Momentum Conservation Equations Research Articles

A framework to obtain wave, energy, and momentum conservation equations

Abstract A new method for obtaining wave, energy, and momentum conservation equations for Dirac and Maxwell systems is presented. This method makes use of the algebraic features of quaternion products. A framework that uses quaternions to describe quantum physics and electrodynamics has been introduced. In this approach, mass and charge produce electric and magnetic fields that satisfy Maxwell's equations. Quaternionic mass leads to massive electrodynamics based on quantum mechanics concepts. The conservation of energy and momentum is not affected by quaternionic mass. Quaternionic Maxwell's equations with quaternionic mass yield intriguing phenomena that can be examined experimentally. These equations generalize the classical Wilczek axion electrodynamics to quantum one.

Year-round performance evaluation of a solar-powered compact HDH desalination system for remote water scarce regions

ABSTRACT Climate change is intensifying global hydrological stress, increasing evaporation, degrading water quality, raising water temperatures, and altering runoff periods. This study introduces a fully solar-powered humidification-dehumidification (HDH) desalination system designed to address water scarcity in remote and arid regions. The significance of the research lies in its potential to provide a sustainable, off-grid water supply using renewable solar energy, which is particularly relevant in areas with limited infrastructure. The aim of the study is to evaluate the year-round performance of the system by developing a comprehensive mathematical model based on mass, energy, and momentum conservation equations. The model simulates the system’s behavior under varying solar conditions, enabling the optimization of key parameters. The system combines thermal photovoltaic panels and evacuated tube solar water collectors, enhancing energy efficiency through the pre-heating of seawater. The model is implemented in MATLAB, and the performance is evaluated over a full annual cycle. Results show that the system achieves a peak efficiency of 42% during high solar months, with monthly productivities of up to 238.87 L/m2, while the lowest performance occurs in December, with 14% efficiency and 63.02 L/m2 productivity. These findings underscore the system’s capability to provide a sustainable water source year-round.

Thermo-Magnetic Bioconvection Flow in A Semi-Trapezoidal Enclosure Filled With A Porous Medium Containing Oxytactic Micro-Organisms: Modelling Hybrid Magnetic Bio-Fuel Cells

Abstract Hybrid fuel cells are becoming increasingly popular in 21st century energy systems engineering. These systems combine multiple features including various geometries, electromagnetic fluids, bacteria (micro-organisms), thermo-solutal convection and porous media. Motivated by these developments in the present work we simulate the two-dimensional magnetohydrodynamic (MHD) natural triple convection flow in a semi-trapezoidal enclosure saturated with electrically conducting water containing oxytactic microorganisms and oxygen species. Darcy?s model is deployed for porous media drag effects. The primitive governing partial differential conservation equations for mass, momentum, energy, oxygen species and motile micro-organism species density are transformed using a vorticity-stream function formulation and non-dimensional variables into a nonlinear boundary value problem. A numerical solution is obtained using a finite difference method with incremental time steps. The mathematical model features a number of controlling parameters i.e. Prandtl number, Rayleigh number, Bioconvective Rayleigh number, Darcy parameter, Hartmann (magnetic body force) number, Lewis number, Péclet number, Oxygen diffusion ratio, fraction of consumption oxygen to diffusion of oxygen parameter. Transport characteristics (streamlines, isotherms, oxygen iso-concentration and motile micro-organism concentration) are computed for several of these parameters. Microorganisms? impact on the rate of heat transfer at the boundaries is found to be beneficial or destructive, depending on combination of other parameters in the simulations. Additionally, Nusselt number and oxygen species Sherwood number are computed at the hot vertical wall. The simulations are relevant to hybrid electromagnetic microbial fuel cells.

Starting Electroosmosis in a Fibrous Porous Medium with Arbitrary Electric Double-Layer Thickness

The transient electroosmotic response in a charged porous medium consisting of a uniform array of parallel circular cylindrical fibers with arbitrary electric double layers filled with an electrolyte solution, for the stepwise application of a transverse electric field, is analyzed. The fluid momentum conservation equation is solved for each cell by using a unit cell model, where a single cylinder is surrounded by a coaxial shell of the electrolyte solution. A closed-form expression for the transient electroosmotic velocity of the bulk fluid in the Laplace transform is obtained as a function of the ratio of the cylinder radius to the Debye screening length and the porosity of the fiber matrix. The effect of the fiber matrix porosity on the continuous growth of the electroosmotic velocity over time is substantial and complicated. For a fiber matrix with larger porosity, the bulk fluid velocity takes longer to reach a certain percentage of its final value. Although the final value of the bulk fluid velocity generally increases with increasing porosity, early velocities may decrease with increasing porosity. For a given fiber matrix porosity, the transient electroosmotic velocity is a monotonically increasing function of the ratio of the cylinder radius to the Debye length.

