Energy Conservation Equations Research Articles

Electro-hyperelasticity with phase field for electric breakdown modeling

In this paper, we systematically derive the phase field model for electric breakdown channel propagation. The model includes electric charge, mass, momentum and energy conservation equations as well as Allen–Cahn type equation which governs the phase field evolution. The medium motion is described by the Godunov–Romenski type hyperelastic model. Electromagnetic part of the model consists of Maxwell’s equations in quasi(electro)stationary approximation including electric charge conservation law. Derivation of the model is based on the Coleman–Noll procedure and Gurtin’s microforces and microstress framework.

Development of HAWT wake under thermal stratification conditions

The evolution analysis of the wind wake downstream of a rotor submerged in a stratified atmospheric boundary layer is discussed in this work. The hybrid model AD-CFD is used, to obtain the velocity field. The changes in thermal stratification are taken into account when solving the energy conservation equation. Results from the unstable stratification case indicate a 41% velocity deficit and 30% is found for stable thermal stratification, at z = 1D. this work show that in a stratified atmospheric boundary layer, an isolated wind turbine’s ability to produce electricity is more impacted by stable thermal stratification than by unstable ones.

The Role of Heater Size and Location in Modulating Natural Convection Behavior in Cu-Water Nanofluid-Loaded Square Enclosures

Enhancing the energy efficiency of thermal systems reduces their consumption, lowers costs, and reduces undesired environmental impact, thus making these systems more sustainable. The current work introduces a passive method for heat transfer enhancement that is carried out using natural convection by nanofluid. This work introduces a computational study of the process of natural convection within a square cavity containing Cu/H2O nanofluid. The cavity wall on the left side undergoes partial isothermal heating, while the opposing side is fully cooled isothermally, with all other boundaries maintained adiabatic. A mathematical model formulated based on a 2-D model was used to provide the solution for the system of governing equations of mass, momentum, and energy conservation, employing the finite element technique. A commercial CFD package is utilized to perform the computational simulation. The present investigation delves into the impact of the Rayleigh number, nanoparticle concentration, heater length, and heater location on the flow field and heat transfer characteristics. The model outcomes were displayed for a wide range of the pertinent parameters as 103 ≤ Ra ≤ 106, 0.25 ≤ lh ≤ 1.0, 0.125 ≤ hc ≤ 0.875, and 0.02 ≤ ϕ ≤ 0.10. Also, correlation equations relating the average Nusselt number to these crucial parameters are derived. These equations are simple and can be applied in practice easily in many fields, such as electric and electronic equipment cooling and thermal management of heat sources. Also, these equations gather all the parameters that affect the heat transfer process. They are shedding light on the intricate interplay between these parameters in the natural convection heat transfer process.

Multi-Objective Numerical Analysis of Horizontal Rectilinear Earth–Air Heat Exchangers with Elliptical Cross Section Using Constructal Design and TOPSIS

This study presents a numerical evaluation of a Horizontal Rectilinear Earth–air Heat Exchanger (EAHE), considering the climatic and soil conditions of Viamão, Brazil, a subtropical region. The Constructal Design method, combined with the Exhaustive Search, was utilized to define the system constraints, degree of freedom, and performance indicators. The degree of freedom was characterized by the aspect ratio between the vertical and horizontal lengths of the elliptical cross-section duct (H/L). The performance indicators for the EAHE configurations were assessed based on thermal potential (TP) and pressure drop (PD). The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was applied for multi-objective evaluation, and a methodology for EAHE is proposed. The problem was solved using FLUENT software (version 2024 R2), which employs the Finite Volume Method to solve the conservation equations for mass, momentum, and energy. The (H/L)T,o = 6.0 configuration showed a 16.4% increase in thermal performance for heating and 15.9% for cooling compared to the conventional circular duct. Conversely, the (H/L)F,o = 1.0 configuration reduced pressure loss by 65.33%. The integration of Constructal Design with TOPSIS facilitated the identification of optimized geometries that achieve a balance between performance indicators and those that specifically prioritize thermal or fluid dynamic aspects, being this approach an original scientific contribution of the present work.

