Time-dependent Flux Research Articles

Unsteady heat conduction with phase change applied to a novel thermal plug and abandonment process

The continuous exploration of oil wells has increased the demand for plug and abandonment procedures. Current techniques used for well plugging involve the cementing process, which is extremely expensive and difficult to perform. Aiming to overcome these challenges, a new approach in this area has been investigated. This novel technology, named here as Thermal Plug and Abandonment (TP&A), proposes a chemical mixture that would be introduced through the production tube or the steel casing. Then, this mixture is ignited and the exothermic reaction generates enough heat to melt the wellbore components. After the cooling stage, the solidified mass composed by these components and the products of the reaction will serve as a seal to plug the well. Under such circumstances, this work aims to investigate this new technology assuming a thermite mixture that is introduced through the steel casing. For that, a numerical analysis is employed to investigate the heat conduction and the phase change through the oil well structure, which is modelled as a two-dimensional axisymmetric domain. The heat generated by the reaction is approached as a spatial and time-dependent heat flux profile that was estimated based on experiments found in literature. The thermal behavior is assessed to discover if the heat generated by the reaction is enough to form a plug composed by all components found in an oil well environment. It was found that temperatures are high enough to melt most part of the steel and a significant amount of the cement layer. The investigation also found that temperatures heavily drop through the cement layer, which avoids any notable melting of the cap rock. Finally, the heat fluxes’ profiles were increased, and it was found that a TP&A procedure that accounts for a seal composed by only the thermite products and the melted steel layer might be a more practical approach.

How a four-dimensional de Sitter solution remains outside the swampland

We argue that, in the presence of time-dependent fluxes and quantum corrections, four-dimensional de Sitter solutions should appear in the type IIB string landscape and not in the swampland. Our construction considers generic choices of local and non-local quantum terms and satisfies the no-go and the swampland criteria, the latter being recently upgraded using the trans-Planckian cosmic censorship. Interestingly, both time-independent Newton constant and moduli stabilization may be achieved in such backgrounds even in the presence of time-dependent fluxes and internal spaces. However, once the time-dependence is switched off, any four-dimensional solution with de Sitter isometries appears to have no simple effective field theory descriptions and is back in the swampland.

Precise control of time-varying effusion cell flux in molecular beam epitaxy

We outline a method to control time-varying effusion cell flux in molecular beam epitaxy. This can be used to grow 2D nanostructures with precise continuously graded alloys, and we explore the specific case of controlling an Al cell for the growth of continuously graded Al xGa 1 − xAs parabolic quantum wells. We develop a simple model of the Al cell’s thermal dynamics, including the effects of shutter transients. This model’s parameters can be empirically derived using a beam flux monitoring ion gauge. Though simple, this model can already be used to generate near-arbitrary time-varying fluxes (within the physical limits of the cell). For growths that require higher precision than the simple model can achieve, we introduce an iterative correction scheme to eliminate any lingering errors. Using this method, we control the composition in a 3 THz Al xGa 1 − xAs parabolic quantum well array to a root mean squared error of just ± 0.18 %Al. This accuracy is achieved at the standard growth rates necessary for thick structures (0.15–0.25 nm/s). The approach is quite generally applicable to other composition profiles or other situations where time-dependent flux control is necessary, and it could be extended to other effusion cells.

Modification of the Matalon-Packter Law for Self-Organized Periodic Precipitation Patterns by Incorporating Time-Dependent Diffusion Flux.

Spontaneous pattern formation is common in both inanimate and living systems. Although the Liesegang pattern (LP) is a well-studied chemical model for precipitation patterns, various recent LP systems based on artificial control could not be easily evaluated using classical tools. The Matalon-Packter (MP) law describes the effect of the initial electrolyte concentration, which governs the diffusion flux (Fdiff), on the spatial distribution of LP. Note that the classical MP law only considers Fdiff through the initial concentration of electrolytes, even though it should also depend on the volume of the reservoir used for the outer electrolyte because of the temporal change in the concentration therein due to diffusion. However, there has been no report on the relationship between the MP law, the reservoir volume, and Fdiff. Here, we experimentally demonstrated and evaluated the effect of the reservoir volume on LP periodicity according to the classical MP law. Numerical simulations revealed that the reservoir volume affects the temporal modulation of Fdiff. By expressing the MP law as a function of estimated Fdiff after a certain period of time, we provide a uniform description of the changes in periodicity for both small and large reservoir volumes. Such modification should make the MP law a more robust tool for studying LP systems.

