Mass Equations Research Articles

Numerical Study of Inclined Geometric Configurations of a Submerged Plate-Type Device as Breakwater and Wave Energy Converter in a Full-Scale Wave Channel

The climate crisis represents one of the greatest contemporary global challenges, requiring actions to mitigate its impacts and sustainable solutions to meet the growing demands for clean energy and coastal protection. Therefore, the study of devices such as the submerged plate (SP), which simultaneously acts as a breakwater (BW) and wave energy converter (WEC), is especially relevant. In this context, the present numerical study compares the efficiency of an SP device under regular waves across different geometric configurations considering inclination angles. To achieve this, a horizontal SP was adopted as a reference. Its thickness and total material volume were kept constant while ten alternative geometries, each with a different inclination for the SP, were proposed and investigated. The computational domain was modeled as a full-scale regular wave channel with each SP positioned below the free surface. The volume of fluid (VOF) multiphase model was employed to represent the interaction between water and air. The finite volume method (FVM) was applied to solve the transport equations for volume fraction, momentum, and mass. The SP’s efficiency as a BW was evaluated by assessing the free surface elevation upstream and downstream of the SP, while its efficiency as a WEC was measured by evaluating the axial velocity below the SP. Results indicated that the efficiency of the SP can vary significantly depending on its inclination, with the optimal case at θ = 15° showing improvements of 11.95% and 16.59%, respectively, as BW and WEC.

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.

Application of an adaptive observer for the detection and location of pipeline leak

Leakages in hydrocarbon transport pipelines are a recurring problem. Their real-time diagnosis is a priority task. Timely resolution of leaks helps avoid human casualties, environmental harm, and infrastructure damage. This work focuses on simulating the hydrodynamic behavior along a pipeline to enable timely leak detection and localization through a novel computational tool. The proposed mathematical model identifies discrepancies between the mass and momentum equations and an adaptive observer’s estimation, which considers the leaking fluid like a system perturbation. The flow volume balance method confirms the existence of a leakage. A fluid quantifier estimates the total leaked volume during the detection period. The estimation error between the measured and estimated variables for the adaptive observer approximates the leakage location. The developed software was validated by comparing the results with a real leak scenario in a 20-inch diameter, 15 km long liquefied petroleum gas pipeline. The results demonstrate the tool’s feasibility for real-time leak detection, localization, and quantification, showcasing its potential for addressing recurring pipeline leaks.

Effects of Congestion in Human Lung Investigated Using Dual-Scale Porous Medium Models.

Chronic obstructive pulmonary disease (COPD) is a primary chronic respiratory disease associated with pulmonary congestion that restricts airflow and thereby affects the exchange of gases between the alveoli and the blood capillaries in the lungs. Dual scale-global and local-porous medium models have been developed and reported in this work, to study the effects of air-side congestion on the blood-oxygen content in the alveolar region of the human lung. The human lung is model as a global, equivalent, heterogeneous porous medium comprising three zones with distinct permeabilities related to their progressively complex branching structure. Airflow for each breathing cycle is determined by solving mass and momentum transfer equations across the three porous medium zones. The congestion is introduced by appropriate modification of the porous medium properties of the zones considered. The congestion-affected air velocity reaching Zone 3 is given as input to a separate "local model" employed at several locations of the alveoli of Zone 3. The local model determines the oxygen content in the blood flow in the capillaries of the alveoli by solving suitable mass, momentum and species transport equations. The transient simulation results performed for a long duration of multiple breathing cycles, demonstrate that a normal, healthy human lung is functional for up to 40% volume congestion or when 50% of the lung is congested to about 23.5%. Increasing congestion beyond this value, quickly-within a few hours-depletes the oxygen exchange in the blood flow of the alveolar region (of Zone 3), leading to hypoxemia. The effects of congestion progression on oxygen exchange dynamics determined through the dual-scale porous medium modelling approach provide researchers and medical professionals with in silico predictive estimates to generate treatment strategies for chronic respiratory diseases.