A TVD WAF scheme based on an accurate Riemann solver to simulate compressible two-phase flows

PurposeThis study aims to propose a robust total variation diminishing (TVD) weighted average flux (WAF) finite volume scheme for investigating compressible gas–liquid mixture flows.Design/methodology/approachThis study considers a two-phase flow composed of a liquid containing dispersed gas bubbles. To model this two-phase mixture, this paper uses a homogeneous equilibrium model (HEM) defined by two mass conservation laws for the two phases and a momentum conservation equation for the mixture. It is assumed that the velocity is the same for the two phases, and the density of phases is governed by barotropic laws. By applying the theory of hyperbolic equations, this study establishes an exact solution of the Riemann problem associated with the model equations, which allows to construct an exact Riemann solver within the first-order upwind Godunov scheme as well as a robust TVD WAF scheme.FindingsThe ability and robustness of the proposed TVD WAF scheme is validated by testing several two-phase flow problems involving different wave structures of the Riemann problem. Simulation results are compared against analytical solutions and other available numerical methods as well as experimental data in the literature. The proposed approach is much superior to other strategies in terms of the accuracy and ability of reconstruction.Originality/valueThe novelty of this work lies in its methodical extension of a TVD WAF scheme implementing an exact Riemann solver developed for compressible two-phase flows. Furthermore, other novelty lies on the quantitative calculation of different Riemann problem two-phase flows. Simulation results involve the verification of the constructed methods on the exact solutions of HEM without any restriction of variables.

Analytical Solutions for Electroosmotic Flow and Heat Transfer Characteristics of Nanofluids in Circular Cylindrical Microchannels with Slip-Dependent Zeta Potential Considering Thermal Radiative Effects.

This study analyzes the impact of slip-dependent zeta potential on the heat transfer characteristics of nanofluids in cylindrical microchannels with consideration of thermal radiation effects. An analytical model is developed, accounting for the coupling between surface potential and interfacial slip. The linearized Poisson-Boltzmann equation, along with the momentum and energy conservation equations, is solved analytically to obtain the electrical potential field, velocity field, temperature distribution, and Nusselt number for both slip-dependent (SD) and slip-independent (SI) zeta potentials. Subsequently, the effects of key parameters, including electric double-layer (EDL) thickness, slip length, nanoparticle volume fraction, thermal radiation parameters, and Brinkman number, on the velocity field, temperature field, and Nusselt number are discussed. The results show that the velocity is consistently higher for the SD zeta potential compared to the SI zeta potential. Meanwhile, the temperature for the SD case is higher than that for the SI case at lower Brinkman numbers, particularly for a thinner EDL. However, an inverse trend is observed at higher Brinkman numbers. Similar trends are observed for the Nusselt number under both SD and SI zeta potential conditions at different Brinkman numbers. Furthermore, for a thinner EDL, the differences in flow velocity, temperature, and Nusselt number between the SD and SI conditions are more pronounced.

Investigation on Influence of Transverse Jet Incidence Angle on Radiation of Plume

To study the effects of different incidence angles on the flow mixing and infrared suppression characteristics of the jet, the transverse jets were introduced on the basis of the axisymmetric convergent nozzle model, and the effects of five different transverse jets on the flow mixing and infrared suppression characteristics of the jet were studied. The flowfield and temperature field are obtained by solving the N-S (Navier-Stokes equation is the momentum conservation equation of viscous fluid) equation with the finite volume method. The infrared radiation intensity of the jet is obtained by using Reverse Monte Carlo method and narrowband model. The results showed that the transverse jet induces pair vortex structures that gradually increase in the direction of the flow. In addition, the vorticity increases with the increase of jet incidence angle, and the mixing ability of the cold flow and the high-temperature core region becomes stronger. The length of the high-temperature core region decreases continuously with the increase of the transverse jet incidence angle θ and reaches a minimum when θ=150°. Compared to the condition without the transverse jet, the length of the high-temperature core region is shortened by 38.9%. The intensity of radiation decreases with the increase of the transverse jet incidence angle. When the incidence angle θ is 150 deg, the radiation intensity of the plume decreases by 34.9%.

