The importance of modulated gravity in the nonlinear dynamics of Newtonian fluids flowing through a permeable Darcy porous medium in achieving fluid buoyancy control, porous media dynamics, and microgravity studies, which are important for environmental science and space exploration, is growing, particularly in the context of triple‐diffusive convection. However, limited information is available on the dynamics of Newtonian fluids undergoing triple‐diffusive convection through permeable media when modulated gravity is introduced, particularly using the Ginzburg–Landau technique. In this case, the fluid convective system is subjected to vertical gravitational vibrations. The physical system considered involves a porous layer, stretched indefinitely in the x ‐direction, sandwiched between two parallel plates at z = 0 and z = d . The temperature and concentration of the bottom plate are higher than those at the top plate due to heating, salting, and saturation of the porous layer with Newtonian fluid from below. The gravitational acceleration is time‐dependent, consisting of both a constant gravity term and a time‐dependent oscillatory component. The amplitude of gravity modulation is assumed to be small, relevant to practical applications. The presence of a third diffusive component increases the critical thermal Darcy–Rayleigh number required for the onset of convection, demonstrating that triple‐diffusive convection has a higher threshold than double‐diffusive convection. The modulation amplitude () plays a critical role in the behavior of disturbance amplitude, demonstrating that significant variations in convection characteristics are contingent upon the presence of gravitational modulation.

Accurately predicting turbulent water flow in duct systems remains a challenging problem, particularly when anisotropic turbulence effects are significant. Bridging the gap between industrial applications and academic research requires a deeper understanding of such complex flows. This study investigates a less commonly analyzed configuration involving a horizontal aluminum duct transitioning into a converging wavy duct. The wavy section consists of 2.5 full sinusoidal periods, ending in a reduced outlet diameter. In addition, the effect of incorporating four minor/secondary inlets, arranged as branches at different angles, was examined and presented herein. Aluminum was selected for its low density and corrosion resistance, which are beneficial in experimental and industrial setups. Initially, the duct was analyzed in an unbranched configuration. The study then progressed to include the four secondary/minor branch inlets at various angles. The simulation results were validated by comparison with a solution for a simple flow in a 70 mm duct. Additional verification was provided by employing other CFD codes, along with grid convergence index and mesh sensitivity analyses, improving the confidence in the simulation results. Branch angles influences turbulence intensity depending on flow conditions and angle magnitude. Sharper branch angles are particularly effective, inducing greater turbulence at the converged outlet. Higher inlet temperatures and velocities lead to increased Reynolds stress due to enhanced energy transfer and elevated turbulent kinetic energy. Specifically, an increase in inlet velocity at a 45 ° branch angle further augments turbulent momentum transfer, resulting in more controlled mixing along the duct.

The dynamics of water‐liquid flow through aluminum circular pipes are examined to investigate the effects of half‐cycle length in converging wavy ducts with diverging outlets. This study provides insights into flow control, energy efficiency, enhanced heat transfer, and turbulence management, all of which have significant industrial applications. The SpaceClaim‐generated duct designs have 40 mm major inlet diameters and 10 mm minor inlets on either side, with an output diverging to 10 mm. The Shear Stress Transport (SST) k‐ model in ANSYS Fluent 2024R2 is used for better management of pressure gradients and precise prediction of boundary layer behavior. Meshing and simulation followed a strict methodology, assuring precision and dependability. It is worth noting that increasing the number of sinusoidal half‐cycles increases turbulence, which raises the Reynolds number and enhances the cooling effect. Longer wavy ducts are shown to increase flow acceleration, resulting in greater output velocities and more turbulent kinetic energy production. Turbulent viscosity in a 2.5‐period sinusoidal wavy duct rises dramatically with inflow velocity and temperature. A 12.5‐period sinusoidal wavy duct is substantially more turbulent viscosity than a 2.5‐period duct. These findings have important implications for applications that require improved heat dissipation and flow control, including heat exchanger design and thermal management systems.