Going Forward with the Nancy Grace Roman Space Telescope Transient Survey: Validation of Precision Forward-modeling Photometry for Undersampled Imaging

The Nancy Grace Roman Space Telescope (Roman) is an observatory for both wide-field observations and coronagraphy that is scheduled for launch in the mid-2020s. Part of the planned survey is a deep, cadenced field or fields that enable cosmological measurements with type Ia supernovae (SNe Ia). With a pixel scale of 0.″11, the Wide Field Instrument will be undersampled, presenting a difficulty for precisely subtracting the galaxy light underneath the SNe. We use simulated data to validate the ability of a forward-model code (such codes are frequently also called “scene-modeling” codes) to perform precision supernova photometry for the Roman SN survey. Our simulation includes over 760,000 image cutouts around SNe Ia or host galaxies (∼10% of a full-scale survey). To have a realistic 2D distribution of underlying galaxy light, we use the VELA simulated high-resolution images of galaxies. We run each set of cutouts through our forward-modeling code which automatically measures time-dependent SN fluxes. Given our assumed inputs of a perfect model of the instrument point-spread functions and calibration, we find biases at the millimagnitude level from this method in four red filters (Y106, J129, H158, and F184), easily meeting the 0.5% Roman inter-filter calibration requirement for a cutting-edge measurement of cosmological parameters using SNe Ia. Simulated data in the bluer Z087 filter shows larger ∼ 2–3 mmg biases, also meeting this requirement, but with more room for improvement. Our forward-model code has been released on Zenodo.

Theoretical analysis of transient solution phase concentration field in a porous composite electrode with time-dependent flux boundary condition

Energy conversion and storage in a Li-ion cell involves multiple closely coupled transport processes, such as species diffusion through solid and solution phases in the electrode. Mathematical modeling of these processes is critical for fully understanding and optimizing the performance of a Li-ion cell. While a number of analytical and numerical models have been presented for solution phase diffusion, most of such work is based on the assumption of a constant current density. This paper presents analytical modeling of solution phase diffusion in a separate–electrode composite for a generalized, time-dependent current density. An analytical solution for the concentration field in a separator–electrode composite in such conditions is derived using the method of eigenfunction expansion. Good agreement with past work as well as numerical simulations is shown. Results for linear, periodic and step-function boundary conditions are discussed. The theoretical analysis presented here may help accurately model realistic processes where the applied current changes over time, for example, cyclic charge and discharge in an electric vehicle, or sudden changes in the battery load. Results presented here contribute towards the fundamental understanding of solution phase diffusion in Li-ion cells, and provide a basis for improving electrochemical energy conversion and storage processes.

Unsteady convective heat transfer from a flat plate with heat flux that varies in space and time

Convective heat transfer due to laminar fluid flow past a flat plate is a standard problem in heat transfer. While constant heat flux or temperature along the plate is often assumed for solving such problems, there may be several practical scenarios where the heat flux along the plate varies as a function of both space and time. Developing an analytical solution for the resulting plate temperature distribution is important for understanding and optimizing the thermal performance of such systems. While some work exists on analyzing problems with time-dependent or space-dependent heat flux, there is a lack of work on the general problem where the heat flux is a function of both space and time. This paper presents a solution for this problem by solving the integral form of the energy equation, along with the use of fourth-order Karman-Pohlhausen polynomials for velocity and temperature distributions in the momentum and thermal boundary layers. A non-linear, first order, hyperbolic partial differential equation for the plate temperature is derived in response to the time- and space-varying plate heat flux. This equation is shown to agree well with results from past work for several special cases. Numerical solutions for the generalized equation are presented. Based on this approach, the plate temperature distribution is predicted for several heat flux profiles that may be of interest in practical applications. Results from this work improve our understanding of unsteady convective heat transfer, and contribute towards modeling and optimization of practical engineering systems where such phenomena occur.

Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems

This paper studies the reconstruction of the spatial-dependent-heat transfer coefficient γ(x) and- heat flux q(x), using the Levenberg–Marquardt (L–M) connected with the surrogate functional method and the modified conjugate gradient method (MCGM) (problem I). In addition to studying the reconstruction of γ(x) and space–time-dependent heat flux q(x,t) using the MCGM (problem II). The numerical results obtained by the L–M and MCGM demonstrate the efficiency, accuracy, and robustness of the proposed methods. The obtained results are compared with those obtained from an inverse approach connected with COMSOL Multiphysics under the same conditions. Finally, a conclusion and some remarks are presented.

HBV Core Protein Is in Flux between Cytoplasmic, Nuclear, and Nucleolar Compartments.

ABSTRACTHepatitis B virus (HBV) core protein (Cp) can be found in the nucleus and cytoplasm of infected hepatocytes; however, it preferentially segregates to a specific compartment correlating with disease status. Regulation of this intracellular partitioning of Cp remains obscure. In this paper, we report that cellular compartments are filled and vacated by Cp in a time- and concentration-dependent manner in both transfections and infections. At early times after transfection, Cp, in a dimeric state, preferentially localizes to the nucleolus. Later, the nucleolar compartment is emptied and Cp progresses to being predominantly nuclear, with a large fraction of the protein in an assembled state. Nuclear localization is followed by cell-wide distribution, and then Cp becomes exclusively cytoplasmic. The same trend in Cp movement is seen during an infection. Putative nucleolar retention signals have been identified and appear to be structure dependent. Export of Cp from the nucleus involves the CRM1 exportin. Time-dependent flux can be recapitulated by modifying Cp concentration, suggesting transitions are regulated by reaching a threshold concentration.

Developing a Modeling Framework to Simulate Compound Flooding: When Storm Surge Interacts With Riverine Flow

Compound flooding is a physical phenomenon that has become more destructive in recent years. Moreover, compound flooding is a broad term that envelops many different physical processes that can range from preconditioned, to multivariate, to temporally compounding, or spatially compounding. This research aims to analyze a specific case of compound flooding related to tropical cyclones where the compounding effect is on coastal flooding due to a combination of storm surge and river discharge. In recent years, such compound flood events have increased in frequency and magnitude, due to a number of factors such as sea-level rise from warming oceans. Therefore, the ability to model such events is of increasing urgency. At present, there is no holistic, integrated modeling system capable of simulating or forecasting compound flooding on a large regional or global scale, leading to the need to couple various existing models. More specifically, two more challenges in such a modeling effort are determining the primary model and accounting for the effect of adjacent watersheds that discharge to the same receiving water body in amplifying the impact of compound flooding from riverine discharge with storm surge when the scale of the model includes an entire coastal line. In this study, we investigated the possibility of using the Advanced Circulation (ADCIRC) model as the primary model to simulate the compounding effects of fluvial flooding and storm surge via loose one-way coupling with gage data through internal time-dependent flux boundary conditions. The performance of the ADCIRC model was compared with the Hydrologic Engineering Center- River Analysis System (HEC-RAS) model both at the watershed and global scales. Furthermore, the importance of including riverine discharges and the interactions among adjacent watersheds were quantified. Results showed that the ADCIRC model could reliably be used to model compound flooding on both a watershed scale and a regional scale. Moreover, accounting for the interaction of river discharge from multiple watersheds is critical in accurately predicting flood patterns when high amounts of riverine flow occur in conjunction with storm surge. Particularly, with storms such as Hurricane Harvey (2017), where river flows were near record levels, inundation patterns and water surface elevations were highly dependent on the incorporation of the discharge input from multiple watersheds. Such an effect caused extra and longer inundations in some areas during Hurricane Harvey. Comparisons with real gauge data show that adding internal flow boundary conditions into ADCIRC to account for river discharge from multiple watersheds significantly improves accuracy in predictions of water surface elevations during coastal flooding events.

Simultaneous reconstruction of thermal boundary condition and physical properties of participating medium

A hybrid optimization technique, which combines decentralized fuzzy inference method (DFIM) and sequential quadratic programming (SQP) algorithm, is developed to reconstruct the thermal boundary condition and physical properties of participating medium simultaneously. The coupled radiation-conduction heat transfer in the medium is solved by finite volume method in combination with discrete ordinate method. The reconstruction task is formulated as an inverse problem which is solved by the hybrid DFIM-SQP technique from the knowledge of surface temperature and exit radiative intensity. Retrieval results demonstrate that the time-dependent heat flux, absorption coefficient, scattering coefficient and thermal conductivity of participating medium can be accurately retrieved by the present methodology. The proposed DFIM-SQP technique is more accurate and efficient in solving the simultaneous reconstruction problem than DFIM, conjugate gradient method, SQP, particle swarm optimization and krill herd algorithms.

