Time-dependent Flux Research Articles

Evaluation of diaphragm wall heat exchanger potential

Diaphragm wall foundations adapted for use as ground heat exchangers are an attractive proposition to achieve low-carbon heating and cooling with heat pumps in larger non-domestic buildings. As the extent of a diaphragm wall installation is driven by geotechnical questions and the number of storeys, key system design considerations are the peak and seasonal capacity of the ground heat exchanger and the proportion of the building demands that can be satisfied. Dynamic simulations of prototypical office buildings in a range of climatic conditions have been used to analyse heat exchange potentials using a Dynamic Thermal Network (DTN) heat exchanger model. Systematic evaluations of the time-dependent heat fluxes between three boundaries (heat exchanger, basement, ground surface) have been made to maximize heat exchange potentials and overall system efficiency given temperature constraints over 20 years operation. This has allowed maximum heat exchange potentials to be evaluated for a range of design parameters and climates to enable preliminary design of diaphragm wall heat exchanger systems and assessment of hybridized solutions. Considering short timescale dynamic effects suggests peak heat exchange rates higher than previously reported. In some climates seasonal operation is found to be constrained by temperature limits according to ground thermal properties.

Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditions

Solid-liquid phase change heat transfer problems appear in a broad variety of engineering systems, such as thermal management and latent energy storage. Boundary conditions in such systems often vary with time, for example, due to sinusoidal heating, or step changes in externally applied temperature or heat flux. Unfortunately, phase change problems with time-dependent boundary conditions do not generally admit an exact solution, and therefore, approximate analytical solutions are of much interest. This paper presents an eigenfunction expansion based technique for solving one-dimensional phase change heat transfer problems with time-dependent temperature or heat flux boundary conditions. The temperature field is expressed as a series solution of appropriate eigenfunctions, and with time-dependent coefficients, which are determined by deriving and solving an ordinary differential equation that accounts for the time-dependent nature of the boundary condition. Solutions for Cartesian, cylindrical and spherical problems are derived. Results are found to be in excellent agreement with past work and numerical simulations. The effect of Stefan problem on the nature of phase change propagation is studied. Two practical problems involving sinusoidal and step function boundary conditions are also solved and analyzed in detail. In addition to improving the fundamental understanding of phase change heat transfer, this work may also contribute towards design and optimization of practical engineering problems involving phase change heat transfer.

Thermal analysis of simultaneously evolving laminar pulsatile flow through two large parallel plates with time-dependent heat flux boundary conditions

Understanding unsteady convective heat transfer (UCHT) behavior of simultaneously evolving laminar pulsatile flow between two large parallel plates exposed to time-dependent thermal boundary conditions is the goal of this research. The time-dependent sinusoidal velocity waveform is applied at the entrance of the two large parallel plates exposed to time-dependent sinusoidal heat flux boundary conditions (TSHBC). The finite volume technique is used in the present work. The current results have been compared to the literature data under the same operating conditions and found to be in good concurrence. The influence of various parameters, for instance, amplitude, frequency, phase difference, heat flux ratio, and the Reynolds number on the transient Nusselt number, is investigated. An improvement in energy transfer is observed when the pulsatile flow between two large parallel plates with TSHBC than the non-pulsatile flow with a fixed heat flux type boundary. Furthermore, the energy transfer improvement is observed once the velocity and heat flux waveform frequency is equal. The applicability of the present work could be found in the solar heating system, cooling of electronic devices, etc., whereby a more robust understanding of the unsteady convective heat transfer could facilitate the design and develop an efficient system.

Performance evaluation of AHWR flux mapping system during normal operational scenarios

In large nuclear reactors, a number of appropriately distributed in-core neutron detectors are used for monitoring and control of neutron flux distribution in the core. In Advanced Heavy Water Reactor (AHWR) too, a set of 168 self-powered neutron detectors installed vertically at 6 locations in 28 in-core detector housing units has been proposed to be used. This configuration arrived at using the K-means clustering approach, has been found to reconstruct the core neutron flux distribution for a number of steady-state flux shapes. For practical application, in addition to steady-state, the optimized set of in-core detectors should provide reasonably accurate core monitoring for regular reactor operations as well. This paper investigates the accuracy characteristics of flux mapping using the proposed set of 168 in-core self-powered neutron detectors in the reconstruction of time-varying flux shapes encountered during normal reactor operations. Time-dependent flux shapes arising due to perturbations such as the movement of reactivity devices, refuelling and xenon spatial oscillations are considered for this study. Flux reconstruction is performed using the well-known flux synthesis method. From the analysis, it can be observed that the proposed set of in-core detectors reliably reconstructs the flux distribution in the reactor even during the normal operational scenarios. The maximum RMS error in mesh flux using 168 SPNDs and 35 eigenmodes is found to be 4.45% across all the operational scenarios considered.