Three-dimensional bioconvection in a nanofluid film over a wedge surface with entropy generation and nonlinear radiation: A revised Buongiorno model

ABSTRACT The advances in the field of nanotechnology tends to improve the rate of heat extraction and transmission from foreseeable causes and has fascinated researchers and scientists. Furthermore, nanofluids are having a useful impact on various fields such as nuclear industries, powered lasers, chilling of microelectronic devices, solar energy capture, transformers oil cooling, and in cancer diagnosis. Hence, magnetohydrodynamic (MHD) three-dimensional bioconvective flow of nanofluid accommodating gyrotactic microorganisms over a wedge surface with zero nanoparticles mass flux boundary conditions is studied, using large Reynolds number approximation. The additional novelty of the study is the implementation of the revised Buongiorno model, which deliberates the effects of thermo-migration and Brownian diffusion of nanoparticles, together with passive control of nanoparticles fraction on the wedge surface. The self-similar form of conservation equations of energy, nanoparticle fraction, gyrotactic microorganisms, and momentum are handled numerically. T The results of the Blasius and the Hiemenz flows are retrieved as special cases of the model. It was found that the temperature of the nanofluid increases considerably when considering the nonlinear thermal radiation compared to the linear radiant heat. Increasing the strength of the Brownian diffusion increases the heat transport but reduces the mass transport.

Optimal control of Hydrocarbon Reducer (HC) injection based on Trust-Region-Reflective Algorithm (TRRA) and physical models for Diesel Oxidation Catalyst (DOC)

The aim of this paper is to control the DOC outlet gas temperature between 600 ± 15 °C by optimizing the hydrocarbon (HC) injection into the Diesel Oxidation Catalyst (DOC) for active regeneration of the downstream Diesel Particulate Filter (DPF). First, based on the physical model of the DOC thermal dynamics, the energy conservation equation for the gas phase temperature is simplified by using variable substitution, and the energy conservation equation for the solid phase temperature is simplified by considering only the heat generated by the HC injection. By solving the simplified model using the Trapezoidal Rule-Backward Differentiation Formula 2 (TR-BDF2) method and optimizing the model parameters in combination with the Gauss-Newton method, the computational efficiency and accuracy were significantly improved. Next, the DOC downstream temperature observer is designed by combining the solution characteristics of the DOC model with the unscented Kalman filter (UKF) algorithm to ensure that the catalyst operates within the optimal temperature range. Then, this paper verifies the accuracy of the model and observer through bench tests covering four steady-state operation conditions and World Harmonized Transient Cycle (WHTC) test cycle, and the results show that the model and observer exhibit high accuracy in both steady-state and transient operation conditions. Finally, the DOC temperature was successfully maintained between 600 ± 15 °C by optimizing the control of the HC injection rate, thus achieving the expected temperature control target. These research results provide theoretical and practical support for diesel engine emission control and DPF active regeneration.

Solidification process of hollow metal droplets impacting a substrate

Recently, there has been a renewed interest in hollow droplet impact, as the internal bubble makes a difference in the spreading morphology during thermal spraying and three-dimensional printing. This paper is dedicated to the solidification process of a hollow metal droplet impacting a cold substrate. The influence of initial impact velocity and substrate temperature on the spreading process is numerically investigated by employing a phase-field method coupled with a solidification model. Solidification was shown to strongly alter droplet spreading and the flow state of the center liquid column. To describe the flow state of the center liquid column, three patterns, namely ‘no-jet’, ‘transition region’, and ‘counter-jet’ are defined. The simulation results show that the formation of the center counter-jet is inhibited by the solidification layer when Péclet number Pe<357, where Pe is the ratio of convection rate to diffusion rate. In addition, the critical Pe at which the phenomenon of counter-jet occurs gradually rises with the substrate temperature falling. Finally, a quantitative analysis of the maximum spreading diameter is proposed by establishing an energy conservation equation. The predicted diameters are in good agreement with the simulated results. It allows us to provide a general expression for the hollow droplets' maximum spreading diameter, using the impact and temperature parameters.