Development of experimental methodology for estimation of thermo-physical properties of engineering materials using inverse method

In the present article, a novel experimental methodology is proposed for the simultaneous estimation of unknown thermal conductivity (k) and specific heat capacity (cp) of engineering materials. The experimental method involves radiative heating of the test sample and measuring its temperature response at two different locations. Proper arrangements have been made to realize one-dimensional heat conduction within the test sample. The one-dimensional heat conduction equation with convection-radiation heat loss boundary condition is considered as the forward model as it best mimics the experimental heat transfer. The inverse problem is formulated as a parameter estimation problem, and solved using Levenberg-Marquardt algorithm. First, numerical estimations were carried out with synthetic temperature data. It was found that the time-dependent heat flux boundary condition is more suitable to estimate the properties of higher thermal conductivity materials. Then, real-time temperature measurements were carried out on Stainless Steel (SS), Mild Steel (MS), Brass (BS), Aluminium (Al), and Copper (Cu) test samples. The estimated k of SS, MS, BS, Al, and Cu in (W/(m K)) is 14.03, 54.63, 103.21, 221.53 and 379.89, respectively. And, the estimated cp of SS, MS, BS, Al, and Cu in (J/(kg K)) is 500.44, 460.84, 395.01, 939.58, and 398.43 respectively. The estimated thermal properties are also validated against experimentally measured values obtained using the Modified Transient Plane Source (MTPS) sensor. It was found that the estimated k and cp in case of SS has a deviation of 7% and 4%, respectively.

Uniform fertilization method based on differential pressure tank with optimal fertilizer concentration and constant fertigation flux

Nonuniformity in fertilization causes water and soil pollution, thus negatively affecting the yield and quality of crops. Differential pressure tanks are widely used in China. However, such tanks hardly overcome nonuniformity in fertilization. In this study, a flux control method is derived for uniform fertilization on the basis of differential pressure tank with optimal (constant) fertilizer concentration and constant fertigation flux. The fertilizer continuity equation is applied for the flux control method by a uniform distribution assumption of fertilizer concentration in the tank. In accordance with four free parameters, the flux control method is used to divide the constant fertigation flux into two time-dependent fluxes; one flux flows into the tank to remove fertilizers uniformly, and another flux directly flows through the main pipe to mix with outlet fertilizers for an optimal fertilizer concentration in the fertigation system. On the basis of the flux control method, a grade control methodology is further proposed for the convenient and easy division of fertigation flux. In addition, a numerical model for mixed water and fertilizer flow is proposed to verify whether the flux control method is feasible for uniform fertilization. The flux control method is meaningful for improving the management and efficiency for water–fertilizer use in China.

Theoretical investigation of the Freeman resonance in the dissociative ionization of H2+

The dissociative ionization of $H_2^+$ in linearly polarized, 400 nm laser pulses is simulated by solving a three-particle time-dependent Schr\"odinger equation in full dimensionality. The joint energy spectra (JES) are computed for $\cos^8$ and flat-top envelopes using the time-dependent surface flux (tSurff) methods. In JES, the energy sharing $n$ photon energies $\omega$ of nuclear kinetic energy release (KER) $E_N$ and electronic KER $E_e$ are well represented by $E_N+E_e=n\omega-U_p+E_0$ for $\cos^8$ pulses, but satisfy $E_N+E_e=n\omega+E_0$ for flat-top envelope, exposing a deviation of the ponderomotive energy $U_p$, which has been observed in experiments, where $E_0$ is the ground energy of $H_2^+$. The analysis of the wavefunction for electrons and protons after the pulse are presented, where we find $U_p$ is absorbed by the Freeman resonances between two excited ungerade states.

Temporal evolution of fluxes in driven quantum dots

Driven mesoscopic system is a topic of great recent interest. The temporal evolution of the fluxes (particle and energy) are studied in a system of a driven single level quantum dot. At a very low reservoir temperature T→0 and for common chemical potentials of the two reservoirs, we have presented analytical expressions for time dependent particle and energy fluxes in a very simple form. Apart from these fluxes, the behavior of the dot occupation and the power developed in the system due to the presence of the time dependent drive are also being studied. Importantly, for a very low frequency of the drive, one finds a directed energy flow towards the leads. Increasing the frequency from low to medium, one finds change in the direction of the energy flow, which depends on time. These results can also be verified experimentally.