Delving into the intricacies of vortex viscosity and spin gradient viscosity is a cornerstone of fluid dynamics, unveiling profound insights into the behavior of rotating fluids. These fundamental parameters are essential for the precise modeling of vortical structures and rotational flows, providing an invaluable understanding of phenomena such as turbulence, mixing, and the dynamics of rotating systems. This article explores the significant impact of the couple stress coefficient and heat transfer analysis on vortex viscosity, spin gradient viscosity, microinertia density, and viscous dissipation within the magnetohydrodynamic oscillatory flow of micropolar fluid. Specifically, the study focuses on the significance of tapered wavy channels submerged in a porous medium. The present study significantly advances the understanding of micropolar fluid flow, providing essential insights applicable to diverse technological fields, from materials engineering to thermal management systems. The methodology employed entails the utilization of a modified Boussinesq approximation and a time-dependent flow model, accompanied by the non-dimensionalization of governing equations through non-similarity transformations. The numerical solutions, acquired via the implicit Crank-Nicolson finite difference method, unveil intricate details of microrotation, velocity, and temperature profiles, thereby underscoring the profound impact of the studied parameters on fluidic dynamics. At the left boundary of the channel, the microrotation profile diminishes with varying vortex viscosity, while at the right boundary, it exhibits an increase. Conversely, variations in spin gradient viscosity manifest the opposite effect across the channel.

The dynamics of blood conveying gold nanoparticles (GNPs) are helpful to the health workers while air conveying dust particles over rockets is helpful to space scientists during the testing phase. However, little is known on the significance of thermal diffusivity in these aforementioned cases. In this report, the partial differential equation suitable to unravel the implication of increasing partial slip and viscous dissipation on the dynamics of the mixture of (i) blood and nano size of GNPs (ii) air and dust particles on an object with an increasing diameter (uhspr) is investigated. The density, zero shear rate viscosity, heat capacity, and thermal conductivity treated in this study vary with volume fraction nanoparticles. In the second case, the interaction between the solid particles and air is incorporated into the momentum equation using the Stokes drag. Transformation and parametrization of the two‐dimensional nonlinear partial differential equations were obtained with the aid of suitable similarity variables. Thereafter, the numerical solutions of the corresponding boundary valued problems were obtained using the classical Runge–Kutta integration scheme together with shooting techniques and Matlab bvp5c package. Enhancement in the rate of viscous dissipation is a major factor suitable to increase the velocities of both fluids, boost temperature distribution across both fluids, and local skin friction coefficients. There exist a significant difference between the effect of partial slip on the dynamics of blood‐gold nanofluid and dusty fluid.

The interaction between water motion efficiency, outlet control mechanisms, and energy dynamics management hinges significantly on turbulence characteristics. However, understanding the influence of input velocities and duct features on outlets remains elusive. This study employs the realizable k - epsilon viscous model and Reynolds-averaged Navier-Stokes equations (RANS equations) to explore transient water dynamics encountering a cold front through ducts leading to convergence or divergence. Using Ansys Fluent 2023R2 and the waterlight workflow, meticulous meshing of the ducts is executed to capture flow intricacies accurately. Grid independence, suitable boundary conditions, and solver settings are carefully considered to ensure reliable results for investigating four key research questions. Duct bending introduces non-uniformities in velocity distribution, impacting exit velocity and altering flow characteristics and turbulence. In Case III, centrifugal forces from a 90 degrees bend result in higher outlet velocities at the convergent exit and secondary flow patterns like swirls and vortexes. Additionally, entrance velocities influence Reynolds numbers, affecting mixing, heat transfer coefficients, and flow regimes, thereby optimizing thermal conductivity. This comprehensive investigation sheds light on optimizing water dynamics and energy management across various duct configurations, offering valuable insights into efficient flow control and thermal performance enhancement.

It is unknown how the dynamics of ethylene glycol conveying SWCNTs and MWCNTs nanoparticles compare when there is a stratification of concentration and temperature such that the process by which an electric current travels past resistance and transforms some of its energy into heat is essential. The nondimensional governing equations were transformed via similarity transformation and solved numerically through Runge-Kutta 45 Fehlberg method. The computations have shown that the thermal convective term depleted the flow profile of SWCNTs and MWCNTs but boosted the velocity field and thermal diffusion. The induced electromagnetic force by the magnetic field and rising porosity term decrease the characteristic flow dimension. Finally, SWCNTs and MWCNTs are positively influenced by Ohmic magnetic dissipation and negatively influenced by radiation. The SWCNTs and MWCNTs are positively influenced by joule dissipation but negatively influenced by radiation. The thermal convective term reduces the flow profile of SWCNTs and MWCNTs but enhances the velocity field and thermal diffusion. Notably, the Nusselt number proportional to the heat transfer across the motion of SWCNTs nanofluid increases at the rate of 0.55466. Reverse is the case of MWCNTs nanofluid, where the same heat transfer rate decreases with a higher volume fraction at -0.7801.

