Energy Transport Equations Research Articles

Coherent turbulent flow structure under plunging breaker on movable grain bed simulated by 3D DEM-MPS method

ABSTRACT Breaking waves transport momentum, gas, and sediment vertically. Recent particle image velocimetry (PIV) measurements have elucidated the coherent vortex and turbulence structures under breaking waves. However, clarifying three-dimensional fluid motion under breaking waves with PIV remains challenging. Although particle methods have performed wave-breaking simulations, they have never been validated through velocity distributions for breaking waves above movable sediment beds. This study simulated the sediment transport process under plunging waves using a 3D Lagrangian fluid-particle mixture model. The investigation focuses on the first wave plunging for a fundamental investigation. Our simulation shows the instantaneous velocity distributions at different wave phases, which agree with the PIV measurement. A physically-based turbulence extraction method is introduced: a numerical filter based on the coherence between the water elevation and horizontal velocity. Visualized three-dimensional vortex and turbulence structures are consistent with previous studies. The transport equation of the kinetic turbulence energy investigates the turbulence budget near the bed surface and emphasizes the negative contribution of the fluid-particle interaction. Our findings show that a contribution of the pressure gradient to offshore sediment transport. The pressure gradient is difficult to correlate to the water surface gradient and is derived from the large vortex induced by the plunging wave.

A numerical framework for modeling evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets

This paper presents a comprehensive numerical framework for simulating the evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets. The framework incorporates a detailed description of chemical reactions in the gaseous phase and is capable of modeling pure evaporation, autoignition, and hot-wire ignition scenarios.The transport equations for mass, species, and energy are solved in both the liquid (droplet) and gaseous (surrounding atmosphere) phases. Diffusion in the liquid phase is described using the Stefan–Maxwell theory, while in the gaseous phase, both molecular and thermal diffusion are considered. The model also includes the thermophoretic effect for carbonaceous particles and accounts for gas radiation through various models, ranging from optically-thin approximations to more complex methods like the P1 and discrete ordinate methods. Non-gray radiative effects are handled using the Weighted-Sum-of-Gray-Gases Model (WSGGM). Liquid/gas interface conditions are evaluated by imposing flux continuity of mass and energy, along with thermodynamic equilibrium for species. Deviations from ideal thermodynamic behavior in the liquid droplet are managed by incorporating a suitable activity coefficient or by using a proper cubic equation of state. Additionally, the presence of supporting fibers is modeled using a simplified one-dimensional approach. The transport equations are solved using the method of lines, with spatial discretization performed via the finite difference method on a body-fitted grid. The resulting system of Differential–Algebraic Equations (DAEs) is then solved using a fully-coupled approach.Thanks to its generality in terms of kinetic and thermodynamic descriptions and the reduced computational time, the proposed framework offers significant potential for advancing our understanding of the complex combustion processes of multi-component liquid fuels and for enhancing the planning and execution of experiments involving isolated fuel droplets.

Flow Field Characteristics at the Spanwise Edge of a Vegetative Canopy Model

This study investigates the complex flow field across a spanwise vegetative model canopy edge focusing on turbulent transport processes. Utilizing stereoscopic particle image velocimetry, the three velocity components were measured in wall-parallel planes at various elevations within canopy across the spanwise canopy edge. Conventional ensemble averaged results were contrasted with those obtained by conditionally averaged flow properties across instantaneous internal interfaces in the flow to understand their contribution to the ensemble average. The conditional average captured the strong gradients in mean velocities, Reynolds stresses, vorticity, swirling strength, and turbulent kinetic energy production across the dynamically changing instantaneous interface. In contrast, the conventional ensemble average smeared out the strong gradients. Small magnitudes of advective terms in the turbulent kinetic energy transport equation suggested weak secondary transverse flows in the present model canopy. The turbulent flow structure across the spanwise canopy edge was further investigated using Quadrant-Hole analysis for both averaging approaches. Conventional ensemble averaged results indicated a shift from sweep to ejection dominance when moving from canopy into the open patch, while the conditional average showed only sweep dominated transport. In contrast to a homogeneous canopy layout, below canopy height at the canopy edge, sweeps and ejections lose their dominance in vertical turbulent transport. The present results show that the dynamics of internal interfaces govern the ensemble averaged results and a possible implementation into existing models is proposed. The present results are expected to increase understanding of spanwise turbulent transport and aid in developing strategies to mitigate desertification.