Inverse Estimation of Time-Dependent Heat Flux in Stagnation Region of Annular Jet on a Cylinder Using Levenberg–Marquardt Method

All solving methods available in literature are formulated for direct solution of stagnation point flow and its heat transfer impinging on the surfaces with known boundary conditions. In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving the inverse heat transfer problem of an annular jet on a cylinder and estimating the time-dependent heat flux using temperature distribution at a specific point. For this purpose, the numerical solution of the dimensionless temperature and the convective heat transfer in a radial incompressible flow on a cylinder rod is carried out as a direct problem. Using similarity variable and appropriate transformations, momentum and energy equations are converted into Semi-similar equations. The heat flux is then estimated by applying the Levenberg–Marquardt approach. This technique is an iterative approach based on minimizing the least-square summation of the error values, the error being the difference between the estimated and measured temperatures. Results of the inverse analysis indicate that the Levenberg–Marquardt algorithm is an efficient and acceptably stable technique for estimating heat flux. This method also exhibits considerable stability for noisy input data. The maximum value of the sensitivity coefficient is related to the estimation of exponential heat flux and its value is 0.1619 also the minimum value of the sensitivity coefficient is 5.6210-6 which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.481 and 0.489, respectively the reason for the increase in the errors in estimating these functions is the existence of points where the first derivative of the function does not exist.

2D linear finite element simulation of laser metal heating for digital twins

In the context of laser-based additive manufacturing, the thermal behavior of the substrate is relevant to define process parameters vis-à-vis piece quality. The existing literature focuses on two process variables: (a) lumped laser power and (b) process speed. However, this literature does not consider other variables, such as those related to the laser power distribution. To fill this vacuum, this manuscript includes the laser power spatial distributions (Gaussian, uniform circular and uniform rectangular) in addition to (a) and (b) above in 2D linear substrate heating simulations. The laser energy is modeled as a time dependent heat flux boundary condition on top of the domain. The total laser delivered power was identical for all spatial distributions. The results show that the laser intensity spatial distribution strongly affects the maximum temperature, and the depth and width of the heat affected zone. These 2D finite element simulations prove to be good options for digital twin based design environments, due to their simplicity and reasonable temperature error, compared to non-linear analysis (considered as ground truth for this case). Future publications address non-linear finite element simulations of the laser heating process (including convection and radiation and temperature dependent substrate properties).

Semi-derivative integral method to transient heat conduction time-dependent heat flux boundary conditions

Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.

ANALYSIS AND COMPARISON OF APOLLO3® AND TRIPOLI-4® NEUTRON NOISE SOLVERS

Neutron noise analysis addresses the description of small time-dependent flux fluctuations in reactor cores, induced by small global or local perturbations of the macroscopic cross sections due to density fluctuations of the coolant, to vibrations of fuel elements, control rods, or structural materials. The general noise equations are obtained by assuming small perturbations around a steady-state neutron flux and by subsequently taking the Fourier transform in the frequency domain. Recently, new neutron noise solvers have been implemented in diffusion and transport theory in APOLLO3®, the multi-purpose deterministic transport code developed at CEA, and a new stochastic solver has been implemented for the neutron noise analysis in the frequency domain in the Monte Carlo code TRIPOLI-4®, also developed at CEA. In this paper, we compare the two solvers for the case of fuel pin oscillations in a simplified UOX fuel assembly, in view of proposing the examined configurations as a benchmark for neutron noise calculations.

Magnetophotothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat flow

A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect. The system equations for coupled plasma, heat conduction with phase-lags (PLs), and motion equations are introduced and solved by using the Laplace transform technique. The photothermal, thermal, and elastic waves in a rotating solid cylinder of semiconductor material are analyzed with the proposed model. The cylinder surface is constrained and subjected to a time-dependent pulse heat flux. The sensitivity of the physical fields for the angular velocity, PLs, and thermal vibration parameters is investigated. In addition, the effects of the effective parameters on the physical quantities are graphically illustrated and discussed in detail.