Numerical Simulation of Run-Up Wave Using Nonlinear Shallow Water Equations with Staggered Grid at Canti Beach, South Lampung

Tsunamis, wave triggered by underwater earthquakes or volcanic eruptions, can achieve significant run-up heights upon reaching shore. Run-up refers to the maximum vertical distance a tsunami wave reaches above the normal sea level. This study employs a numerical model to simulate the run-up wave at Canti Beach, South Lampung Regency, during the 2018 Sunda Strait tsunami. The method approximates solutions to the shallow water model consisting of mass and momentum conservation equations using the finite difference method in staggered grid grids and incorporates the upwind method for nonlinear terms. Bathymetry data from GEBCO was projected in two dimensions using the haversine formula. The numerical scheme includes a wet-dry procedure for simulating run-up waves. Results indicate that waves with a 60-second period and 0.09-meter amplitude create a 40.0195-meter inundation area, although this amplitude is significantly lower than the observed data from the 2018 Sunda Strait tsunami. Additionally, a simulation with a 0.1-meter amplitude results in a 1.8299-meter run-up height, closely matching the observed data. This study demonstrates that nonlinear shallow water equations can effectively estimate run-up height and inundation area at Canti Beach.

An entropy analysis model and irreversibility assessment of solid oxide fuel cells based on the Gibbs relation of charged particles

Energy conversion is the main purpose of various fuel cells, but the irreversibility of thermodynamic processes – including electrochemical reactions and heat and mass transfer in fuel cells – lead to a decrease in energy efficiency. In this paper, we develop a systemic theoretical model to evaluate the irreversibility of solid oxide fuel cells (SOFCs). By combining the conservation equations for energy, mass, and momentum with the Gibbs relation for charged particles, we establish the energy-balance equation for SOFCs and derive the entropy generation rates (EGRs) associated with electrochemical reactions and charged particle transfer processes. We solve the coupling multiphysics model in a three-dimensional computational unit of a SOFC, and calculate the EGRs and entropy flux rate based on the proposed thermodynamic model and the numerical results. We analyse the conversion and transfer mechanisms of energy based on the distributions of different local EGRs and the entropy flux rate, and the influence of various thermodynamic processes, such as mass transfer, heat transfer, and flow, on the overall operation of SOFCs. The results show that the EGR due to electrochemical reactions in the SOFC is the largest and is mainly due to activation and concentration polarisation. Complex heat and mass transfer processes occur in the corner region formed at the intersection of the channel, the current junction, and the electrode, leading to a higher localised EGR. We also evaluate the effects of variations in the anode gas mass flow rate, the oxygen fraction, and the channel length on thermodynamic efficiency. This study contributes to the understanding of the complex mechanisms of irreversible losses in SOFCs and provides guidance for further improving the thermodynamic efficiency of SOFCs.

Thermoregulation of integrated photovoltaic panels with bio-based phase change materials

Although photovoltaic (PV) technology has achieved significant advancements in harnessing irradiation to generate electricity, different questions remain open, especially regarding the adverse effects of high temperatures on the PV system. As the temperature of PV panels increases, their energy-conversion efficiency decreases, reducing the overall electricity production. High temperatures also accelerate the degradation of the PV panel, leading to shorter operational lifespans and higher maintenance costs. Hence, reducing the PV panel temperature throughout the day can prevent thermal degradation and increase its efficiency. In the present work, we numerically evaluate the thermal behavior of a PV system integrated with a phase change material (PCM). The numerical model uses the Finite Volume Method to solve the conservation equations of mass, momentum, and energy. A 3D transient thermal model incorporating the PCM enthalpy formulation was developed to analyze the PV panel temperature. The thermal model considers the energy transfer by conduction, convection, and radiation throughout the day. A mean absolute deviation of 3% was obtained for the PV panel temperature by comparing it with experimental data available in the literature. After the numerical model validation, the PCM was changed to a bio-based PCM (bioPCM) consisting of la uric acid, whose melting point is relatively high (from 44–46 °C), allowing its use in regions of high solar incidence. Furthermore, it has a high latent heat of fusion, being chemically stable and non-toxic. Using the proposed bioPCM, a temperature reduction of 9 °C was obtained, increasing the energy production, on average, by 9% compared to a conventional PV without PCM. Overall, using the proposed bioPCM can avoid excessive losses of energy-conversion efficiency under high irradiance conditions and extend the lifespan of photovoltaic panels.