Numerical Analysis for a Non-isothermal Incompressible Navier–Stokes–Allen–Cahn System

In this paper we develop the numerical analysis for a non-isothermal diffuse-interface model, in dimension N=2,3,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=2, 3,$$\\end{document} that describes the movement of a mixture of two incompressible viscous fluids. This model consists of modified Navier–Stokes equations coupled with a phase-field equation given by a convective Allen–Cahn equation, and energy transport equation for the temperature; which admits a dissipative energy inequality. We propose an energy stable numerical scheme based on the Finite Element Method, and we analyze optimal weak and strong error estimates, as well as convergence towards regular solutions. In order to construct the numerical scheme, we introduce two extra variables (given by the gradient of the temperature and the variation of the energy with respect to the phase-field function) which allows us to control the strong regularity required by the model, which is one of the main difficulties appearing from the numerical point of view. Having the equivalent model, we consider a fully discrete Finite Element approximation which is well-posed, energy stable and satisfies a set of uniform estimates which allow to analyze the convergence of the scheme. Finally, we present some numerical simulations to validate numerically our theoretical results.

A Thermal Model for a Hybrid Gas Bearing System in Oil-Free Turbochargers

Abstract With little drag friction, gas bearings operate at high rotor speed and high temperature and thus enable long operating life along with material damping for mechanical energy dissipation. However, most computational tools for modeling gas bearings are not accessible to bearing manufacturers or potential end-users, and the models are restricted to specific geometries and operating conditions or are missing important features, thus limiting their utility. This paper presents the thermal energy transport in a hybrid gas bearing for oil-free turbochargers with integrated heat and fluid flow models to produce a comprehensive thermo-hydrodynamic analysis predictive tool, and to design and evaluate air-lubricated gas bearings by predictions and experiments. An efficient algorithm couples the solution of the Reynolds equations and the thermal energy transport equations in the film between the rotor and a pad of the hybrid gas bearing, and updates the temperature-dependent viscosity and film thicknesses during the iterative process. The test repeats and averaged for each rotor speed from 2 krpm to 22 krpm at intervals of 2 krpm, for supply pressure varying along 25 psi to 100 psi and predicted film temperature matches well with the measured one. The parameters of interest in this analysis include the gas supply condition, bearing configuration, and the gas properties at high altitudes and high rotation speeds. The parametric study results show the density and kinematic viscosity are the most dominant properties of the gas lubrication for the film temperature.

Effective battery pack cooling by controlling flow patterns with vertical and spiral fins

Battery Thermal Management System (BTMS) is essential for dissipating heat and controlling temperature distribution within the battery pack of an electric vehicle to maintain its optimal operating temperature. This research focuses on the influence of cooling fins in achieving balanced temperature distribution inside the battery pack. Vertical and spiral fins are attached around 21,700 cylindrical cells for this investigation. ANSYS FLUENTsoftwareis employed to conduct the numerical simulations, where a finite volume approach is used to solve the mass conservation, Navier–Stokes, and energy transport equations. The study also uses a set of polynomial functions to calculate the heat generation inside the cells. It assesses the effects of the Reynolds number, fin loop number, and outlet section of BTMS at numerous discharge rates. The findings indicate that the spiral fins significantly impact the thermal performance, reducing Tmax by 21.31 % due to the enhanced flow circulations within the BTMS. A high Reynolds number also positively affects Tmax by reducing the temperature uniformity caused by the shorter time for air-cooling contact with the cell surfaces. More specifically, at a Reynolds number ≥9433, a Z-type BTMS with the spiral fins can maintain the temperature uniformity at a temperature difference of 5 °C. Among the six different BTMSs analysed, a U-type BTMS is reported to have the best performance, reducing Tmax and ΔTmax by 4.11 % and 38.1 %, respectively. The pressure drop in this case is also reduced by 8.46 %, thus lowering the overall power consumption.