Numerical and geometric investigation of pool boiling heat transfer in cavities with isothermal rectangular corrugations

This numerical work presents a geometrical investigation of a corrugated isothermal surface placed in a two-dimensional cavity subjected to unsteady, turbulent pool boiling flows. The main purposes are maximizing the heat transfer rate between the isothermal surface and the surrounding water flow, and the volume of vapor generated into the cavity. The geometric investigation followed the constructal design method, being the ratio Hi/Li (i = 1, 2 or 3) of the corrugations varied for three different numbers of corrugations: N = 1, 2, and 3, keeping constant the corrugations area. The volume of fluid (VOF) and Lee's evaporation-condensation models are used to estimate the volume fractions of water vapor/liquid and interfacial mass transfer. The unsteady Reynolds Averaged Navier Stokes (URANS) continuity, momentum and conservation of energy equations, and volume fraction transport equation, are solved using the finite volume method (FVM) available in software Ansys FLUENT. For closure of turbulence, the k - ɛ model is adopted. For validation of the model, the heat flux and convection heat transfer coefficient obtained for a pool boiling bared surface case are compared with Rohsenow's correlations, and differences lower than 7.0 % are reached. Results indicated a strong influence of the ratio Hi/Li and number of corrugations (N) in the heat transfer rate per unit depth (qs) and dimensionless volume of vapor (Vdim) generated into the cavity. The highest intrusion of the corrugations led to the generation of few large and many small scales, benefiting the thermal performance, regardless of the performance indicator employed. The optimal configuration, N = 3 and H3/L3 = 2.0 improved 49 % and 188 % the Vdim and qs compared with the worst corrugated case, showing the importance of the geometry of the corrugation in this problem.

Enhancing building energy efficiency: Numerical analysis of a hybrid thermoelectric ventilation system and earth-air heat exchange with photovoltaic-thermoelectric power integration for heating and cooling loads

The lack of studies on hybrid systems combining thermoelectric ventilation (TEV) and earth-air heat exchangers with a photovoltaic-thermoelectric generator (PV-TEG) as the power supply for the hybrid system is addressed in this research. This study aims to investigate the effectiveness and performance of such a combined system in providing the required thermal load of a building. To simulate the performance of TEV and PV-TEG systems, energy conservation equations for various components of the system were formulated for the quasi-state mode. The performance of the earth-air heat exchanger system was evaluated using the effectiveness-number of transfer units method. The resulting set of algebraic equations was then solved using a MATLAB code. Results indicated significant preheating (5.41–15.03 °C) and precooling (0.7–10.22 °C) effects during the daily hours of 15-February and 15-July, respectively. Additionally, the TEG component effectively reduced PV temperatures by 3.54 °C–16.99 °C in 15-February and 3.99 °C–21.54 °C in 15-July. The system also demonstrated a high monthly useful thermal energy output (1215–1584 kWh) in the cold months (December to March), contrasting with higher monthly useful thermal exergy (712–763 kWh) in the summer months. Furthermore, increasing the number of TEGs from 10 to 50 resulted in significant improvements in the yearly average energy and exergy proficiency indexes (PIya,en and PIya,ex) by 164.97 % and 459.82 %, respectively. The supply air mass flow rate and the length and depth of the earth-air duct were identified as the second and third most influential parameters affecting these indexes. Moreover, the system at CPV concentration ratio of 3 provided the highest PIya,en and PIya,ex of 1.512 and 14.65, respectively.

A space-time meshfree method for heat transfer analysis in porous material

Abstract Porous material batteries are a new type of battery technology that uses porous materials as electrode materials, with advantages such as long lifespan. In the present study, we manily propose a space-time meshfree method for heat transfer problems in porous material energy storage battery. The thermal behavior is demonstrated based on a numerical solution of the energy conservation equation. A simple space-time meshless collocation scheme, which is based on a new type space-time radial basis function, is presented to get the approximate solution of the energy conservation equation. The energy conservation equation was transferred into a system of linear algebraic equations. By introducing prescribed boundary conditions, the heat transfer analysis in porous material energy storage battery can be shown with numerical results. Numerical discussions show that the proposed meshless collocation method is appropriate to simulate thermal behavior in porous material energy storage battery, while the traditional finite element method failed to provide the reasonable results for the tested examples in this paper.