Numerical analysis of dipole-induced interactions in casson micropolar ferrofluids: Impacts on fluid flow and heat transfer under external magnetic fields

Abstract This study examines micropolar ferrofluids containing microstructures under the influence of an external magnetic field. The presence of ferroparticles and the magnetic field can lead to the generation of dipoles among these particles, which may significantly affect the fluid flow and heat transfer properties of the ferrofluid. The research utilizes a mathematical framework incorporating the equations of mass, momentum, angular momentum, and energy, alongside Maxwell’s equations of electromagnetism. This framework leads to a system of partial differential equations, which are subsequently converted into ordinary differential equations and solved using the BVP4C numerical method. The results, presented through graphs and tables, demonstrate how variations in physical parameters related to microstructures, dipole interactions, and the Casson fluid model influence fluid flow and heat transfer characteristics. The findings show that the fluid’s skin friction increases with higher micro-rotation and fluid parameters, while it decreases with a stronger magnetic parameter along the plate. The angular velocity of the ferrofluid increases due to the presence of a larger number of microstructures near the wall, which contribute to higher angular velocity gradients.

Proof of chiral symmetry breaking from anomaly matching in QCD-like theories

We critically reconsider the argument based on ’t Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional quantum chromodynamics-like theories with Nc>2 colors and Nf flavors. The main line of reasoning relies on a property of the solutions of the anomaly matching and persistent mass equations called Nf-independence. In previous works, the validity of Nf-independence was assumed based on qualitative arguments, but it was never proven rigorously. We provide a detailed proof and clarify under which (dynamical) conditions it holds. Our results are valid for a generic spectrum of massless composite fermions including baryons and exotics. Published by the American Physical Society 2024

Climatic and Anthropogenic Influences on Long-Term Discharge and Sediment Load Changes in the Second-Largest Peninsular Indian Catchment

In recent decades, understanding how climate variability and human activities drive long-term changes in river discharge and sediment load has become a crucial field of research in fluvial geomorphology, particularly for South Asia’s densely populated and environmentally sensitive regions. This study analyses spatio-temporal trends in water discharge (Qd) and sediment load (Qs) in the Krishna basin, Peninsular India’s second-largest catchment. Using nearly 50 years of daily discharge, sediment concentration, and rainfall data from the Central Water Commission (CWC) and India Meteorological Department (IMD), we applied Mann–Kendall, Pettitt tests, and double mass equations to detect long-term trends, abrupt changes, and the relative influence of climate and anthropogenic effects. Results showed a notable decline in the annual discharge, with 15 of 20 stations showing decreasing trends, especially along the Bhima, Ghataprabha, and lower Krishna rivers. The annual stream flow data showed a 53% decline in the mean Qd from 26.01 × 109 m3 year−1 before 2000 to 12.32 × 109 m3 year−1 after 2000 at the terminal station. Eight of ten gauging stations showed a significant decrease (p-value < 0.05) in their annual sediment load, with a 76% reduction across the Krishna basin after its changepoint in 1983. The Pettitt test identified a statistically significant downward shift in discharge at seven stations. Double mass plots indicate that anthropogenic factors, such as large-scale reservoirs and water diversion, are the main contributors, accounting for 82.7% of sediment decline, with climatic factors contributing 17.1%. The combined trend analysis and double mass plots confirm these findings, underscoring the need for further study of human impacts on the basin’s hydro-geomorphology. This study offers a clear and robust approach to quantifying the relative effects of climate and human activities, providing a versatile framework that can enhance understanding in similar studies worldwide.

