Transport Equation Research Articles

Functional renormalization group study of thermodynamic geometry around the phase transition of quantum chromodynamics

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, T, and quark number chemical potential, μ. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization group approach. We use recent developments to recast the flow equation into the form of an advection-diffusion equation. We adopt the local potential approximation for the effective average action. We focus on the thermodynamic curvature, R, in the (μ,T) plane, in proximity of the chiral crossover, up to the critical point of the phase diagram. We find that the inclusion of fluctuations results in a smoother behavior of R near the chiral crossover. Moreover, for small μ, R remains negative, signaling the fact that bosonic fluctuations reduce the capability of the system to completely overcome the fermionic statistical repulsion of the quarks. We investigate in more detail the small μ region by analyzing a system in which we artificially lower the pion mass, thus approaching the chiral limit in which the crossover is actually a second order phase transition. On the other hand, as μ is increased and the critical point is approached, we find that R is enhanced and a sign change occurs, in agreement with mean field studies. Hence, we completely support the picture that R is sensitive to a crossover and a phase transition, and provides information about the effective behavior of the system at the phase transition. Published by the American Physical Society 2024

Anisotropic Fourier Heat Conduction and phonon Boltzmann transport equation based simulation of time domain thermo-reflectance experiments

The anisotropic Fourier Heat Conduction Equation (FHCE) and the multidimensional phonon Boltzmann Transport Equation (BTE) were solved numerically in cylindrical coordinates and in time domain to simulate a Time Domain Thermo-Reflectance (TDTR) experimental silicon/aluminum substrate/transducer setup. The out-of-phase response of the probe laser was predicted at various beam offset distances for a pump laser pulse frequency of 80 MHz and modulation frequency of 10 MHz and compared against experimental measurements for a silicon substrate. The isotropic FHCE was also solved for comparison. Results show that the isotropic FHCE with bulk thermal conductivity of 145 W/m/K significantly underpredicts the out-of-phase temperature difference, particularly at smaller beam offsets. With an isotropic thermal conductivity of 105 W/m/K, the computed results match experimental data at smaller beam offsets well, but overpredicts the experimental data at larger beam offsets. An almost-perfect match is obtained by using an anisotropic thermal conductivity wherein the radial (in-plane) thermal conductivity is set to 85 W/m/K and the axial (through-plane) conductivity is set to 130 W/m/K. The multidimensional frequency and polarization dependent phonon BTE is next solved. The BTE results for the out-of-phase temperature difference match experimental observations well at small and intermediate beam offsets, but overpredicts the experimental data at larger beam offsets. FHCE results are fitted to the BTE predictions, and the extracted (best fit) thermal conductivity is found to be 110 W/m/K.

Kinetics Parameters Estimation for the Coupled Neutron-Photon Point Kinetics Model in Monte Carlo Eigenvalue Calculations

The delayed photoneutron effect should be considered in the point kinetics equation (PKE) applied to D2O and beryllium-moderated or -reflected systems because of its importance on reactor kinetics. This paper proposes neutron-photon-coupled PKE with a clear definition of adjoint-weighted kinetics parameters after providing the mathematical derivation from the neutron and photon transport and precursor equations. The Monte Carlo algorithms to estimate the kinetics parameters are induced from their definition and implemented in the eigenvalue calculation module of McCARD. They are verified through homogeneous infinite-medium problems with few-group neutron and photon cross sections by comparing with analytic solutions. The proposed PKE and kinetics parameters estimation methods are applied for the kinetics analyses of the artificial control rod drop transient problem in the RB reactor. Photonuclear physics is also implemented in a time-dependent Monte Carlo simulation to calculate the reference data of neutron amplitude in the core to be compared with the PKE results. As good agreement is shown in the neutron amplitude, it is validated that the developed PKE is capable of predicting the reactor kinetics considering photoneutrons.

A BDF2 method for a singularly perturbed transport equation

A singularly perturbed transport equation is considered. A variable two-step backward differentiation formulas (BDF2) on a Shishkin-type mesh is used to discrete the first-order derivatives of the singularly perturbed transport equation. The stability and error analysis are derived by using the discrete orthogonal convolution kernels. It is proved that the scheme is second-order uniformly convergent with respect to the small parameter, which improves previous results. Numerical experiments are presented to support the theoretical result.