A transient network model for cross-regional layered fire smoke diffusion in high-rise buildings

At present, research on smoke diffusion in high-rise building fires mainly focuses on the single smoke layer propagation within a limited area, with less attention paid to the smoke propagation under the joint action of the fire floor and the vertical shaft area. Moreover, research on fire spread often focuses on the composition of combustible materials and building structures, neglecting natural ventilation. To address the above issues, we propose a transient network model for layered smoke diffusion (CLDTN) based on multi-region integration and complex control parameters. This model considers the smoke stratification mode of the fire floor affected by the fire source and ventilation, as well as the vertical stratification mode of the shaft affected by the stack effect, achieving cross-regional smoke stratification and diffusion modeling through smoke coupling. Then, a time-dependent transient network model is used to analyze furniture materials and open ventilation conditions of doors and windows, and a differential equation for energy conservation in multiple scene layers is constructed to analyze the dynamic behavior of smoke propagation.The comparative experiment of smoke propagation between CLDTN and the Fire Dynamics Simulator (FDS) shows that CLDTN is more efficient in computation time and the model is more accurate.

A unifying bubble-layer-based theoretical model for flow boiling and application to a rod bundle

Current analyses of flow boiling primarily utilize two−/three-dimensional numerical simulations or one-dimensional empirical correlations/models. To develop a quasi-two-dimensional theoretical model, a unifying bubble-layer-based theoretical model is proposed, which can be applicable to the entire flow boiling process, from the single-phase liquid flow to the dryout point. This model considers bubble behaviors in each region and heat and mass transfer at the interfaces of two regions, consisting of conservation equations of mass, momentum, and energy, supplemented by a few empirical correlations. A sensitivity analysis of these correlations is conducted, revealing that the slip ratio correlation and bubble condensation rate correlation have the most significant impacts. Using experimental data on void fraction, the most accurate combination of empirical correlations is identified, with a total absolute error of 27.9 %. The verification ranges are 0.1-8Mpa for pressure, 182-1700 kW/m2 for heat flux, 240-2200 kg/m2s for mass flux, 0.83–1.76 for Prandtl number, and 4.4e3–2.98e5 for Reynold number. Finally, this model is applied to the analysis of the NHR200-II rod bundle, revealing the variations of several two-phase parameters under micro-boiling conditions and the influence of operating conditions on the length proportion of different flow sections, serving as important references for analyzing the impact of boiling on reactor reactivity.

The Impact of Flow-Thermal Characteristics in Ship-Board Solid Oxide Fuel Cells

Hydrogen is increasingly recognized as a clean and reliable energy vector for decarbonization in the future. In the marine sector, marine solid oxide fuel cells (SOFCs) that employ hydrogen as an energy source have already been developed. In this study, a multi-channel plate-anode-loaded SOFC was taken as the research object. A three-dimensional steady-state computational fluid dynamics (CFD) model for anode-supported SOFC was established, which is based on the mass conservation, energy conservation, momentum conservation, electrochemical reactions, and charge transport equations, including detailed geometric shapes, model boundary condition settings, and the numerical methods employed. The polarization curves calculated from the numerical simulation were compared with experimental results from the literature to verify the model’s accuracy. The curved model was applied by enlarging the flow channels or adding blocks. Numerical calculations were employed to obtain the current density, temperature distribution, and component concentration distribution under the operating conditions of the SOFC. Subsequently, the distribution patterns of various physical parameters during the SOFC operation were analyzed. Compared to the classical model, the temperature of the curved model was reduced by 1.3%, and the velocities of the cathode and anode were increased by 4.9% and 5.0%, respectively, with a 2.42% enhancement in performance. The findings of this study provide robust support for research into and the application of marine SOFCs, and offer they insights into how we may achieving “dual carbon” goals.

Prediction of wellbore gas hydrate generation based on temperature-pressure coupling model in deepwater testing

With the advancement of oil and gas exploration and development technology, the development of the world's oil and gas resources is gradually advancing from land and shallow waters to deep waters. During the development of gas wells in deepwater regions, the temperature of the wellbore decreases from the bottom of the well to the wellhead, and therefore, common well conditions of high pressure, low temperature, and the presence of free water are encountered, which can lead to gas hydrate plugging of the pipeline and affect the transportation of natural gas. Simulation of temperature and pressure along the wellbore and identification of gas hydrate-generating zones in the wellbore can be used to take timely preventive measures and minimize losses. In this study, a wellbore gas hydrate generation and prediction model is developed by combining the mass, momentum, and energy conservation equations, and the model is solved by the fourth-order Runge-Kutta method, taking into account the temperature-pressure coupling in the wellbore. The effects of gas production, specific heat capacity, thermal conductivity, tubing size, test duration, and ground temperature gradient on the location of gas hydrate generation and the amount of inhibitor used were analyzed in a case study well in the South China Sea. Some suggestions for practical engineering operations, such as increasing the gas production in moderation and choosing smaller tubing sizes within the acceptable range, were given. The study's results can provide a theoretical basis for flow assurance for hydrocarbon production in the wellbore of deepwater gas wells.