Peristaltic pumping of viscoelastic fluid in a diverging channel: effects of magnetic field and surface roughness

Purpose Surface properties (smooth or roughness) play a critical role in controlling the wettability, surface area and other physical and chemical properties like fluid flow behaviour over the rough and smooth surfaces. It is reported that rough surfaces are offering more significant insights as compared to smooth surfaces. The purpose of this study is to examine the effects of surface roughness in the diverging channel on physiological fluid flows. Design/methodology/approach A mathematical formulation based on the conservation of mass and momentum equations is developed to derive exact solutions for the physical quantities under the assumption of low Reynolds numbers and long wavelengths, which are appropriate for biological transport scenarios. Findings The results reveal that an increase in surface roughness reduces axial velocity and volumetric flow rate while increasing pressure distribution and turbulence in skin friction. Research limitations/implications These findings offer valuable insights for biological flow analysis, highlighting the effects of surface roughness, non-uniformity of the channel and magnetic fields. Practical implications These findings are very much applicable for designing the pumping devices for transportation of the fluids in non-uniform channels. Originality/value This study examines the impact of surface roughness on the peristaltic pumping of viscoelastic (Jeffrey) fluids in diverging channels with transverse magnetic fields.

Operational features of collecting pipelines in the presence of transit and groundwater level slope

The conditions of operation for pressure collecting drainage pipelines in melioration systems that function in the presence of transit flow and groundwater surface levels have been considered. The system of differential equations describing the fluid motion with variable flow rate in the drainage pipe has been analyzed, taking into account the inflow of liquid from the surrounding soil through the side walls in a filtration mode. This system of equations consists of the hydraulic equation of variable mass and a modified filtration equation. The pipeline under study is laid horizontally and operates with a groundwater level slope. A significant complication in the operation of such pipes is the presence of transit flow that enters their initial cross-section and is transported along the entire length of the drainage pipeline. By introducing new variables, the original system is transformed into a dimensionless form. The solution to this system of equations is presented. It is shown that, in this case, the solution to the original system of equations depends on the magnitude of four main factors: the resistance coefficient of the collection drainage pipeline «ζl»; the generalized parameter «A» which comprehensively considers the structural and filtration characteristics of the flow under consideration; the slope of the groundwater level «I»; and the magnitude of the transit flow «Qtr» The analysis employs the concept of an infinitely long horizontal drainage pipeline that operates with a groundwater level slope and transit flow, or, equivalently, a pipeline with infinite filtration capacity of the side wall surfaces. Based on the conducted analysis, relatively simple and convenient analytical expressions have been obtained for calculating the variation of flow rate and head loss along the length of the drainage pipeline operating with transit flow. To simplify the calculations, corresponding auxiliary graphical dependencies have been proposed.

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.

Conjugated Heat Transfer of the stator of an synchrounous electrical machine

Electrical energy generation in remote islands and ships are mainly due the energy conversion from chemical (fuel) to mechanical by an engine and converted from mechanical to electrical by an alternator. The losses in the alternator during the energy conversion are responsible for the increase of its temperature. In order to control the temperature level of the equipment, it is necessary to control how heat is evacuated. The present work numerically evaluates the heat dissipation in the stator of an electrical machine and its temperature maximum levels. Heat is generated in the cooper (windings) and steel (stator main body) during the energy conversion and is evacuated due the forced airflow throughout the stator. In order to reduce computational costs, due geometrical symmetry, one quarter of the machine was modeled. In addition to symmetry, the momentum boundary conditions consist in inlet, outlet and noslip at the walls and the thermal boundary conditions consist in imposed heat fluxes. In order to isolate the inlet and outlet boundary conditions, they were positioned at least 10 times the respective channel height far from the stator. The model is transient and the initial flow field is at rest (0 m/s) and at ambient temperature (300 K). The geometry was constructed using Salome-Meca software and the mesh was generated using the snappyHexMesh solver from OpenFOAM v11. The foamMultiRun solver from OpenFOAM was employed to create the numerical model. It solves the mass, momentum and energy equations in transient regime. The numerical schemes employed were linearUpwind (second order) for the advective terms, Gauss for the diffusive terms (linear) and the backward time discretization (second order). The turbulence model employed was the K-omega SST. The model predicted where were the regions inside the stator with intese heat transfer, which implies in lower temperature magnitudes and also where there were temperature peaks. Then correlation between the temperature and flow fields were discussed.

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.

