks of PFBR.

Experimental evaluation of sodium to air heat exchanger performance

Sodium to air heat exchangers (AHXs) is used in Prototype Fast Breeder Reactor (PFBR) circuits to reject the decay heat produced by the radioactive decay of the fission products after reactor shutdown, to the atmospheric air. The heat removal through sodium to air heat exchanger maintains the temperature of reactor components in the pool within safe limits in case of non availability of normal heat transport path. The performance of sodium to air heat exchanger is very critical to ensure high reliability of the decay heat removal systems in sodium cooled fast breeder reactors. Hence experimental evaluation of the adequacy of the heat transfer capability gives confidence to the designers. A finned tube cross flow sodium to air heat exchanger of 2MW heat transfer capacity with sodium on tube side and air on shell side was tested in the Steam Generator Test Facility at Indira Gandhi Center for Atomic Research, India. Heat transfer experiments were carried out with forced circulation of sodium and air, which confirmed the adequacy of heat removal capacity of the heat exchanger. The testing showed that 2.34MW of heat power is transferred from sodium to air at nominal flow and temperature conditions. A one dimensional computer code developed for design and analysis of the sodium to air heat exchanger was validated by the experimental data obtained. An equivalent Nusselt number, Nueq is derived by approximating that the resistance of heat transfer from sodium to air is contributed only by the film resistance of air. The variation of Nueq with respect to the Reynolds number was studied.

Heat transport and thermal rectification in molecular junctions: A minimal model approach

Heat conduction properties are investigated in a molecular junction modeled as a two-strand ladder with strongly asymmetric thermal transport pathways. By confining anharmonic contributions to only one of the strands, it is shown that tuning of the interstrand coupling can lead to normal heat transport and to the emergence of a well-defined temperature gradient. More interestingly, thermal rectification is obtained around a critical value of the interstrand interaction and by appropriate asymmetries induced by the coupling to the thermal baths.

Controlling the heat flow: Now it is possible

We discuss the problem of heat conduction in 1D nonlinear chains in relation to the dynamical properties of the system. We provide convincing numerical evidence for the validity of Fourier law of heat conduction in linear mixing systems. Therefore, deterministic diffusion and normal heat transport which are usually associated with full hyperbolicity, actually take place in systems without exponential instability. We then show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.

Normal and anomalous heat transport in one-dimensional classical lattices

We present analytic and numerical results on several models of one-dimensional (1D) classical lattices with the goal of determining the origins of anomalous heat transport and the conditions for normal transport in these systems. Some of the recent results in the literature are reviewed and several original "toy" models are added that provide key elements to determine which dynamical properties are necessary and which are sufficient for certain types of heat transport. We demonstrate with numerical examples that chaos in the sense of positivity of Lyapunov exponents is neither necessary nor sufficient to guarantee normal transport in 1D lattices. Quite surprisingly, we find that in the absence of momentum conservation, even ergodicity of an isolated system is not necessary for the normal transport. Specifically, we demonstrate clearly the validity of the Fourier law in a pseudo-integrable particle chain.

The impact of paleogeography, pCO 2, poleward ocean heat transport and sea level change on global cooling during the Late Ordovician

We performed sensitivity experiments with the global climate model GENESIS on two stages of the Upper Ordovician (Caradocian, ∼454 Ma; Ashgillian, ∼446 Ma) under a range of atmospheric pCO 2 values (8–18× PAL; Pre-industrial Atmospheric Level), high and low sea level, and two values of poleward ocean heat transport in order to determine the importance of these variables on global cooling. We then coupled a three-dimensional ice sheet model to the global climate model in order to investigate the necessary boundary conditions for ice sheet formation. All simulations with a high sea level and normal heat transport remain free of ice sheets, even with pCO 2 levels as low as 8× PAL. In the Caradocian simulations, ice sheets form in three scenarios: (1) with pCO 2 of 8× PAL and a low sea level and normal poleward ocean heat transport, (2) with pCO 2 of 8× PAL and a high sea level and reduced (50% of normal) poleward ocean heat transport, and (3) with pCO 2 of 15× PAL and a low sea level and reduced poleward ocean heat transport. In the Ashgillian simulations, ice sheets form in only two scenarios: (1) with pCO 2 of 8× PAL and a low sea level and normal poleward ocean heat transport, or (2) with pCO 2 of 8× PAL and a high sea level and reduced poleward ocean heat transport. The ice sheets in the Ashgillian experiments are larger and thicker than the ice sheets in the Caradocian simulations because the southward movement of Gondwana increased land area in the higher southern latitudes where ice sheets could grow. The threshold for glaciation under Ashgillian paleogeography is 8× PAL and either a low sea level (exposed shelves) or a reduced poleward ocean heat transport. While the paleogeographic evolution and a drop in pCO 2 during the Late Ordovician cooled the global climate, changes in additional factors were required to initiate ice sheet formation, such as a drop in sea level, a reduction in poleward ocean heat transport, or a combination of both.

Heat conductivity in linear mixing systems.

We present analytical and numerical results on the heat conduction in a linear mixing system. In particular we consider a quasi-one-dimensional channel with triangular scatterers with internal angles which are irrational multiples of pi, and we show that the system obeys the Fourier law of heat conduction. Therefore, deterministic diffusion and normal heat transport which are usually associated with full hyperbolicity, actually take place in systems without exponential instability.

Coupled normal heat and matter transport in a simple model system.

We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system is a Lorentz gas with fixed freely rotating circular scatterers which scatter point particles via perfectly rough collisions. Upon imposing either a temperature gradient and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds. Transport in this system is normal in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are nontrivially coupled, satisfying Onsager's reciprocity relations.

Conceptual Design Features for a Passive Light Water Cooled and Moderated Pressure Tube Reactor (PLPTR)

Key conceptual features are developed for a passive light water cooled and moderated pressure tube reactor having a total thermal output of 4029 MW (thermal) and net electric power of 1260 MW (electric) compatible with passive safety features that can ensure integrity of the fuel and reusability of the major reactor components without the requirement of delivery of emergency coolant makeup inventory. The concept of passive heat removal applied in this design combines heat storage, thermal conduction, radiation, natural circulation of light water in a moderator system under one atmosphere, and a natural draft air cooling system. Feasibility studies concerning normal heat transport, accident decay heat removal, materials compatibility, and reactor physics for criticality and feedback effects were carried out for the associated design features

Model simulation of heat and water transport dynamics in an airway.

Heat and water transport processes in the respiratory tract depend on environmental conditions, breathing patterns, and the physiological state of the respiratory system. To study these processes, we have developed a mathematical model of the dynamics of temperature and water vapor in the radial and axial directions of an idealized trachea. The model is expressed as two implicit finite-difference equations and solved using an alternating-direction algorithm. Using these equations, we simulated the effects of inspired gas temperature and humidity, velocity profile, and flow rate on heat and water transport between the gas and airway wall. Under inspired gas conditions of low temperature or high relative humidity, supersaturation occurs. Increasing either the velocity gradient at the wall or the flow rate increases the heat and water transport rates. However, these rates change by only 10 percent when the velocity gradient is doubled, and by about 35 percent when flow rate undergoes a two-fold change. The model can be used with in-vivo data from the trachea to test hypotheses concerning normal and abnormal heat and water transport.