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This study investigates the behavior of viscous hybrid ferromagnetic fluids flowing through plain elastic sheets with the magnetic polarization effect. It examines flow in a porous medium using Stefan blowing and utilizes a versatile hybrid ferrofluid containing MnZnFe₂O₄ and Fe₃O₄ nanoparticles in the C2H2F4 base fluid, offering potential real-world applications. The study focuses on steady, laminar and viscous incompressible flow, analyzing heat and mass transfer aspects, including thermal radiation, Brownian motion, thermophoresis and viscous dissipation with convective boundary condition.

The governing expression of the flow model is addressed with pertinent non-dimensional transformations, and the finite element method solves the obtained system of ordinary differential equations.

The variations in fluid velocity, temperature and concentration profiles against all the physical parameters are analyzed through their graphical view. The association of these parameters with local surface friction coefficient, Nusselt number and Sherwood number is examined with the numerical data in a table.

This work extends previous research on ferrofluid flow, investigating unexplored parameters and offering valuable insights with potential engineering, industrial and medical implications. It introduces a novel approach that uses mathematical simplification techniques and the finite element method for the solution.

Ferrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions.

The leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties.

Multiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter.

The novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.

The purpose of this paper is to investigate micropolar magnetohydrodynamics (MHD) fluid flow passing over a vertical plate. Three different base fluids have been used that include water, ethylene glycol and ethylene glycol/water (50%–50%). Also, a nanoparticle was used in all of the base fluids. The effects of natural convection heat transfer and magnetic field have been taken into account.

The main purpose of solving the governing equations is to scrutinize the effects of the magnetic parameter, the nanoparticle volume fraction, micropolar parameter and nanoparticles shape factor on velocity, temperature and microrotation profiles, the skin friction coefficient and the Nusselt number. These surveys have been considered for three base fluids simultaneously.

The results indicate that for water-based fluids, the temperature profile of lamina-shaped nanoparticles is 38.09% higher than brick-shaped nanoparticles.

This paper provides micropolar MHD fluid flow analysis considering natural convection heat transfer and magnetic field in three different base fluids. The aim of assessments is the diagnosis of some parameter effects, such as magnetic parameter and nanoparticle volume fraction, on velocity, temperature and microrotation profiles and components. Also, the use of mixed base fluids presented as a novelty in this paper.

For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery.

Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field.

It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force.

The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

The boundary-layer analysis is required to reveal the fluid flow behavior in several industrial processes and enhance the products’ effectiveness. Therefore, this research aims to investigate the buoyancy or mixed convective stagnation-point flow (SPF) and heat transfer of a micropolar fluid filled with hybrid nanoparticles over a vertical plate. The nanoparticles silver (Ag) and titanium dioxide (TiO₂) are scattered into various base fluids to form a new-fangled class of (Ag-TiO₂/various base fluid) hybrid nanofluid along with different shape factors.

The self-similarity transformations are used to reformulate the leading requisite partial differential equations into renovated non-linear dimensionless ordinary differential equations. The numerical dual solutions are gained for the transmuted requisite equations with the help of the bvp4c built-in package in MATLAB software. The results are validated by comparing them with previously available published data for a particular case of the present study.

The impact of various pertaining parameters such as nanoparticle volume fraction, material parameter, shape factor and mixed convective on temperature, heat transfer, fluid motion, micro-rotation and drag force are visualized and scrutinized through tables and graphs. It is observed that dual or non-uniqueness outcomes are found for the case of buoyancy assisting flow, whereas the solution is unique in the buoyancy opposing flow case. Additionally, the fluid motion and micro-rotation profiles decelerate in the presence of nanoparticle volume fraction, while the temperature augments.

The mixed convective stagnation point flow conveying TiO₂/Ag hybrid nanofluid with micropolar fluid with various shape factors is the significant originality of the current investigation where multiple outcomes are obtained for the assisting flow. The various base fluids such as glycerin, water and water–ethylene glycol (50%:50%) are considered in the present problem. The bifurcation values of the considered problem do not exist, probably because of various base fluids. To the best of the authors’ knowledge, this work is new and original which were not previously reported.

This study aims to investigate the flow and heat transfer of a hybrid nanofluid through an exponentially stretching/shrinking sheet along with mixed convection and Joule heating. The nanoparticles alumina (Al₂O₃) and copper (Cu) are suspended into a base fluid (water) to form a new kind of hybrid nanofluid (Al₂O₃-Cu/water). Also, the effects of constant mixed convection parameter and Joule heating are considered.

The governing partial differential equations are transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The transformed nonlinear ODEs are solves using the bvp4c solver available in MATLAB software. A comparison of the present results shows a good agreement with the published results.

Dual solutions for hybrid nanofluid flow obtained for a specific range of the stretching/shrinking parameter values. The values of the skin friction coefficient increases but the local Nusselt number decreases for the first solution with the increasing of the magnetic parameter. Enhancing copper volume fraction and Eckert number reduces the surface temperature, which intimates the decrement of heat transfer rate for the first and second solutions for the stretching/shrinking sheet. In detail, the first solution results show that when the Eckert number increases as 0.1, 0.4 and 0.7 at λ = 1.5, the temperature variations reduced to 10.686840, 10.671419 and 10.655996. While in the second solution, keeping the same parameters temperature variation reduced to 9.750777, 9.557349 and 9.364489, respectively. On the other hand, the results indicate that the skin friction coefficient increases with copper volume fraction. This study shows that the thermal boundary layer thickness rises due to the rise in the solid volume fraction. It is also observed that the magnetic parameter, copper volume fraction and Eckert number widen the range of the stretching/shrinking parameter for which the solution exists.