Streamlined workflow for the simulation of submarine landslides with the material point method

Industry demand for numerical simulations is growing every year due to the advances in computer hardware that make increasingly complex and detailed simulations possible. Numerical tools are particularly useful for situations in which the available analytical and experimental tools are limited or unavailable. For that reason, they are a powerful tool for the analysis of natural phenomena, such as submarine landslides. Submarine landslides are commonly accompanied by large deformations and large displacements, which makes them challenging for traditional numerical tools, such as the finite element method. Thus, a numerical tool which is equipped to handle this behavior is necessary. In this paper, we describe a streamlined workflow to simulate submarine landslides that encompass problem modeling, simulation and post-processing. The simulator, developed in-house, uses the Generalized Interpolation Material Point (GIMP) to solve momentum conservation equations and is able to handle large deformations, contact and physical nonlinearities. The proposed workflow acts as a wizard that creates templates for multiple problem definition strategies, automates simulation execution, and provides a range of postprocessing variables to better describe the results. Furthermore, practical examples are presented, detailing the process of mesh and particle definition, simulation execution and analysis of run out distances, deposition height and impact pressure assessment.

On the generation of submarine landslide models for Material Point Method simulations through bathymetric data

Submarine landslides are natural phenomena that can cause economic problems and environmental disasters, as the force of the sliding mass can break pipes, interrupting production and destroying whole ecosystems. By simulating these landslides using bathymetric data, one can optimize the design and construction of subsea equipment to minimize its risks. This work aims to create a wizard that, using bathymetric data, guides the engineer through the process of creation of the simulation input for the submarine landslide study. The simulator used was developed in-house and uses the material point method to solve continuum mechanics momentum conservation equations for a vast library of constitutive models. The wizard objective is to streamline numerical parameters by automating and optimizing model choices inherent to the computational method, allowing the engineer to focus on the physical problem rather than the numerical details. Furthermore, it will be possible to configure a vast range of physical parameters, such as the definition of the sliding mass, the constitutive model and its parameters.

Numerical investigation on the evolution process of hydraulic transport and overcurrent blockage of silted urban rainwater pipelines: An approach based on computational fluid dynamics and discrete element method

During urban flood events, the effect of urban rainwater pipeline siltation on overflow and stagflation intensifies the severity of flood disaster. However, the dynamic coupling mechanism of pipeline sedimentation and water flow is still unclear. To investigate the influence of two-phase flow on the hydraulic transport of siltation particles in rainwater pipelines, the numerical simulation model based on computational fluid dynamics (CFD) and discrete element method (DEM) is constructed. Then, the transient continuity governing equation and conservation equation of momentum are formulated to provide dynamic guidance and boundary constraint for CFD-DEM simulation. On this basis, the optimal drag force model and measurement method of equivalent siltation degree of pipeline are proposed and nested with CFD-DEM, and then, a high resolution numerical simulation model of pipeline sedimentation is formulated. The results show that the siltation degree affects the efficiency of drainage pipeline to a degree of 47%, which is much greater than the degree of influence of 33% for siltation length and 18% for slope. When the siltation degree is 0.1, the thickness of the silted bed surface under the influence of water flow scour is reduced by 33%. It revealed that the influence degree of siltation degree and flow rate was 168% and 20%, respectively, which was much larger than that of siltation length and slope. This study can provide technical support for subsequent pipeline cleaning and maintenance as well as flood prevention and mitigation.