A pair of entrapping or coalescing bubbles affected by convection during downward solidification

In this study, the development of solute concentration and velocity fields of a pair of entrapping or coalescing bubbles during downward solidification is provided. The gas-induced pores in the metal not only deteriorates the properties of the processed workpiece by causing stress concentration and defects within the material, but pore formation in sea ice also plays an important role in global warming. Using COMSOL Multiphysics version 5.2, the unsteady, two-dimensional transport equations of mass, momentum, energy, and concentration are solved. The results show that bubble coalescence is facilitated by decreasing solid thermal conductivity and interpore spacing. Unlike the symmetric distribution of concentration observed with a low Henry's law constant and liquid solute diffusivity, an asymmetric distribution occurs, with high and low concentration gradients near the leading and rear edges of each bubble, respectively, due to the liquid velocity from the upstream direction. An outward flow in the opposite direction occurs near the triple-phase line, resulting in an inflection region in the iso-concentration field. The thickness of the concentration boundary layer surrounding the pores also decreases with decreasing Henry's law constant and liquid solute diffusivity, as well as with increasing ambient pressure, gravitational acceleration, solid thermal conductivity, and surface tension. The predicted contact angle during solidification aligns well with Abel's equation. Solute segregation associated with the formation of multiple pores can be controlled.

Performance Analysis of a Water-Injected Twin-Screw Compressor in a High-Temperature R718 Heat Pump

Abstract High-temperature heat pumps with twin-screw compressors and water (R718) as the working fluid show promising potential for providing industrial heat and process steam at temperature levels of up to 200 °C. This paper presents a simulation approach for a two-layered simulation structure of a water-based high-temperature heat pump system including a twin-screw compressor with water-injection. The heat pump process with two-phase steam compression is investigated with respect to various aspects. In addition to controlling the compressor outlet temperature, the evaporation of the injected liquid leads to an increase in the displaced mass flow rate on the sink side of the heat pump. This effect is analyzed in detail for various system operating points using a thermodynamic simulation framework for the R718-based heat pump cycle and a comprehensive compressor model. The main target of the presented paper is the analysis of system performance and the detailed investigation of the interdependencies. Performance of the twin-screw compressor is determined by means of two-phase chamber model simulations. In the chamber model method thermodynamic properties of both injected liquid and steam are calculated based on the conservation equations of mass and energy for the compression process. Adequate sub-models for internal leakage and heat and mass transfer between vapor and liquid phase are applied. Integral results of the compressor simulations are embedded in the heat pump system simulation using a characteristic map. In conclusion, this paper contributes to the understanding of advanced compression technologies in the field of high-temperature heat pumps, offering a detailed examination of a water-injected steam compressor’s applicability and efficiency in a practical system setting.

Constant of atoms and new equation of electromagnetic force

We present new equations for atoms (new atomic constant connecting atomic area, number of electrons and atomic mass and new equation of calculating electromagnetic force) with new concepts and results of atomic radii in good agreement with known determined calculations. All atoms consist of a certain number of electrons & nucleons and have certain masses with certain diameters contained in a certain area with certain velocities with a certain uniform distribution with a certain constant hold and bound by a certain fundamental force (electromagnetic force), so the main equations of all atoms are controlled by these physical parameters. The calculations confirmed that the mass, the area and number of electrons of any atom give a constant value. The new equation with a new atomic constant is used to calculate previously undetermined atomic radii (van der Waals radii). A new equation of electromagnetic force of atoms can be determined by three main physical parameters (mass, distance, velocity of light).

Development of a Dynamic Model for a Shell-and-Tube Type Gas-to-Gas Polysulfone Hollow Fiber Membrane Humidifier and Optimization of Operating Conditions and Fiber Dimensions to Maximize PEMFC Stack Power in Hydrogen Fuel Cell Vehicles