Three-dimensional thermal-electrochemical-hydrodynamic numerical study of vanadium redox flow battery with different flow fields and non-homogeneously compressed electrode

This paper presents a concise 3D numerical study of Vanadium Redox Flow Batteries (VRFBs) with different flow field designs and non-homogeneously compressed electrodes. The model integrates mass, momentum, charge, and energy transport equations, including reaction kinetics for vanadium species. Four flow field designs (conventional, parallel, serpentine, and interdigitated) are evaluated for heat distribution uniformity. The model accounts for non-uniform electrode properties due to compression. Numerical results are validated against experimental data, exploring the impact of operating parameters such as current density, flow rate, and temperature on thermal behavior. The study also compares heat generated by electrochemical reactions, ohmic losses, and chemical activation across different flow fields. The findings revealed the highest temperature gradient and non-uniformity (in terms of temperature) with conventional designs followed by interdigitated, parallel and serpentine. Importantly, the study consistently highlights elevated temperatures in the discharge condition across all configurations. This emphasizes the need for precise temperature control to prevent VO₂+ precipitation. These insights from VRFB optimization efforts are thoroughly presented in this paper.

Viability of the steam-based extraction of extra-heavy crude oil using nanoparticles: Exergy and life-cycle assessment

The growing energy demand has prompted the research community to seek more efficient and sustainable resource extraction methods, particularly in the case of crude oil. Investigating the potential of nanotechnology to enhance crude-oil recovery from extra-heavy and heavy crude-oil reserves is crucial for optimizing resource utilization, improving economic viability, minimizing environmental impacts, driving technological advancement, ensuring energy security, and meeting market demands. In this study, we investigated the implementation of exergy analysis (ExA) on nanotechnology in oil-recovery processes, which has not previously been explored. This involved a life-cycle assessment (LCA) to evaluate the environmental impacts and to complement the ExA in order to optimize operations. To environmentally and thermodynamically analyze the extraction process of extra-heavy crude oil, four scenarios were evaluated: i) steam injection at 0.5 quality; ii) steam injection at 1.0 quality; iii) steam injection at 0.5 quality with 500 mg L−1 of nanoparticles; and iv) steam injection at 1.0 quality with 500 mg L−1 of nanoparticles. The nanofluids used (AlNi1 and AlNi1Pd1) consisted of 500 mg L−1 of alumina (Al2O3) doped with a 1.0 % mass fraction of nickel (Ni) (i.e., AlNi1), and the same amount of alumina doped with a 1.0 % mass fraction of Ni and palladium (Pd) (i.e., AlNi1Pd1). Both nanofluids were supplemented with 1000 mg L−1 of Tween 80. The experiments were conducted in a laboratory and numerical simulation was used to upscale the different scenarios. Considering the equilibrium K-values model, a multiphase/multicomponent flow model coupled with an energy transport equation was utilized. Nanocatalyst transport, as per the experimental data, involved non-equilibrium transference between the liquid phases and the rock surface. The laboratory data were used to calibrate the model, which was then scaled up to reservoir conditions to estimate the oil recovery obtained from deploying in-situ upgrading processes at the field scale. Exergy calculations were performed on the involved flows and porous media in order to assess the crude-oil quality throughout the process. An LCA was implemented to evaluate the reduction in environmental impact achieved by using steam injection at X = 1.0 quality, with and without nanoparticles. The results of the ExA showed that using nanoparticles allowed crude oil with a higher energy quality to be obtained. Furthermore, the ExA showed that the increase in steam quality had a more significant effect on the exergy destroyed in the process than the use of nanomaterials, demonstrating the good performance of the proposed technology. Environmental analyses showed that marine ecotoxicity, urban land occupation, particulate matter formation, and global warming potential were the most-impacted categories, significantly contributing to total environmental impacts, after the fossil depletion impact category for all scenarios. In conclusion, using bimetallic nanoparticles in crude-oil extraction produces a better product with better energy and environmental performance.

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.

Building a reduced order model from CFD data on leaves to evaluate optimal climate conditions

Climate control in vertical farms or greenhouses is crucial in order to have the optimal climate for the plants. This climate can be simulated using Computational Fluid Dynamics (CFD). This way, different ventilation methods can for example be compared. Previously, plants were modeled as a porous zone, in which additional source terms are added to the energy or transpiration transport equation. In this study, ten different leaves under different orientations are studied. The heat and mass balance for each leaf is solved and the boundary layer is adequately resolved. Different leaf orientations and positions to the flow are used, so that each leaf has its own distinct boundary layer. Leaf temperature and humidity are a function of the incoming flow, but also of the incoming temperature, humidity and stomatal resistance. In order to be able to quickly assess the effects of changing boundary conditions, on the temperature and humidity of the leaves, a Reduced Order Model (ROM) is made from the CFD-data. This method allows to quickly assess the effects of a stomatal resistance, the incoming radiation or a changing inlet temperature or humidity. A ROM was built using the data from one simulation. In order to see whether the ROM is able to predict other configurations, two additional cases were solved in CFD and were compared to the ROM. Leaf temperatures and humidities only differed maximally 3.14% and were quite good at predicting this. Predicted leaf transpiration rates differed slightly more, as these differed maximally 10.5%. Overall, the ROM has proven to be a valuable and numerically cost-effective tool to predict overall leaf climate and can be a good tool when later the climate of a full plant is simulated.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Numerical simulations of temperature loads on multilayer Laue lenses