By improving the understanding of fluid behaviour and allowing the development of cutting-edge technologies that enhance fluid-related processes in various sectors, advances in fluid dynamics serve a crucial role in both science and engineering. Sequel to the broad applicability of fluid dynamics leading to more efficient, sustainable, and innovative solutions for real-world challenges associated with the motion of liquids and gases, reviews of the recent advancements are far-fetched. The scope of the review was structured to focus on recent published facts on lift generation and drag reduction of aeroplanes, Computational Fluid Dynamics, turbulence modelling, and multiphase flow. Research synthesis which focuses on summarizing the state of the art of research facts on fluid dynamics was adopted. It is worth concluding that fluid dynamics principles stand as a cornerstone, unequivocally driving the relentless advancement of aerospace and automotive engineering, crucially contributing to the development of drag reduction techniques, precision control of lift generation, streamlined shapes for drag minimization, innovative wing profiles for enhanced lift, and effective boundary layer control for drag reduction. Recent advancements in Computational Fluid dynamics have revolutionized engineering simulations, providing unparalleled accuracy and efficiency in modelling complex fluid flow phenomena, from aerodynamics to hydrodynamics, thereby significantly accelerating the design and optimization processes across various industries. Studying of multiple fluid phases moving through a system simultaneously causes complicated interactions, phase transition events, and a variety of flow patterns, making it a complex but essential research topic. Experts face challenges validating Computational Fluid Dynamics results due to insufficient experimental data.

In response to the unanswered relevant questions surrounding atherosclerosis, it becomes imperative to investigate arterioles using sophisticated mathematical modelling techniques to shed light on critical stress and strain patterns influenced by gravity. The primary objective of this study is to scrutinize flow characteristics and probe stress and strain distributions experienced by the intima layer of arterioles, encompassing coronary, renal, cerebral, mesenteric, and pulmonary arteries, under gravitational forces. This investigation employs a fluid-structure interaction methodology utilizing arbitrary Eulerian-Lagrangian formulation. The study delves into blood flow characteristics within coronary, renal, cerebral, mesenteric, and pulmonary arterioles using the fluid-structure interaction technique, employing an arbitrary Eulerian-Lagrangian formulation. It thoroughly examines various biomechanical parameters such as the Cauchy-Green stress tensor, Principal strain, Piola-Kirchoff stress tensor, deformation tensor, and volume strain along the intima layer under the gravitational influence, elucidating vulnerable regions prone to endothelial dysfunction. Higher values of delta V are found at the left shoulder and in the intima's post stenosis area due to the pressure gradient along the flow channel, whereas other intima regions show a null volume strain. A thorough understanding of stress distribution is essential to create focused therapies to lessen vascular health problems. The stress in the post-stenosis region seems to affect the endothelial layer to a significant extent.

A comprehensive examination of turbulent Reynolds numbers at regular, converging, and diverging outlets may be referred to as necessary knowledge for optimizing fluid dynamics in engineering applications as it enhances understanding of flow behavior and improves design efficiency. This report presents the variation of turbulent Reynolds number, turbulent kinetic energy, and effective viscosity of three kinds of fluids (i.e. air, water, and kerosene) in y-shaped cylindrical copper ducts with regular, converging, and diverging outlets. The SpaceClaim was used to design the duct such that the diameter of the two inlets is 40 mm. The diameters of the diverged and converged outlets are 70 mm and 10 mm respectively. The SST k-omega viscous model in Ansys Fluent 2023R2 was adopted as a better approach for handling adverse pressure gradients and capturing boundary layer behavior. The simulation and meticulous meshing of the ducts were achieved using waterlight workflow. Reliable and valid results were obtained after adopting suitable boundary conditions, grid independence, and solver settings. Worth concluding that when the entry velocities of cold and hot water are equal and small in magnitude, higher turbulent Reynolds numbers (Rey) occur at the diverged outlet due to enhanced mixing and vorticity. The substantial difference in velocities of hot and cold air (2 m/s for hot air and 12 m/s for cold air) leads to strong mixing and a resultant airflow that is significantly influenced by the properties of the cold air. Higher inlet velocities, whether from hot or cold fluids (i.e. air, water, and kerosene), increase the velocity magnitudes at all outlets, but the effects vary depending on which inlet velocity is increased. Fluid thermal conductivity plays a crucial role in determining static temperature at outlets, with higher conductivity fluids (air and water) showing higher temperatures than lower conductivity fluids (kerosene).