In polymer electrolyte membrane fuel cell (PEMFC) systems, effective water management is key to enhancing both efficiency and lifespan of the system. The necessity of keeping the system optimally hydrated to improve proton conductivity, while avoiding the issue of water flooding, emphasizes the crucial role of humidification technologies. In this study, the permeation characteristics of polysulfone hollow fiber membranes for transferring water vapor from moist air were experimentally and theoretically investigated. Experiments were conducted to assess the effect of operating conditions (e.g., inlet temperature, relative humidity, and temperature differences) on the performance of the humidifier under various feed flow rates using the membrane humidifier module in a hydrogen fuel cell vehicle. Additionally, detailed theoretical analyses were undertaken to comprehend the permeation phenomena of air through the membrane, which were correlated with experimental data to validate the model (relative error of <5%). The developed model incorporates transport equations for species, mass, momentum, and energy balances across both bulk streams, taking into consideration the heat and concentration boundary layer near the membrane. Furthermore, it introduces a new dual-mode sorption model that incorporates temperature dependence into the solution-diffusion mechanism across the membrane. The performance of the humidifier in two different flow configurations, counter and parallel-flow, was compared to illustrate the spatial variations in heat and mass transfer rates. To investigate the dynamic behavior of the PEMFC system, a system model integrating of a lumped dynamic model of an air compressor, a one-dimensional dynamic model of an intercooler (i.e., heat exchanger), and a one-dimensional dynamic model of a PEMFC stack was developed, as well as a dynamic model of a membrane humidifier. To maximize stack power in a PEMFC system, using a Pareto chart and response surface methodology, the degree of influence of valuables of the membrane humidifier was determined, and optimal operating points and geometric designs of the humidifier for enhanced efficiency and PEMFC stack performance were systematically identified.

Muscular robusticity and strength in the lower extremities in elite handball players

The relationship between structural and functional of parameters of skeletal muscles in young athletes needs further observations. The analyses of their age-group differences, sexual dimorphism, asymmetry characteristics in body regions, in sports having different pattern of physical loading could serve important information in this topic. 175 elite Hungarian handball players aged between 14 and 21 years were examined in 2023. Muscle mass component of the body segments was estimated by DEXA method and muscle thickness of the anterior mid-thigh region was measured by a new ultrasonic technique. The strength of knee extensor muscles was assessed by using an isokinetic protocol (Kineosystem dynamometer). A strong association between muscle robusticity and strength in the thigh region was confirmed in males, but not in females. Asymmetry in muscle mass reflected in the asymmetry in the knee extensor strength. A new predictive equation of muscle mass in the jumping leg and the total body from the muscle thickness in the anterior mid-thigh region of jumping leg was introduced. The exploration and understanding of asymmetric structural and functional adaptations can help athletes and trainers in planning the training and training interventions to reduce the risk of injuries.

A consistent, volume preserving, and adaptive mesh refinement-based framework for modeling non-isothermal gas–liquid–solid flows with phase change

This work expands on our recently introduced low Mach enthalpy method (Thirumalaisamy and Bhalla 2023) for simulating the melting and solidification of a phase change material (PCM) alongside (or without) an ambient gas phase. The method captures PCM’s volume change (shrinkage or expansion) by accounting for density change-induced flows. We present several improvements to the original work. First, we introduce consistent time integration schemes for the mass, momentum, and enthalpy equations, which enhance the method stability. Demonstrating the effectiveness of this scheme, we show that a system free of external forces and heat sources can conserve its initial mass, momentum, enthalpy, and phase composition. This allows the system to transition from a non-isothermal, non-equilibrium, phase-changing state to an isothermal, equilibrium state without exhibiting unrealistic behavior. Furthermore, we show that the low Mach enthalpy method accurately simulates thermocapillary flows without introducing spurious phase changes. To reduce computational costs, we solve the governing equations on adaptively refined grids. We investigate two cell tagging/untagging criteria and find that a gradient-based approach is more effective. This approach ensures that the moving thin mushy region is always captured at fine grid levels, even when it temporarily falls within a subgrid level. We propose an analytical model to validate advanced computational fluid dynamics (CFD) codes used to simulate metal manufacturing processes (welding, 3D printing). These processes involve a heat source (like a laser) melting metal or its alloy in the presence of an ambient (inert) gas. Traditionally, studies relied on artificially manipulating material properties to match complex experiments for validation purposes. Leveraging the analytical solution to the Stefan problem with a density jump, this model offers a straightforward approach to validating multiphysics simulations involving heat sources and phase change phenomena in three-phase flows. Lastly, we demonstrate the practical utility of the method in modeling porosity defects (gas bubble trapping) during metal solidification. A field extension technique is used to accurately apply surface tension forces in a three-phase flow situation. This is where part of the bubble surface is trapped within the (moving) solidification front.