Open Quantum System Simulation of Faraday's Induction Law via Dynamical Instabilities.

We propose a novel type of a Bose-Hubbard ladder model based on an open quantum-gas-cavity-QED setup to study the physics of dynamical gauge potentials. Atomic tunneling along opposite directions in the two legs of the ladder is mediated by photon scattering from transverse pump lasers to two distinct cavity modes. The resulting interplay between cavity photon dissipation and the optomechanical atomic backaction then induces an average-density-dependent dynamical gauge field. The dissipation-stabilized steady-state atomic motion along the legs of the ladder leads either to a pure chiral current, screening the induced dynamical magnetic field as in the Meissner effect, or generates simultaneously chiral and particle currents. For a sufficiently strong pump the system enters into a dynamically unstable regime exhibiting limit-cycle and period-doubled oscillations. Intriguingly, an electromotive force is induced in this dynamical regime as expected from an interpretation based on Faraday's law of induction for the time-dependent synthetic magnetic flux.

Time dependent hydrogen ENAs fluxes and structure of the heliosphere in the solar magneto-gravitational field

Energetic neutral atoms (ENAs) consisting mainly of hydrogen with energies of several keV and coming from the outer heliosphere have been detected by various spacecraft missions. The characteristics of the energy spectrum of ENAs include a dependence on the proton distribution at the heliospheric boundaries where the solar wind interaction with the local interstellar medium (LISM) occurs. We determine here the time-dependent differential flux for the neutral hydrogen atoms resulting from the kinetic exchange of energy in the outer heliosphere under the solar magnetic field. With the proton flow along the magnetic field lines, the mean kinetic energy of the particles is shown to increases due to the magnetic field line compression at the outer heliosphere, causing the acceleration of the solar wind protons to the observed range of speeds. Also, the toroidal field driven compression and expansion of the magnetic field lines corresponds to the temperature variations observed in the INCA line-of-sight observations of the ENAs in the inner heliosheath, where as the pickup ions retain their accelerated speed inside the heliosphere in the subsequent motion up to ∼1au.

Effect of Phase-Lags Model on Thermoelastic Interactions of Nonlocal Elastic Hollow Cylinder with Voids Material in the Presence of Time-Dependent Heat Flux

Effect of Phase-Lags Model on Thermoelastic Interactions of Nonlocal Elastic Hollow Cylinder with Voids Material in the Presence of Time-Dependent Heat Flux

Vacuum Dependent Bell Local Hidden Variable Models and Generalized C.H.S.H. Inequalities

We extend a previous model of the author which generalizes Bell local hidden variable models to the case of entangled photon pairs assuming that the standard Bell correlation functions depend on a hidden vacuum index. We deduce a generalization of Bell theorem assuming that classical observables are not dichotomic and that photon pair emission and detection is not a stationary stochastic process. We derive a photon imperfect polarization correlation functions due to rotational invariance breaking induced by hidden vacuum spin currents. We implement formally this approach deducing a generalization of C.H.S.H. inequalities which asymptotically converges to the standard one and which might be competitive with standard quantum mechanics predictions. We suggest to test this inequalities conceiving new E.P.R.-Bell like tests with time dependent detector efficiency and photon flux. Finally, we suggest to apply these generalized inequalities to the correlation functions of entangled classical spinning waves realized recently with metamaterials.

The wall heat flux partitioning during the pool boiling of water on thin metallic foils