We present numerical simulations of the heat loads on novel diffractive X-ray optics, known as multilayer Laue lenses, exposed to high-intensity X-ray beams produced by an X-ray free electron laser (XFEL). These lenses can be used to focus XFEL beams to nanometer spots. The temperature distribution within the lens and temperature evolution as a function of incident pulse frequencies were calculated for two different lens geometries and several material pairs and material ratios of the MLLs. Simulations considered the special pulse structure of European XFEL with X-rays being delivered in pulse trains. After defining the geometric model, computational grid, material properties, and boundary conditions, a grid sensitivity study was carried out. We solved the transient heat energy transport equation in solids for mixed boundary conditions. The results of these simulations will help select materials and lens geometry for future XFEL experiments.

DNS of Marangoni effects on a suspension of droplets in microgravity using the unstructured conservative level-set method

The multi-marker unstructured conservative level-set (UCLS) method for two-phase flow with variable surface tension is used for the Direct Numerical Simulation of thermocapillary-driven motion of a bi-dispersed suspension of droplets in microgravity. The so-called Marangoni stresses induced by surface tension gradients on the interface lead to a coupling of the momentum transport equation and the thermal energy transport equation. The finite-volume method discretizes the transport equations on three-dimensional collocated unstructured meshes. The UCLS method performs interface capturing with mass conservation of the fluid phases, whereas the multiple marker approach circumvents the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters schemes discretize the convective term in transport equations. Numerical and physical findings are reported.

LES of autoignition process in a turbulent droplet-laden mixing layer – impact of an evaporation model and discretisation method

This paper focuses on the numerical modelling of the autoignition process in an ethanol-air mixture within a turbulent droplet-laden temporally evolving mixing layer, utilising the Large Eddy Simulation (LES) method. We compare results obtained by implementing two notably distinct discretisation methods (second-order Total Variation Diminishing – TVD, and fifth-order Weighted Essentially Non-Oscillatory – WENO) in the species and energy transport equations. Additionally, we examine three widely recognised evaporation models (the ‘ D 2 ’ model, the Abramzon–Sirignano model, and a non-equilibrium model based on the Langmuir-Knudsen law). For modelling the combustion process, we employ the Eulerian Stochastic Field method and a laminar chemistry model. The simulations encompass two droplet diameter distributions, one with low and the other with significant diameter non-uniformity. Furthermore, nine distinct initial conditions are considered. Our findings indicate that adjusting the discretisation scheme or the evaporation model can yield simulation outcomes differing to a substantial degree, similar to the impact of modifying the actual properties of the spray droplets or their initial distribution. This is particularly pronounced in the case of sprays featuring a narrowed droplet diameter distribution. We found that the Abramzon–Sirignano model results in the most rapid autoignition. The TVD scheme contributes to a more even spatial distribution of the evaporated fuel, consequently facilitating quicker evaporation and faster autoignition. Using the WENO scheme generates higher fuel vapor gradients near the droplets, leading to less intense evaporation and slower fuel transport in space.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Waste discharge concentration and quadratic thermal radiation influences on time-dependent nanofluid flow over a porous rotating sphere

The nature of waste discharge concentration on time-dependent nanofluid flowing over a rotating sphere is examined in the conducted research. The linear and quadratic radiation influences are considered in the energy transport equation. The flow generation occurs due to a sphere’s revolution with time-dependent angular velocity. The term external pollutant concentration is modeled in the concentration equation. Titanium dioxide ( Ti O 2 ) nanoparticles are inserted into base-liquid water ( H 2 O ) . Similar variables are reported for the conversion of the problem. The converted problem is computed through the Runge–Kutta–Fehlberg (RKF) scheme. The study outcomes obtained from a numerical scheme are presented with the help of graphs. The rise in the linear and quadratic thermal radiation factors will enhance the thermal profile. Improvement in local pollutant external source and external pollutant source parameters will improve the concentration profile. The mass transfer rate will improve by adding the solid volume fraction and escalated values of local pollutant external source constraints.