Simulation of Nonlinear and Nonisothermal Reactive Liquid Chromatography considering Finite Mass-Transfer Rates and Various Adsorption Scenarios.

A multicomponent nonisothermal lumped kinetic model (LKM) of fixed-bed liquid chromatographic reactor is introduced and numerically approximated. The model incorporates nonlinear Bi-Langmuir and Toth adsorption isotherms, reaction kinetics, axial and temporal variations of concentrations, and enthalpies of reaction and adsorption. The resulting model equations constitute a nonlinear coupled system of convection-diffusion-reaction partial differential equations (CDR-PDEs) for mass and energy balances in both the mobile and stationary phases, augmented by differential mass balances in the stationary phase and algebraic expressions for reaction rates and adsorption isotherms. Due to the nonlinearity of adsorption isotherms and reaction kinetics, which is impeding the derivation of closed-form solutions, a local-projection discontinuous Galerkin finite element (DG-FE) method is applied for space discretization. The emerging semidiscrete system of ordinary differential equations in time is solved numerically by employing a total variation bounded (TVB) Runge-Kutta method. To analyze the process performance, parametric studies are conducted using numerical simulations. A series of rigorous consistency tests are elucidating the interplay between thermal and concentration gradients, showcasing the impact of temperature on reactor performance, and highlighting the aspects of reactant conversion into products. Subsequently, a thorough comparison is performed among the considered adsorption isotherms to scrutinize the numerical findings and to augment the originality of research. The results obtained verify the validity of model equations and precision of the numerical technique used. Moreover, the outcomes of this study can be utilized to understand mass and energy distributions in nonequilibrium and nonisothermal liquid chromatographic reactors and to provide profound insights into the complexities of this separation-conversion process.

Fractional modeling of bioconvection in Jeffrey nanofluids with gyrotactic organisms

AbstractThe current study examines how mass and heat transfer affect mobility of Jeffrey fluid while taking sun radiation across the vertical plate into account. In the polyvinyl alcohol water base fluid, the study combines gyrotactic organisms with copper nanoparticles. Microorganisms classified as gyrotactic respond to gravitational and viscous forces by swimming and orienting themselves, which results in the formation of patterns known as bioconvection, which is the result of the collective movement of these microorganisms. The main goals are to address the growing uses of solar plates by creating a unique mathematical model for flow and thermal properties of the parabolic trough solar collector (PTSC) installed on solar panel. Sunlight is directed onto a single focal line by curved mirrors in PTSCs, which heat the fluid moving over the plate at this focused line. The momentum, heat, and mass equations are solved by the model using Fourier and Fick's laws. The Laplace transform is then used to convert the solution sets into dimensionless Partial differential equation (PDE) for the velocity, energy, and mass fields. The innovative aspect of this model is its in‐depth examination of non‐Newtonian nanofluids, which are boosted by the addition of gyrotactic organisms and copper nanoparticles to increase heat transfer efficiency. The impacts of several factors on flow characteristics, including the Lewis number, mass Grashof number, Grashof number for bioconvection, magnetic and electric parameters, Peclet number, chemical reaction parameter, and Prandtl number, are shown graphically. Increasing the radiation parameters and volume fraction results in a noticeable improvement in the temperature profile. By demonstrating the superior heat transfer capabilities of non‐Newtonian nanofluids in solar energy applications, this work advances the field. It is particularly relevant to microchip cooling, solar energy systems, and thermal energy systems. In summary, the work provides a comprehensive model that advances our understanding of heat and mass transfer in non‐Newtonian nanofluids that are exposed to ambient sunlight. In the future, the model will be employed in real solar energy systems to confirm its effectiveness. The findings have applications in the development of temperature control technology and solar energy systems that are more effective.