• We study nucleate boiling on substrates of small thermal capacity using IR camera. • Microlayer does not fully evaporate due to limited thermal capacity of the heater. • Microlayer evaporation and rewetting are less important compared to thick heaters. • Most energy is removed by convective effects created by bubble growth and departure. • We re-derived heat flux partitioning model to quantify each heat transfer mechanism. In this work, we studied the wall heat flux partitioning during the pool boiling of water on thin metallic surfaces. We conducted boiling experiments on surfaces where we engineered nucleation sites by nanosecond-fiber-laser texturing. These nucleation sites form triangular lattice patterns with different pitches. We measured the time-dependent temperature and heat flux distributions on the boiling surface using an infrared camera. We developed post-processing algorithms to measure, based on these distributions, all the fundamental boiling parameters used in heat flux partitioning models (e.g., nucleation site density, bubble wait and growth time, and bubble footprint radius) and the actual partitioning of the heat flux, i.e., how much heat is transferred by evaporation of the microlayer, rewetting of the surface, and convective effects. This work reveals that the mechanisms of heat transfer on substrates of small thermal capacity are very different compared to substrates of large thermal capacity. With water, the bubble microlayer typically does not dry out and the surface temperature at rewetting is practically the same as the rewetting fluid temperature. These effects limit the efficiency of microlayer evaporation and rewetting heat transfer. Instead, convective effects generated by the bubble growth process remove most of the energy from the heated surface. This behavior is captured by a heat flux partitioning model that we re-derived from first principles to describe the heat transfer mechanisms on substrate of small thermal capacity.

Thermoelastic Modeling of Time Fractional Heat conduction in Circular Disk with Internal Heat Generation

In this paper, thermoelastic modeling of a circular sector disk is done under the influence of fractional time theory of thermoelasticity to evaluate the changes in temperature flow, displacement and stress behavior subjected to internal heat generation within it. At the fixed edge a time dependent heat flux is applied while thermally insulation type boundary are maintained at upper part of surface as well as the lower part surface is kept at zero temperature. Also certain boundary surfaces at 0 are fixed as a function of temperatures field , 1 f 2 f which is function of respectively. Furthermore, method of Integral transformations is employed to determine the required solution of equation of heat conduction. The obtained expressions areof Bessel’s type and in form of series. For numerical analysis the pure aluminum circular sector disk considered and obtained results are plotted as shown in figures.

Seasonal variations of subsurface seismic velocities monitored by the SEIS-InSight seismometer on Mars

SUMMARYThe SEIS (Seismic Experiment for Interior Structure) seismometer deployed at the surface of Mars in the framework of the NASA-InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission has been continuously recording the ground motion at Elysium Planitia for more than one martian year. In this work, we investigate the seasonal variation of the near-surface properties using both background vibrations and a particular class of high-frequency seismic events. We present measurements of relative velocity changes over one martian year and show that they can be modelled by a thermoelastic response of the Martian regolith. Several families of high-frequency seismic multiplets have been observed at various periods of the martian year. These events exhibit complex, repeatable waveforms with an emergent character and a coda that is likely composed of scattered waves. Taking advantage of these properties, we use coda wave interferometry (CWI) to measure relative traveltime changes as a function of the date of occurrence of the quakes. While in some families a stretching of the coda waveform is clearly observed, in other families we observe either no variation or a clear contraction of the waveform. These various behaviors correspond to different conditions of illumination at the InSight landing site, depending on the season. Measurements of velocity changes from the analysis of background vibrations above 5 Hz are consistent with the results from CWI. We identify a frequency band structure in the power spectral density (PSD) that can be tracked over hundreds of days. This band structure is the equivalent in the frequency domain of an autocorrelogram and can be efficiently used to measure relative traveltime changes as a function of frequency. We explain how the PSD analysis allows us to circumvent the contamination of the measurements by the Lander mode excitation which is inevitable in the time domain. The observed velocity changes can be adequately modelled by the thermoelastic response of the regolith to the time-dependent incident solar flux at the seasonal scale. In particular, the model captures the time delay between the surface temperature variations and the velocity changes in the subsurface. Our observations could serve as a basis for a joint inversion of the seismic and thermal properties in the first 20 m below InSight.

Natural convection in a cavity with time-dependent flux boundary

Numerical simulations have been carried out to investigate the unsteady natural convection flow in a cavity subjected to a sidewall heat flux varying sinusoidally with time. With all walls non-slip and the upper and lower boundaries and the other sidewall adiabatic, the heating and cooling produces an alternating direction natural convection boundary layer that discharges hot fluid to the top and cold fluid to the bottom of the cavity, generating a time-varying thermal stratification in the cavity interior. Scaling analysis has been conducted for different flow regimes based on the forcing frequency, with the characteristic time scales being the forcing period and the boundary layer development time. The scaling relations are then verified using the simulations, with the results showing overall good agreement with the derived scaling relations.