Influence of concentration on thermophoresis of spherical aerosol particles within a Brinkman medium

Abstract We are examining the thermophoretic movement of a uniform mixture of spherical aerosol particles, all with the same properties, as they are situated within a porous material. These particles can have various thermal conductivity and surface characteristics. This analysis focuses on situations where the Péclet and Reynolds numbers are small. The influence of particle interactions is carefully considered by using a unit cell model, a well-established method known for its accurate predictions in the context of sedimentation for monodisperse suspensions of spherical particles. The porous medium is represented as a Brinkman fluid characterized by a Darcy permeability, which can be determined directly from experimental observations. This medium is considered to be uniform and isotropic, and the solid matrix is in thermal equilibrium with the fluid flowing through the voids of the medium. The Knudsen number is assumed to be low, enabling the description of fluid flow through the porous medium using a continuum model that includes temperature jump, thermal creep, frictional slip, and thermal stress slip at the aerosol particle’s surface. The conservation equations for energy and momentum are individually tackled within each cell. In this model, each cell represents a spherical particle enclosed by a concentric shell of surrounding fluid. The thermophoretic particle migration velocity is determined across different cases. We derive analytical expressions for this average particle velocity, expressing it in terms of the particle volume fraction. It is observed that different cell models yield somewhat varied results for particle velocity. Generally, with a fixed permeability parameter characterizing the porous medium, an increase in the thermal stress slip coefficient tends to decrease the normalized thermophoretic velocity across the different cell models. The results are in good agreement with the available data as documented in the existing literature. Additionally, a parallel examination of aerosol sphere sedimentation is provided.

A parallel compositional reservoir simulator for large-scale CO2 geological storage modeling and assessment

Storing CO2 in deep aquifers and depleted gas reservoirs is an effective way to achieve carbon neutrality. However, the numerical simulation of CO2 storage in these formations is challenging due to the complexity of gases-brine systems. The number of gas species included in the gases-brine fluid models of existing simulators cannot meet the rapidly evolving CO2 sequestration scenarios. To address this intricate issue, we developed a three-dimensional fully implicit parallel CO2 geological storage simulator (PRSI-CGCS) on distributed-memory computers based on our in-house parallel platform. This simulator uses a compositional fluid model with a diverse range of gas species, including CO2, C1 ~ C3, N2, H2S, as well as newly added gases H2 and O2, which may be encountered in geological CO2 storages. Besides, we provide more suitable scaling factors for different gases in the stability analysis bypassing (SAB) method to accelerate the gases-brine phase equilibrium calculations. PRSI-CGCS does not incorporate energy conservation equations, and salt precipitation or dissolution is also not considered. Numerical experiments show that our simulator is scalable, robust and validated to simulate large-scale CO2 storage problems with hundreds of millions of grid blocks on a parallel supercomputer cluster. Besides, after our modification on scaling factors, the SAB method can reduce the number of stability analyses by 61.39 % to 88.71 %, thereby reducing simulation time. Furthermore, case studies indicate that injecting O2 and H2 along with CO2 reduces the stability or capacity of CO2 storage and increases the pressure required for injection. However, this impact is not significant when the impurity content is less than 10 %.