Concentration modulation research is critical because it provides a thorough understanding of how fluctuations in concentration affect a wide range of sectors, from environmental science to medicines, eventually leading to more effective problem-solving and innovation. However, nothing is known about concentration modulation on weakly nonlinear thermal instability in a rotating porous layer holds profound significance as it contributes to the advancement of our understanding in the field of fluid dynamics and thermal sciences, offering valuable insights into the complex interplay of factors that govern heat transfer phenomena in rotating porous media. The mass transfer in a rotating porous medium is subjected to imposed time-periodic solutal boundaries. A weakly nonlinear analysis investigates mass transfer in the porous medium. The cubic Ginzburg Landau amplitude equation calculates the mass transfer coefficient. Stationary and oscillatory convections are discussed in the presence of rotating solutal Rayleigh numbers. The onset of convection is observed through the stability curves for stationary and oscillatory solutal critical Rayleigh numbers as a function of wavenumber. Taylor number delays the onset of solutal convection, while the internal solute Rayleigh number has an opposite effect on the stationary solutal convection. It was also observed that the mass transfer rate was higher for the modulated system than the unmodulated one. This study revealed that mass transport is proportional to Vadasz number, internal solute Rayleigh number, amplitude of modulation and inversely proportional to Taylor number and frequency of modulation.

The creation of boundary layers, heat and mass transfer mechanisms, flow separation and reattachment, and the beginning of turbulence are some variables that affect the fluctuations in concentration and temperature of fluid flow undergoing leading-edge accretion. Surface roughness associated with leading-edge accretion susceptible to convective heating in aerodynamics. However, when convective heating at the wall is sufficient, more is needed to know about the change in local skin friction coefficients, heat and mass transfer rates, and leading-edge accretion. This study presents the dynamics of a ternary-hybrid nanofluid along a convectively heated surface during leading-edge accretion to determine the impacts of convective and unstable accelerations. The base fluid of the nanofluid is water, while the three nanoparticles are spherical carbon nanotubes, cylindrical graphene, and platelet aluminum oxide. The non-dimensionalized governing equations that describe the transport phenomenon were numerically solved using MATLAB’s built-in solver, bvp4c. Based on the findings, it is reasonable to conclude that the temperature distribution across the ternary-hybrid nanofluid flow increases as the Biot number increases with the leading-edge accretion for 0≤γ≤π /2 as a result of an increase in convective acceleration while unsteady acceleration decreases. With increasing leading-edge accretion, the heat transmission rate along the heated border decreases. Temperature and concentration profiles rise as leading-edge accretion rise in the zone of rising convective acceleration and decreasing unsteady acceleration.

Considering the Navier Stokes equations paired with the heat equation for ferrohydrodynamic flow of magnetic nanofluid amidst two rotating porous disks, nothing is known on the significance of geothermal viscosity for the magnetic fluid flow between co-rotating porous surfaces. The current analysis considers the effects of changing viscosity and thermal radiation. Additionally, the stretching and angular velocities of the two disks differ. The flow model's estimated basic equations are transformed into nondimensional ordinary differential equations (ODEs) with the proper transformation before being numerically solved using Maple's built-in BVP Midrich approach. For velocity and temperature fields, the effects of active flow parameters such as the depth-dependent viscosity variation parameter, ferro-hydrodynamics interaction parameter, Reynolds number, Prandtl number, Darcy number, Eckert number, and radiation parameter are discussed. It is worth noticing that the temperature field tends to decline as the Darcy parameter is higher estimated. It is worth concluding that there exists a high fluctuating viscosity around the lower disk, the magnitude of horizontal velocity decreased, but vertical velocity increased everywhere else. Furthermore, skin friction becomes more valuable at higher Reynolds numbers and porosity estimates.

In recent years, a great deal of interest has been generated in modern micro‐ and nanotechnologies for micro/nano‐electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro‐organisms. Motivated by bio‐nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple‐stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non‐Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into nondimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Keller‐box technique, a second‐order finite difference method for solving second‐order equations, is used to solve them numerically. On the other hand, the effects of different non‐Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters.