Initial-boundary value problem for transport equations driven by rough paths

In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Hölder p p -rough paths. We introduce a notion of solutions to rough partial differential equations with boundary conditions. Consequently, we will establish a well-posedness for such a solution under some assumptions stated below. Moreover, the solution is given explicitly.

Inversion of the attenuated momenta ray transform of planar symmetric tensors

Abstract We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim's $A$-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of 1-tensors.

Effect of radius-dependent diffusion behavior of various gold nanoparticles on photothermal therapy

Among the various anti-cancer treatments, photothermal therapy (PTT) is gaining traction as it is a non-invasive treatment. PTT is a treatment technique involving the use of a laser to raise the temperature of the target tumor until it dies. In this study, the effects of PTT under various conditions of squamous cell carcinoma (SCC) occurring in the skin were numerically analyzed and optimized. Gold nanoparticles (AuNPs) with different radii were injected into the center of the SCC. Subsequently, the diffusion behavior of the AuNPs was analyzed to calculate the distribution area of the AuNPs that changed over time. Furthermore, at each elapsed time point after injection, the temperature distribution in the tissue was calculated, as treatment was performed using varying laser intensities. The diffusion coefficient of AuNPs was calculated using the Stokes–Einstein equation, and diffusion behavior of AuNPs in biological tissues was analyzed using the convection–diffusion equation. Additionally, temperature distribution was analyzed using the Pennes bioheat equation. The effect of PTT under each condition was quantitatively analyzed using apoptotic variables. As a result, As the radius of AuNPs increased, the optimal treatment start time was derived as 2 h, 8 h, 8 h, and 12 h, respectively, and the laser intensity at that time was derived as 0.44 W, 0.46 W, 0.42 W, and 0.42 W, respectively. The study findings will provide reference for the optimization of the efficacy of PTT.

Propagation of nanosecond discharge in an air gap containing a water droplet: modelling and comparison with time-resolved images

The plasma-water interface is a complex medium characterized by interesting physical and chemical phenomena useful for many applications such as water processing or material synthesis. In this context, optimizing the transport of reactive species from plasma to water is crucial, and it may be achieved by increasing the surface-to-volume ratio of the processed object. Herein, we study the characteristics of a streamer produced by nanosecond discharge in air gap with a droplet of deionized water. The discharge is characterized experimentally by electrical measurements as well as by 1 ns-intergated ICCD images. To report plasma properties that are not accessible through experiment, such as the spatio-temporal evolution of electron density, electric field, and space charge density, a 2D fluid model is developed and adapted to the experimental geometry. Due to the fast propagation of the ionization front, the droplet is considered as a solid dielectric. The model solves Poisson’s equation as well as the drift-diffusion equation for electrons, positive ions, and negative ions. The utilized transport coefficients are tabulated as a function of the reduced electric field. Helmholtz equations are also included in the model to account for photoionization. The electron impact ionization source obtained from the model is compared to experimental 1 ns-integrated ICCD images, and a good agreement is observed. Finally, the model is used to investigate the influence of droplet dielectric permittivity and wetting angle (the angle between a liquid surface and a solid surface) on the properties of the discharge. Overall, the data reported herein demonstrate that the model can be used to investigate plasma properties under different conditions.

An Eulerian–Lagrangian method of fundamental solutions for the advection–diffusion equation with time dependent coefficients

This paper investigates the application of the Eulerian–Lagrangian method of fundamental solutions (ELMFS), a truly meshless method that couples the Euler–Lagrange Method (ELM) with the time-dependent method of fundamental solution (MFS). It is applied to solve the transient advection–diffusion equation with transport coefficients exhibiting constant and temporally exponential behaviors. The stability and accuracy of the proposed method were analyzed in terms of condition numbers, location of source points, and error metrics. The stability results for constant coefficients of partial differential equations are presented in a map and compared with well-established stability criteria for explicit in-time mesh methods, such as the Courant–Friedrichs–Lewy and Von Neumann criteria. These comparisons demonstrate that ELMFS has larger stable regions.