Flow of viscoelastic films over grooved surfaces with partial wetting

We consider the steady flow of a viscoelastic film over an inclined plane featuring periodic trenches normal to the main flow direction. The trenches have a square cross-section and side length 5–8 times the capillary length. Owing to the orientation of the substrate, the film fails to coat the topographical feature entirely, forming a second gas–liquid interface inside the trench and two three-phase contact lines at the points where the free surface meets the wall of the trench. The volume of entrapped air depends on material and flow parameters and geometric conditions. We develop a computational model and carry out detailed numerical simulations based on the finite element method to investigate this flow. We solve the two-dimensional mass and momentum conservation equations using the exponential Phan-Thien & Tanner constitutive model to account for the rheology of the viscoelastic material. Due to the strong nonlinearity, multiple steady solutions possibly connected by turning points forming hysteresis loops, transcritical bifurcations and isolated solution branches are revealed by pseudo-arc-length continuation. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, capillarity and viscosity on the characteristics of each steady flow configuration. The results of our simulations indicate that fluid inertia and elasticity may or may not promote wetting, while shear thinning and hydrophilicity always promote the wetting of the substrate. Interestingly, there are conditions under which the transition to the inertial regime is not smooth, but a hysteresis loop arises, signifying an abrupt change in the film hydrodynamics. Additionally, we investigate the effect of the geometrical characteristics of the substrate, and our results indicate that there is a unique combination of the geometry and viscoelastic properties that either maximizes or minimizes the wetting lengths.

Influence of scanning speed on spheroidization effect in electron beam selective melting

Electron beam selective area melting (EBM) technology has been developing rapidly due to its manufacturing advantages, but the balling phenomenon affects the quality of the parts and leads to porosity and hole problems. This paper focuses on the effects of scanning speed and powder bed thickness on the spheroidization phenomenon during single-orbit melting. The discrete element method (DEM) is used to establish a three-dimensional powder bed model, simulate the electron beam melting of powder by solving the mass, energy and momentum conservation equations, and analyse the melt pool dynamics by applying the volume of fluid (VOF) method. The results show that the surface quality of the melt pool decreases with the increase of the scanning speed and the thickness of the powder bed, especially when the scanning speed is high, the melt pool is unstable and voids may appear, the substrate is not completely melted or the contact angle is greater than 90 degrees, which ultimately leads to the spheroidization phenomenon. Meanwhile, by analysing the transient evolution and melting state of the melt pool at high scanning speeds, the causes of the formation of the spheroidization phenomenon are revealed.

Hydromagnetic Nanofluid Flow Through Stretching Convergent-divergent Conduit with Heat and Mass Transfer

This present study investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with variable magnetic field and variable thermal conductivity with skin friction, heat and mass transfer using spectral relaxation numerical technique. The nanofluid considered in this current study is electrically conducting which is subjected to constant pressure gradient and magnetic field considered to be variable applied at an angle. The two walls which are non-parallel are not intersecting so as to allow nanofluid to flow, the angle in between the non-parallel walls is <i>θ</i>. The equations governing the nanofluid flow are continuity, energy, magnetic induction and conservation of momentum equations. After modelling, the specific equations governing the nano-fluid flow are partial differential equations which are highly nonlinear, the specific equations are first transformed through similarity transformation into a systems of ordinary differential equations. The boundary value problem formed is solved numerically using spectral relaxation numerical technique. The results of effects of varying various dimensionless parameters of the model are represented graphically and results discussed at each stage. The knowledge of nanofluids can be used in nuclear power production where it acts as a coolant. In Africa, South Africa is the only country producing nuclear power for commercial use, different governments on the continent are exploring nuclear energy as a climate-friendly for power production to enhance industrialization even in rural areas. In nuclear power production, water is used as a coolant. Using nanofluid instead of water it could increase the thermophyical properties which increases the rate of cooling. The usage of nanofluids as a coolant could also be used in emergency cooling systems, where they could cool down overheat machines quickly leading to an efficient and improved power plant safety.

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.

Dynamic plastic damage analysis of bending-torsion coupling in cross stiffener systems under mass impact

ABSTRACT This study proposes a simpler theoretical model to predict the bending-torsion coupling dynamic plastic response of cross stiffener systems under mass impact. Traditional methods often rely on torque balance and momentum conservation equations, which involve complex and difficult calculations. To simplify this process, the study uses the law of energy conservation and applies the variational method to solve the dynamic plastic damage of the cross stiffener system. The plastic response of a single stiffener is first analyzed and compared with existing theories, showing consistent results for maximum displacement. The study then extends the model to more complex conditions, performing comparative analyses on stiffeners of different sizes through numerical simulation. The findings show that the maximum displacement at the load and node remains within a reasonable range, with a displacement difference of only 0.9 mm and an error margin of 4.79% in one of the test conditions.

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.

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.