One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x-direction and between two concurrent plates at z=0 and z=d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (Nu), Sherwood number proportional to mass transfer of solute 1 (Sh1) and Sherwood number proportional to mass transfer of solute 2 (Sh2) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

As in the case of enhancing the performance of high-temperature superconductors, the dynamics of colloidal mixes of water and copper-based nanoparticles exposed to an inclined magnetic field owing to free convection is a recognized issue. However, nothing is known about the dynamics mentioned above when the radius and inter-particle spacing of copper nanoparticles grow in the presence of Joule dissipation, mass flux owing to a temperature gradient, internal heating, and heat flux due to concentration gradient. When the ratio of momentum to thermal diffusivities is incorporated into the momentum equation using appropriate models, the governing equation (i.e. Partial Differential Equations) that models the transport mentioned above was scaled, solved numerically, and simulated with a focus on the nanoparticle radius and the spacing between copper nanoparticles. The resultant non-linear coupled Ordinary Differential Equation was solved using the MATLAB integrated (i.e. bvp4c software package) and the shooting approach (i.e. fourth-order Runge–Kutta integration strategy shrk4). Just because of the resulting improvement in the temperature distribution, increasing the ratio of momentum to thermal diffusivities leads to a more pronounced local skin friction within the layers adjacent to the wall and heat transfer. Because buoyancy forces are exclusively associated with the growth of concentration difference, they cause the distance covered by the transport phenomenon in terms of the spatial domain to decrease. Higher ratios of momentum to thermal diffusivities cause the full-fledged sheer stress profile, which is proportional to friction across fluid layers, to rise.

Efficiency, management, and control of air and water dynamics subject to cold fronts within ducts are among the problems that occur in the water industry and during the production of gases. This article presents the dynamics of unsteady air and water through a three-inlet t-shaped duct, emphasizing the problem of cold fronts. Attempts were made to remark on the nature of these fluids a few distances after the mixture (70 mm), before turning of the duct, and after turning the duct. The realizable k - epsilon viscous model and energy equation were solved numerically using Ansys Fluent 2022R1. Examination of the residual and mesh independency were considered for checking the convergence of results. Optimal eddies' average kinetic energy per unit mass was formed near the t-junction not because of the earlier formed cold fronts but due to the recirculation of pressure at the 90o bend that affect the velocity of cold fluid substance from the two adjacent inlets (i.e. inlet 2 and inlet 3). Considering the variation of inlet velocity, three cases of cold front formation was examined. When the entry velocities of cold air/water and warm air/water are the same, the formation of the cold front is invisible at the early stage despite the fact that air flows faster than water. A significant difference exists between the heat transfer rate at hot and cold inlets, but the mass transfer is uniform at the three inlets. The optimal temperature across the motion of both fluids occurs at the circular surface 30 mm after the mixture. The duct's bent nature is a factor that greatly influences the mixture of cold and warm liquid substances.

The transport phenomenon of water conveying spherical carbon nanotubes, cylindrical graphene, and platelet aluminum oxide nanoparticles exhibits a linear relationship between the pressure gradient causing the dynamics of ternary-hybrid nanofluid and the velocity. However, it is essential to note that little is known about the computation of roughness at the surface transition zone during the early stages of accretion. The Darcy flow of ternary-hybrid nanofluid was investigated and reported in this paper with the intention to provide insight into the convective and unstable acceleration related to leading-edge accretion. The governing equations roughly represented that the time-dependent fluid flow were nondimensionalized using the Blasius-Rayleigh Stokes variable, and the three-stage Lobatto IIIa integration formula for a finite difference (MATLAB package bvp4c) was used to solve numerically. Based on the analysis of results, it is worth concluding that the velocity decreases significantly due to a growth in the leading-edge accretion (gamma) because the convective acceleration increases while the unsteady acceleration decreases for 0 degrees <=gamma <= 90 degrees. As gamma -> 90 degrees, convective acceleration increases while the unsteady acceleration decreases. As gamma enlarges from 90 degrees to 180 degrees, both forms of the acceleration are decreasing properties, but unsteady deceleration is bound to manifest.

The decline in academic performance in mathematics is a major problem known to not only the guardians but also academicians inspiring the improvement of students' performance most especially in mathematics. This report presents the effects of gender disparities and school type on student attitudes toward mathematics, parental support, active learning practices, the academic performance of students in mathematics and self-efficacy. The observed disparities in male and female students' attitudes toward mathematics and academic achievement are statistically significant. Male students have a more evident and positive attitude toward mathematics than female pupils. Academic achievement of male students is much higher than that of female students. Home support is weak for students who attend a boys-only school or a girls-only school. There is a considerable gap in academic achievement between children who attend a boys or girls school and those who attend a mixed school.