Successive droplet impingement onto heated surfaces of different wettabilities

New high-performance electronic components generate a massive amount of heat per unit of area, and spray cooling is a field of interest for this application. Spray cooling achieves higher heat transfer coefficients than commonly used forced air convection cooling systems. In this study, we performed multiple droplet impingement experiments over heated surfaces in the non-boiling regime, a scenario that is closer to the phenomena of spray cooling than individual droplet impact. This paper focuses on the effects of droplet interactions with surfaces exhibiting distinct wettabilities. A surface thermocouple was used concomitantly as the impact surface and the temperature sensor. The surface thermocouple was originally hydrophilic (uncoated), which later we treated with a low cost commercial superhydrophobic coating (coated). High-speed imaging showed the droplet motion during impact. We proposed a one-dimensional inverse heat conduction semi-analytical solution, adopting a time-dependent droplet heat flux as one of the boundary conditions to represent the droplet cooling effect. We compared the heat transfer performances of both uncoated and coated surfaces for different droplet velocities but same initial temperature. The results showed higher heat transfer rates on uncoated surface relative to the coated one. Also, higher droplet velocities showed higher heat transfer mainly due to the increase in the droplet spreading diameter in contact with the solid. Successive droplets showed lower heat flow for the uncoated surface because of the low thermal effusivity and thickness of the heated solid, where most of the heat is removed by the first droplet. The first droplet thermal resistance and damping effects for the subsequent droplets, reduced the overall cooling performance. On the other hand, for the coated surface we found that the consecutive droplets continued to transfer heat with a similar rate as the previous one, which is desirable for spray cooling. However, the reduced overall heat transfer performance for the coated surface can be explained by the air pockets within the coating structure.

The tunable 0−π qubit: Dynamics and relaxation

In this paper, we present a systematic treatment of a [Formula: see text] qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian are obtained. The effect of the flux noise on the qubit relaxation is obtained using the perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

Heat Transfer Analysis of Laminar Pulsating Flow in a Rectangular Channel Using Infrared Thermography

Abstract While numerous applied studies have successfully demonstrated the feasibility of unsteady cooling solutions, a consensus has yet to be reached on the local instantaneous conditions that result in heat transfer enhancement. This work aims to experimentally validate a recent analytical solution (on a local time-dependent basis) for the common flow condition of a fully developed incompressible pulsating flow in a uniformly heated vessel. The experimental setup is found to approximate the ideal constant heat flux boundary condition well, especially for the decoupled unsteady scenario where the amplitude of the most significant secondary contributions (capacitance and lateral conduction) amounts to 1.2% and 0.2% of the generated heat flux, respectively. Overall, the experimental measurements for temperature and heat flux oscillations are found to coincide well with a recent analytical solution to the energy equation by the authors. Furthermore, local time-dependent heat flux enhancements and degradations are observed to be qualitatively similar to those of wall shear stress from a previous study, suggesting that the thermal performance is indeed influenced by hydrodynamic behavior.

Inflationary Implications of the Covariant Entropy Bound and the Swampland de Sitter Conjectures

We present a proposal to relate the de Sitter conjecture (dSC) with the time dependence of fluxes via the covariant entropy bound (CEB). By assuming an early phase of accelerated expansion where the CEB is satisfied, we take into account a contribution from time-dependent flux compactification to the four-dimensional entropy which establishes a bound on the usual slow-roll parameters ηH and ϵH. We also show an explicit calculation of entropy from a toroidal flux compactification, from a transition amplitude of time-dependent fluxes which allows us to determine the conditions on which the bounds on the slow-roll parameters are in agreement to the dSC.

An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.