The influence of river discharge on energy transport in estuaries and its implication for the equilibrium bed profile

In this paper, we revisit the classical energy transport equation for pure tidal flows in estuaries by including the effects of residual water level and freshwater discharge. Starting from the one-dimensional mass and momentum conservations, we derive analytical expressions for energy flux and its dissipation, which can be used to explore the interaction between tide and river from an energy perspective. It has been shown that the potential energy flux is dominant over the kinetic energy flux, and the energy contribution made by tide-river interaction is negligible compared with that due to tidal flow and freshwater discharge. A critical position corresponding with zero energy flux can be identified, reflecting a balance between along-channel tidal amplitude and residual water level. Assuming the variation of system energy tends to zero, we derive the long-term equilibrium bed profile with a convex-up shape, where we identify the location of a second estuarine turbidity maximum (ETM) at a position determined by the balance between river- and tide-induced energy flux. The dynamic response of tidal propagation extent and critical position with zero energy flux are shown to adjust to reflect seasonal changes towards the formation of a bed profile that is in dynamic equilibrium. Key policy insights A new analytical method is derived to calculate energy transport and energy dissipation in river-tide estuaries. Equilibrium bed profile determined by minimum entropy production has a convex-up shape where the minimum depth coincides with the location of zero along-channel energy flux. The location of a second estuarine turbidity maximum is consistent with the location where there is a balance between river- and tide-induced energy flux.

The significance of chemical reaction, thermal buoyancy, and external heat source to optimization of heat transfer across the dynamics of Maxwell nanofluid via stretched surface

Energy loss during the transportation of energy is the main concern of researchers and industrialists. The primary cause of heat exchange gadget inefficiency during transportation was applied to traditional fluids with weak heat transfer characteristics. Instead, thermal devices worked much better when the fluids were changed to nanofluids that had good thermal transfer properties. A diverse range of nanoparticles were implemented on account of their elevated thermal conductivity. This research addresses the significance of MHD Maxwell nanofluid for heat transfer flow. The flow model comprised continuity, momentum, energy transport, and concentration equations in the form of PDEs. The developed model was converted into ODEs by using workable similarities. Numerical simulations in the MATLAB environment were employed to find the outcomes of velocity, thermal transportation, and concentration profiles. The effects of many parameters, such as Hartman, Deborah, buoyancy, the intensity of an external heat source, chemical reactions, and many others, were also evaluated. The presence of nanoparticles enhances temperature conduction. Also, the findings are compared with previously published research. In addition, the Nusselt number and skin friction increase as the variables associated with the Hartman number and buoyancy parameter grow. The respective transfer rates of heat are 28.26%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} and 38.19%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} respectively. As a result, the rate of heat transmission increased by 14.23%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. The velocity profiles enhanced while temperature profiles declined for higher values of the Maxwell fluid parameter. As the external heat source increases, the temperature profile rises. Conversely, buoyancy parameters increase as it descends. This type of problem is applicable in many fields such as heat exchangers, cooling of electronic devices, and automotive cooling systems.

Heat transfer analysis of a tube-in-tube steam reformer for the application of MGT-SOFC hybrid process

This work deals with the evaluation of a tube-in-tube reformer concept for the realization of the Micro Gas Turbine Solid Oxide Fuel Cell (MGT-SOFC) hybrid process using a semi-validated numerical model. Rigorous heat transfer analysis considering chemical reactions were performed for this concept. To validate the reforming kinetics and heat transfer mechanisms in a catalyst bed, experiments were conducted using a single reactor tube located in a temperature-controlled furnace. Different experimental conditions, such as furnace temperature and space velocity, were considered. A numerical model was replicated according to the single-tube reactor investigated and validated with the experimental results. The catalyst bed is considered as porous material with chemical reactions as internal source terms of species transport equations and energy transport equation. Since the heat transfer into the reformer tubes in the real operating environment is subject to different mechanisms (predominantly convection) than that in a furnace (predominantly thermal radiation), only the parameters on the side of the catalyst bed tuned by the single-tube experiment could be retained for the numerical model of the tube-in-tube concept, which leads to a semi-validated model. Based on this semi-validated model, the performance (such as temperature distribution, conversion rate of the products, etc.) and the applicability of a tube-in-tube reformer concept, considering the variation of boundary conditions, were investigated and evaluated.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.