In practice, the investigation on the flow and heat transfer of a hybrid nanofluid past an exponentially stretching/shrinking sheet with mixed convection and Joule heating is crucial and useful. The problems related to hybrid nanofluid have numerous real-life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical and drug reduction.

In specific, this study focuses on increasing thermal conductivity using a hybrid nanofluid mathematical model. The novelty of this study is the use of natural mixed convection and Joule heating in a hybrid nanofluid. This paper can obtain dual solutions. The authors declare that this study is new, and there is no previous published work similar to the present study.

This paper aims to examine the squeezing flow of hybrid nanofluid within the two parallel disks. The 50:50% water–ethylene glycol mixture is used as a base fluid to prepare Ag–Fe_3O_4 hybrid nanofluid. Entropy generation analysis is examined by using the second law of thermodynamics, and Darcy’s modal involves estimating the behavior of a porous medium. The influences of Viscous dissipation, Joule heating and thermal radiation in modeling are further exerted into concern.

For converting partial differential systems to ordinary systems, a transformation technique is used. For the validation part, the numerical solution is computed by embracing a fourth-order exactness program (bvp4c) and compared with the analytical solution added by the homotopy analysis method (HAM). Graphical decisions expose the values of miscellaneous-arising parameters on the velocity, temperature and local-Nusselt numbers.

Hybrid nanofluid gives significant enhancement in the rate of heat transfer compared with nanofluid. The outcomes indicate that the average Nusselt number and entropy generation are increasing functions of the magnetic field, porosity and Brinkman number. When the thermal radiation rises, the average Nusselt number diminishes and the entropy generation advances. Furthermore, combining silver and magnetite nanoparticles into the water–ethylene glycol base fluid significantly enhances entropy generation performance.

Entropy generation analysis of the magneto-hydrodynamics (MHD) fluid squeezed between two parallel disks by considering Joule heating, viscous dissipation and thermal radiation for different nanoparticles is addressed. Furthermore, an appropriate agreement is obtained in comparing the numerical results with previously published and analytical results.

Thermal and species transport of magneto hydrodynamic Casson liquid over a stretched surface is investigated theoretically in this examination for the three-dimensional boundary layer flow of a yield exhibiting material. The phenomenon of heat and species relocation is based upon modified Fourier and Fick’s laws that involves the relaxation times for the transportation of heat and mass. Conservation laws are modeled under boundary layer analysis in the Cartesian coordinates system. The purpose of this paper is to find the influence of different emerging parameters on fluid velocity, temperature and transport of species.

Reconstructed nonlinear boundary layer ordinary differential equations are analyzed through eigenvalues and eigenvectors. Due to the complexity and non-existence of the exact solution of the transformed equations, a convergent series solution by the homotopy algorithm is also derived. The reliability of the applied scheme is presented by comparing the obtained results with the previous findings.

Physical quantities of interest are displayed through graphs and tables and discussed for sundry variables. It is discerned that higher magnetic influence slows down fluid motion, whereas concentration and temperature profiles upsurge. Reliability of the recommended scheme is monitored by comparing the obtained results for the dimensionless stress as a limiting case of previous findings and an excellent agreement is observed. Higher values of Schmidt number reduce the concentration profile, whereas mounting the values of Prandtl number reduces the dimensionless temperature field. Moreover, heat and species transfer rates increase by mounting the values of thermal and concentration relaxation times.

The phenomenon of heat and species relocation is based upon modified Fourier and Fick’s laws which involves the relaxation times for the transportation of heat and mass. Conservation laws are modeled under boundary layer analysis in the Cartesian coordinates system.

Fluid flows through rotatory disks are encountered in industrial and practical engineering processes, such as computer storage devices, gas turbine rotators, rotating machinery, air cleaning machines, etc. The primary purpose of this research is to examine the combined aspects of variable electrical conductivity, thermal radiation, Soret and Dufour effects on a magnetohydrodynamic Maxwell single-walled carbon nanotubes–graphene oxide–multi-walled carbon nanotubes–copper (SWCNT–GO–MWCNT–Cu)/sodium alginate tetra-hybrid nanofluid flow through a stretchable rotatory disk.

The modeled administrative equations of the present flow problem are converted to a non-dimensional system of ordinary differential equations by applying suitable similarity conversion and then solved numerically by implementing the bvp4c method. The impressions of noteworthy dimensionless parameters on velocity, temperature, concentration distributions, Nusselt number, skin friction and Sherwood number are reported via graphs and tables.

The authors figured out that the developed values of the rotation parameter diminish the temperature but enhance both the radial and angular velocities. Further, the mass and heat transmission rates are better for tetra-hybrid nanofluids than for ternary and hybrid nanofluids.

The present study emphasizes a special type of fluid called the tetra-hybrid nanofluid. The existing literature has not discussed the Maxwell tetra hybrid nanofluid flow through a stretchable rotatory disk with variable electrical conductivity. Besides, the novel aspects of magnetohydrodynamics, thermal radiation, Soret and Dufour effects are also incorporated into the present flow problem.

This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source.

This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios.

The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes.

This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.