TRecX — An environment for solving time-dependent Schrödinger-like problems

tRecX is a C++ code for solving generalized inhomogeneous time-dependent Schrödinger-type equations idΨ/dt=H[t,Ψ]+Φ in arbitrary dimensions and in a variety of coordinate systems. The operator H[t,Ψ] may have simple non-linearities, as in Gross-Pitaevskii and Hartree(-Fock) problems. Primary application of tRecX has been non-perturbative strong-field single and double photo-electron emission in atomic and molecular physics. The code is designed for large-scale ab initio calculations, for exploring models, and for advanced teaching in computational physics. Distinctive numerical methods are the time-dependent surface flux method for the computation of single and double emission spectra and exterior complex scaling for absorption. Wave functions and operators are handled by tree-structures with the systematic use of recursion on the coarse-grain level. Numerical, analytic, and grid-based discretizations can be combined and are treated on the same abstract level. Operators are specified in the input using a script language including symbolic algebra. User-friendly in- and output, error safety, and documentation are integrated by design. Program summaryProgram title: tRecX — time-dependent Recursive indeXing (tRecX=tSurff+irECS)CPC Library link to program files:https://doi.org/10.17632/zdjbnjxzrn.1Developer's repository link:https://gitlab.physik.uni-muenchen.de/AG-Scrinzi/tRecXCode Ocean capsule:https://codeocean.com/capsule/5391166Licensing provisions: GNU General Public License 2Programming language: C++Nature of problem: tRecX is a general solver for time-dependent Schrödinger-like problems, with applications mostly in strong field and attosecond physics. There are no technical restrictions on the spatial dimension of the problem with up to 6 spatial dimensions realized in the strong-field double ionization of Helium. A selection of coordinate systems is available and any Hamiltonian involving up to second derivatives and arbitrary up to three dimensional potentials can be defined on input by simple scripts.Solution method: The method of lines is used with spatial discretization by a flexible combination of one dimensional basis sets, DVR representations, discrete vectors, expansions into higher-dimensional eigenfunctions of user-defined operators and multi-center basis sets. Photo-emission spectra are calculated using the time-dependent surface flux method (tSurff) in combination with infinite range exterior complex scaling (irECS) for absorption. The code is object oriented and makes extensive use of tree-structures and recursive algorithms. Parallelization is by MPI. Code design and performance allow use in production as well as for graduate level training.

Solving variable-coefficient burnup equations by exponential Rosenbrock methods

Burnup calculation is an essential topic in reactor physics analysis, which is based on the neutronic-depletion coupling calculation. High order neutronic-depletion coupling methods have been demonstrated much superior to the traditional coupling methods in terms of accuracy, but introduce the variable-coefficient burnup equations. The straightforward and general method for solving variable-coefficient burnup equations is to discretize the burnup step into several substeps and then approximate variable-coefficient equations by a sequence of constant-coefficient ones. However, substep sizes must be rather small to obtain satisfactory accuracy, which causes numerous computational cost. In this work, a class of one-step methods called exponential Rosenbrock methods is proposed to solve variable-coefficient burnup equations. The major part of the implementation of exponential Rosenbrock methods is computing the matrix exponentials and related φ functions, so the matrix exponential methods for constant-coefficient burnup equations can be applied to exponential Rosenbrock methods directly. Moreover, each exponential Rosenbrock method has a corresponding embedded error estimator for adaptive time-stepping. A 4th-order exponential Rosenbrock method called EXPRB43 is used in this work, and two EXPRB43-based predictor–corrector coupling methods called EXPRB43-CE/LI and EXPRB43-LE/QI are further established by replacing the time step discretization method used in the conventional CE/LI and LE/QI with EXPRB43. To investigate the correctness and performance of EXPRB43 for solving variable-coefficient burnup equations, three artificial test Cases are first constructed by combining three different time-dependent fluxes and a specific cross-section library. The numerical results show EXPRB43 can improve the computational efficiency by 2 to 3 orders of magnitude compared to the straightforward method, and this novel method could easily obtain more accurate and reliable solutions by using an adaptive stepsize controller. Then, a test case for depleting a 2D UO2-Gd fuel pin is investigated to further demonstrate the performance of EXPRB43 in realistic neutronic-depletion coupling problems. By comparing to the conventional CE/LI and LE/QI, EXPRB43-based coupling methods can obtain slightly more accurate solutions especially for several important fission products, such as 155Gd, 157Gd, 135Xe and 149Sm. Although the overall computational errors dominated by the errors of polynomial approximation of the time dependent burnup matrix cover up the improvement of EXPRB43 to the naive substep method, EXPRB43-based coupling methods can be alternative to the conventional ones.

A homogenization method to solve inverse Cauchy–Stefan problems for recovering non-smooth moving boundary, heat flux and initial value

In the paper, we solve two Stefan problems. The first problem recovers an unknown moving boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second problem finds a time-dependent heat flux on the left-end, such that a desired moving boundary can be achieved. Then, we solve an inverse Cauchy-Stefan problem, using the over-specified Cauchy boundary conditions on a given moving boundary to recover the solution. Resorting on a homogenization function method, we recast these problems into the ones having homogeneous boundary and initial conditions. Consequently, the approximate solution is obtained by solving a linear system obtained from the collocation method in a reduced domain. For the first Stefan problem the moving boundary can be determined accurately, after solving a nonlinear equation at each discretized time. For the second Stefan problem, we can obtain the required boundary heat flux without needing of iteration. Numerical examples, including non-smooth ones, confirm that the novel methods are simple and robust against large noise. Moreover, the Stefan and inverse Cauchy-Stefan problems are solved without initial conditions.