The Role of Turbulence Transport in Mechanical Energy Budgets

Abstract In this article, we study the role of turbulence transport on loss prediction using high fidelity scale-resolving simulations. For this purpose, we use eight high-fidelity simulation datasets and compute flux of entropy and stagnation pressure transport equation budgets for all the cases. We find that under certain unsteady inflow conditions, the stagnation pressure coefficient is not a reliable loss metric even at low Mach number conditions. This is due to the turbulence transport terms. The impact of these terms, typically assumed to be negligible, made stagnation pressure loss coefficient underpredict loss from 0% to over 40% when compared to entropy loss coefficient for cases considered here. This effect was most pronounced for the cases with highly unsteady inflow conditions and at low Reynolds numbers.

Mapping of Long-Wavelength Phonon Contribution in the Thermal Transport of Alloyed Semiconductor Superlattices.

The mapping of long-wavelength phonons is important to understand and manipulate the thermal transport in multilayered structures, but it remains a long-standing challenge due to the collective behaviors of phonons. In this study, an experimental demonstration of mapping the long-wavelength phonons in an alloyed Al0.1Ga0.9As/Al0.9Ga0.1As superlattice system is reported. Multiple strategies to filter out the short- to mid-wavelength phonons are used. The phonon mean-free-path-dependent thermal transport properties directly demonstrate both the suppression effect of the ErAs nanoislands and the contribution of long-wavelength phonons. The contribution from phonons with mean free path longer than 1 μm is clearly demonstrated. A model based on the Boltzmann transport equation is proposed to calculate and describe the thermal transport properties, which depicts a clear physical picture of the transport mechanisms. This method can be extended to map different wavelength phonons and become a universal strategy to explore their thermal transport in various application scenarios.

Numerical simulation of natural convection in a rectangular enclosure filled with porous medium saturated with magnetic nanofluid using Buongiorno's two‐component model

AbstractMotivated by studying emerging nanofluid‐based magnetic fuel cells and hybrid direct absorber solar collectors, a numerical study is presented for buoyancy‐driven flow in a vertical enclosure containing a porous medium saturated with magnetized nanofluid flow under a transverse static magnetic field. The enclosure features adiabatic side walls and vertical heat slits, ensuring consistent cold temperatures on the lower and upper bounded walls. The side walls of the regime are insulated, and the hot slits are centrally located on these walls. The finite difference method (FDM) is applied to employ the transformed dimensionless vorticity–stream function (VSF) formulation of the transport equations. The impact of pertinent parameters on isotherm, streamline, iso‐concentration, and average Nusselt and Sherwood numbers are visualized with contour plots and graphs. Increasing Darcy number values tend to amplify the isotherm magnitudes. Higher Hartmann (magnetic) number values, on the other hand, lead to a reduction in local Nusselt number profiles but do not significantly modify the local Sherwood number. The porous medium permeability, as simulated via the Darcy number, has a strong impact on streamlines, thermal contours, and iso‐concentrations. A reduction in Darcy's number suppresses local Nusselt and Sherwood numbers, whereas an elevation in Rayleigh's number enhances them. Increasing the Buongiorno nanoscale Brownian motion parameter enhances local Nusselt and Sherwood numbers at both cold walls of the enclosure. The simulations provide a deeper insight into enclosure flows involving electrically conducting nanofluids in advanced processing systems for nanomaterials and hybrid fuel cells utilizing electromagnetic and liquid fuel technologies.

Ab-initio transport model to study the thermoelectric performance of MoS2, MoSe2, and WS2 monolayers by using Boltzmann transport equation

The potential for thermoelectric applications of two-dimensional materials is quite promising. Using ab-initio calculations, we have investigated the electronic band structure, phonon band structure, electronic density of states, and phonon density of states of monolayers MoS2, MoSe2, and WS2. In order to compute the thermoelectric properties of monolayers MoS2, MoSe2, and WS2, we used the ab-initio model suggested by Faghaninia et al (2015 Phys. Rev. B 91 235123). Within this model, by using inputs from density functional theory and considering all relevant elastic and inelastic scattering mechanisms, we have calculated the thermoelectric properties of monolayers MoS2, MoSe2, and WS2 over various ranges of temperature (T) and carrier concentration (n). The obtained results of Seebeck coefficients (S) and figure of merit (ZT) at T = 300 K for both n/p-types of monolayers MoS2, MoSe2, and WS2 are in good agreement with the findings obtained by other models using the Boltzmann transport equation within a constant relaxation time framework.