In-situ measurement of thermal transmittance of building walls: Evaluation of stored heat flux in heavy-weight walls during the cooling season

The conventional heat flow meter (HFM) method is used to measure the thermal performance of building walls. Typically, this method is applicable for measurements on lightweight walls and when the difference between the indoor and outdoor temperatures exceeds 10 °C. However, modern buildings are constructed using highly insulated high-performance heavy-weight walls. Therefore, an in-situ measurement method is required to overcome the limited measurement environment of the conventional HFM method. In this study, a novel stored heat flux (SHF) method is proposed to overcome the limitations of the existing HFM method. This method estimates the stored heat flux in the wall using the thermal energy-conservation equation of the enclosed system and uses a decrement factor and time lag to calculate the thermal transmittance (U-value). The proposed method can be applied to heavy-weight walls in the cooling season when the difference between the indoor and outdoor temperatures is less than 10 °C. Furthermore, the design U-value can be estimated with higher accuracy than that observed in the conventional HFM method. The results of the relative error analysis for the U-values show that the conventional HFM method was approximately 68 % of the design U-value, while the proposed SHF method was approximately 15 %.

3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid

This work focuses on a numerical study of the natural convection of a non-Newtonian viscoplastic fluid within a cubic enclosure. The viscoplastic behavior is described by the Bingham model. The considered three-dimensional convective flow is confined within a cavity, subjected to a horizontal temperature gradient, where the vertical walls have two imposed temperatures while the rest of the walls are adiabatic. The Navier-Stokes equations, along with the mass and energy conservation equations, are numerically solved. Fluid flow and heat transfer characteristics are systematically studied over a wide range of Rayleigh numbers Ra (103 - 106) and Bingham number Bn (0 - 20). Finally, comparisons were made with previous results obtained in two dimensions in order to analyze the existence of a three-dimensional effect on the flow of the Bingham fluid. The results show that the Nusselt number decreases with the increase of the Bingham number, and for the large values ​​of the latter the heat transfer is done by conduction. It is also noteworthy that the critical Bn of the 2D model is higher than that of the 3D model, which confirms the existence of the three-dimensional effect. This is attributed to the presence of a wall along the Z axis which hinders and limits the flow of fluid within the enclosure.

Construction of Kinetic Model of Vacuum Arc Magnetic Fluid Under External Magnetic Field

The external magnetic field is an important control method of vacuum arc at present. Because of its high efficiency and economy, it has become an important method to study the kinetic model of vacuum arc magnetic fluid. Therefore, the kinetic model of vacuum arc magnetic fluid under the external magnetic field is constructed. Firstly, the mass conservation equation, radial momentum conservation equation, axial momentum conservation equation, energy conservation equation, electromagnetic equations are analyzed. The boundary conditions of the dynamic model are cathode boundary, anode boundary and fluid wall boundary. The fluid dynamics calculation software FLUENT is used as the calculation platform, and its secondary development is carried out. Combining VC++self-programming and self-defined macro functions, according to the boundary conditions, the kinetic model of vacuum arc magnetic fluid under external magnetic field is solved, and the kinetic model analysis of vacuum arc magnetic fluid under external magnetic field is realized. Experimental analysis shows under the action of longitudinal magnetic field, the intensity of longitudinal magnetic field increases, the maximum point of ion rotation speed in the magnetic fluid of vacuum arc moves outward along the edge of vacuum arc, the number density of electrons gradually moves from the central axis to the radial direction, and the high density area increases first and then decreases; Under the action of transverse magnetic field, the intensity of transverse magnetic field increases, the ion pressure in vacuum arc magnetic fluid gradually shifts and increases, and the ion number density also increases.

A comprehensive modeling, analysis, and optimization of two phase, non–isobaric, and non–isothermal PEM fuel cell

This study models a non-isobaric, non-isothermal two-phase flow in a Polymer Electrolyte Membrane Fuel Cell (PEM-FC), focusing on conservation equations for mass, energy, and momentum across its components. Verification involves comparing PEM-FC performance and temperature distribution with experimental and literature data, showing consistent agreements. Results indicate that increasing cathode channel pressure enhances membrane moisture and reduces power loss. Higher oxygen partial pressure improves PEM-FC performance, whereas increased anode channel pressure heightens ohmic losses and lowers output voltage. Temperature distribution reveals highest temperatures near the cathode catalyst layer due to electrochemical reactions. Adjusting pressures in cathode and anode channels affects these temperatures accordingly. PEM-FC power density is optimized using various algorithms, with simulated annealing proving most effective. Optimal values for gas diffusion layer thickness, electrode porosity, and inlet humidity are determined. Under constant current density, power density increases by 6 % compared to baseline conditions, demonstrating effective parameter optimization for enhancing PEM-FC performance.