Thermosolutal and hydromagnetic performance of radiative hybrid nanofluid in a wavy porous enclosure with a plus-shaped baffle

The objective of this article is to explore the thermosolutal transmission rates with hydromagnetic Fe3O4-H2O nanofluid and Fe3O4-Cu-H2O hybrid nanofluid flow in a partially heated wavy porous enclosure with a plus-shaped baffle. A portion of length b on the bottom border is heated and soluted uniformly, while the rest portions of the bottom wall are assumed as adiabatic. The side curved borders are considered as cold and low concentration, while the adiabatic condition is imposed in the upper flat border. A plus-shaped cold baffle is located at the geometric center of the chamber. The porous cabinet is filled with a radiative Fe3O4-H2O nanofluid and Fe3O4-Cu-H2O hybrid nanofluid. The streamfunction (ψ)- vorticity (ζ) form incorporating the energy and species transport equations of coupled Navier-Stokes governing equations are solved by an efficient compact scheme. We have validated our in-house computational code with reliable published numerical and experimental works. This work explores the impacts of various well-defined parameters such as Rayleigh number (104≤Ra≤106), Hartmann number (0≤Ha≤40), Darcy number (10−4≤Da≤10−2), buoyancy ratio (N=1), Lewis number (1≤Le≤20), radiation parameter (1≤Rd≤10), heater size (0.2≤b≤0.8), volumetric heat source/sink coefficient (−10≤Q≤10) and solid volume fraction (0.0≤ϕhnp≤0.04) of the hybrid nanofluid. We have found that for the change in the radiation parameter (Rd) from 1 to 10, energy transfer is improved by 150.67% for Fe3O4-Cu-H2O hybrid nanofluid and 149.80% for Fe3O4-H2O nanofluid whereas solutal transfer is diminished by 4.76% and 4.83%, respectively. Our result revealed that Fe3O4-Cu-H2O hybrid nanofluid is more useful than Fe3O4-H2O nanofluid in the case of double diffusion.

Numerical Analysis Study of Chemically Radiative MHD Williamson Nanofluid Flow over an Inclined Surface with Heat Source

The design and optimization of systems such as nuclear reactors, solar collectors, and thermal power plants may benefit from an understanding of the behaviour of nanofluids with chemical processes, thermal radiation, and magnetic fields over inclined surfaces with heat sources.This review looks at the magnetohydrodynamic (MHD) flow of a Williamson nanofluid over an inclinable stretched sheet and the impact of thermal radiation, heat source, and chemical processes. The outcomes of the generation of heat or absorption, as well as thermal radiation, are all factored into account in the energy equation. On the other hand, the mass transport equation also takes into account chemical interactions.The similarity substitution serves to turn the governed partial differential equations for velocity, temperature, and concentration into ordinary differential equations, which are then numerically resolved with Mathematica's NDSolve program. Changes in temperature, concentration, and dimensionless velocity as a function of various factors are graphically touched upon. The temperature diminishes while the Prandtl number accelerates as the thermal boundary layer thins and the viscosity enrichment. The temperature contour develops along with the magnetic field strength. When all the parameters were compared for a particular case, a very good association was discovered. Depending on the precise conclusions and understandings drawn from the investigation of chemically radiative MHD nanofluid flow over inclined surfaces with a heat source, the applications may range greatly. It's important to remember that such research often aids in the creation of more effective and environmentally friendly solutions in a variety of sectors.

Exergy performance analysis of hydrogen recirculation ejectors exhibiting phase change behaviour in PEMFC applications

A comprehensive analysis of flow behavior and exergy performance was conducted in hydrogen recirculation ejector, taking into account the phase change of humid hydrogen for proton exchange membrane fuel cell (PEMFC) systems. A two-phase nonequilibrium condensation CFD model integrating the entropy transport equations was established. The effect of phase change on ejectors’ performance under various primary pressure, secondary pressure and temperature, and back pressure were analyzed. When primary pressure was adjusted into 3.0 bar, a liquid fraction of 4.56 % was observed at the outlet, while the liquid fraction will increase to 15.35 % when the inlet pressure got to 5.0 bar. Then, the values of mass flow rate and liquid mass fraction on different sections under variable secondary temperature and back pressure were calculated. Finally, it is found that a larger primary pressure brought an increase in exergy destruction. So was exergy destruction ratio. However, increasing secondary pressure leads to the opposite result. With the increase of secondary temperature from 60 to 80 °C, exergy destruction increases from 330.28 to 390.23 kJ/kg but the destruction ratio decreases from 29.85 % to 26.19 %.

A numerical method for two-dimensional transient nonlinear convection-diffusion equations

In this research, we have developed the half-boundary method (HBM) for nonlinear convection-diffusion equations (CDEs), which hold significant importance in nuclear power engineering. The HBM employs a variable relationship between the nodes within the computational domain and the nodes located on half of the boundaries. This approach offers notable benefits, includingthe reduction ofthe maximum matrix order and the optimization the maximum memory storage for calculations. Moreover, the HBM is an efficient and streamlined approach to directly handle Neumann boundary conditions, thanks to the utilization of mixed variables. We primarily investigate the memory usage and accuracy of the proposed algorithm in the unsteady-state CDEs, in context of material nonlinear CDEs, the Burgers’ equation and the system of Burgers' equations. The numerical results obtained demonstrate the method’s potential in simulating flow and heat transfer phenomena, particularly in situations where convection is dominant.

A hybrid CPU‐GPU paradigm to accelerate reactive CFD simulations

AbstractThe solution of reactive computational fluid dynamics (CFD) simulations is accelerated by the implementation of a hybrid central processing unit/graphics processing units (CPU/GPU) Finite Volume solver based on the operator‐splitting strategy, where the chemistry integration is treated independently of the flow solution. The integration of ordinary differential equations (ODEs) describing the finite‐rate chemical kinetics is solved by an adaptive multi‐block explicit solver on GPUs, while the load of the fluid solution is distributed on a multicore CPU algorithm. The resulting speed‐up for reactive CFD simulations is up to 10; the performance gain increases with the size of the mechanism. The proposed implementation is general and can be applied to any CFD problem where the governing equations for the fluid transport are coupled with an ODE system. Code validation is performed against reference solutions on a selection of test cases involving reacting flows.

A spin current detecting device working in the drift-diffusion and degenerate regimes

<p>A semiconductor-based device working in the spin drift-diffusion regime and for probing the injected or generated spin current was considered. The electric field effects on spin transport were analysed. A drift-diffusion equation for spin density was derived and contributions to the spin current were examined. By referring to the techniques of the spin current injection and generation, expressions for the spin current and spin-induced transverse Hall voltage arising from the injected or generated spin-polarized current were derived. The spin current and Hall voltage in dependences of the external electric field and temperature in the degenerate regime were studied. The device operated on the basis of with no external magnetic fields gives a voltage probe of the spin-induced Hall effect. Finally, a way of enhancing the spin current was explored.</p>

Rate-limiting factors in thin-film evaporative heat transfer processes

In this paper, we present a theoretical study aimed at investigating the rate-limiting factors in thin-film evaporative heat transfer processes, considering the finite-rate evaporation kinetics. The problems of evaporation of a flat thin-film in either pure vapours or vapour-inert-gas mixtures are analysed based on the non-dimensionalised macroscopic transport equations for continuum fluids, coupled with out-of-equilibrium kinetic boundary conditions. Both the full numerical solutions and asymptotic analytical solutions at slow evaporation limit are provided and applied to analyse thin water film evaporation. Existing solutions, assuming negligible heat transfer in the gas domain, or negligible temperature jump across the non-equilibrium kinetic layer, or more boldly a thermodynamically equilibrial interface (i.e. its temperature is at the saturation temperature), can be fully recovered from the more general solutions presented here. Our results show that while these assumptions hold in special cases, they can lead to significant errors in many conditions, especially when the film thickness δ is reduced to a few micrometers or thinner. We show that the conventional views that the rate-limiting factors in thin-film evaporative heat transfer is either the heat diffusion through the liquid film or the mass transfer in the gas domain only apply to thick film (i.e. δ≫λ where λ is the mean free path in the vapour phase). As δ decreases to a few micrometer or smaller (more precisely when the Knudsen number Kn increases beyond O(1) in an pure vapour environment or when the kinetic Peclet number Pe is reduced below O(1) in inert gases), the interfacial thermal resistance due to the evaporation kinetics can be on the same orders of magnitude as the thermal resistance in the liquid film. The analysis also allow us to compare the heat transfer processes during the evaporation of a thin-film in pure vapours to those in inert gases, providing deeper insight into the effectiveness of various strategies for exploring the evaporation process in practical thermal management.