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This study comprehensively examines magnetohydrodynamic heat transport characteristics within a thin nanofluid film on a stretchable sheet embedded in a composite medium. By considering factors such as the unsteady nature of sheet velocity, Brownian motion, thermophoresis, thermally radiative heat, irregular heat generation/sink, chemical reactions, and dissipation due to viscous fluid, the research provides valuable insights into the variations in fluid velocity, temperature, and nanoparticles concentration. The computational solution utilizes the efficient numerical method that enables accurate predictions of system behavior under varying conditions. Notable findings include the influence of Schmidt numbers on nanoparticle concentration distribution, the opposing impact of thermophoresis parameter values, and the influence of Brownian motion and heat source/sink on temperature profiles in thin nanofluid film. Also, nanoliquid film thickness is reduced by enhancing the porous parameter values and Hartmann number values. The nanoliquid film becomes thinner when the space‐dependent heat source/sink parameter is considered compared to the temperature‐dependent heat source/sink coefficient. In space‐dependent and temperature‐dependent cases, the increase in these parameters leads to a decrease in the temperature gradient. Furthermore, it is observed that higher thermophoresis values correspond to reduced nanoparticle concentration gradient profiles. Also, enhancement in the chemical reaction values leads to an expansion in the solutal boundary region surrounding nanoparticles, and as a consequence, the concentration gradient of nanoparticles is enhanced. This research has significant potential for optimizing heat performance and advancing innovation in industrial and engineering processes. [ABSTRACT FROM AUTHOR]

In this research, a novel design stochastic numerical technique is presented to investigate the unsteady form magnetohydrodynamic (MHD) slip flow along the boundary layer to analyze the transportation and heat transfer in a solar collector through nano liquids which is a revolution in the field of neurocomputing. Thermal conductivity in variable form is dependent on temperature and wall slips are assumed over the boundary. For mathematical modeling, the solar collector is assumed in the form of a nonlinear stretching sheet and a quite new artificial neural networks (ANNs) based approach is used to solve the current problem in which inverse multiquadric radial basis (IMRB) kernel is sandwiched between a global search solver named genetic algorithms (GAs) and a highly effective local solver named sequential quadratic programming (SQP) i.e. IMRB-GASQP solver. The governing boundary value problem is altered in the form of a system of nonlinear ordinary differential equations (ODEs) through the utilization of similarity transformation and then the obtained system of ODEs is solved using IMRB-GASQP solver by altering the values of distinguished parameters involved in it to observe the fluctuation in the velocity and temperature profiles of nanofluid. The obtained results are effectively compared with the reference solutions using the Adams numerical technique in graphical and tabulated form. An exhaustive error analysis using performance operators is presented while the efficacy of the designed solver using various statistical operators is also part of this research. [ABSTRACT FROM AUTHOR]

The current study aims to investigate heat transfer processes in chemically reacting processes, specifically focussing on the flow of an electrically conducting nanofluid over a curved extended surface. The work tries to describe the complex interaction between heat and mass transport phenomena in many applications, such as the biological sciences, catalytic processes and conflagration by including both homogeneous and heterogeneous processes in the framework. Introducing a convective heating strategy is a new technology that may boost circulation phenomena, perhaps leading to improved heat transfer performance. Additionally, the comparison between the Xue and Tiwari–Das models provides helpful insights into their individual suitability and precision in representing the heat transfer mechanism inside the examined system. The boundary layer approximation is used to handle the mathematical equations. Using the proper similarity variables, the controlling partial differential equations (PDEs) are effectively refined into the dimensionless form and computed numerically utilising the Runge–Kutta Fehlberg 4th–5th-order technique. The suggested characteristics of the physical parameters are examined and their relevant behaviour is illustrated graphically. The outcomes declare that the rise in magnetic parameter will decline velocity while enhance thermal profiles. Homogeneous and heterogeneous reaction strengths will decline the mass distribution while heat source/sink, solid fraction and Biot numbers will improve the temperature profile. In all circumstances, the Xue model exhibits a higher rate of thermal dispersion and temperature profile than the Tiwari–Das model. [ABSTRACT FROM AUTHOR]

The main aim of this investigation is to study the heat transport and entropy generation of human blood as a hybrid nanofluid (HNF) containing gold (Au) and silver (Ag) nanoparticles inside a Darcy–Fochheimer porous stenotic artery in the presence of thermal radiation and magnetic field. The primary reason for adopting Au and Ag nanoparticles as nanomaterials for drug delivery is because they exhibit potential drug transport and imaging properties for treating stenosed artery. Furthermore, velocity slip and convective boundary conditions at the surface of the artery are considered in this study. A method of suitable similarity transformations has been utilised to convert the partial differential equations (PDEs) into dimensionless ordinary differential equations (ODEs) and using the bvp4c built-in solver in MATLAB mathematical software, numerical solutions have been obtained. The plots of the results show that the hybrid nanofluid (Au–Ag/blood) has greater thermal conductance than the normal nanofluid (Au/blood). The temperature and velocity of the blood gradually increase as the percentage of nanoparticles in the blood flow grows. The heat transference rate increases with increase in Biot number (Bi) and radiation (Nr) effect, which helps in removing the toxic plaque from the artery. Due to the contraction of the artery, dual solutions are found, but dual solutions cannot be found beyond the critical values of suction (S) and shrinking (λ ) parameters. The critical values S C from computation are 1.5851, 1.5949 and critical values λ C are 0.652, 0.781 for Au/blood nanofluid (NF) and Au–Ag/blood hybrid nanofluid (HNF), respectively. Also, the stability of blood flow is achieved by finding the lowest eigenvalue. A positive minimum eigenvalue ( β 1 ) denotes the upper stable solution branch, whereas a negative minimal eigenvalue indicates the bottom unstable solution branch. The entropy of the blood as the HNF flow was found to increase with nanoparticle volume fraction ( ϕ 1 , ϕ 2 ), porous parameter (P) and magnetic parameter (M). These results will help greatly to avoid brain stroke or heart attack caused by the burst of an artery. [ABSTRACT FROM AUTHOR]

This paper introduces a novel hybrid two-grid algorithm, combining the advantages of traditional two-level (Xu in SIAM J Sci Comput 15(1):231–237, 1994) and two-step (Huang in Appl Numer Math 118:75–86, 2017) method, for solving the steady magnetohydrodynamic system. This novel algorithm includes two steps: first, a low-order finite element pair is employed to solve the original problem on a coarse mesh grid, enhancing iteration efficiency and reducing computational time; second, a high order finite element pair is used to solve the linearized equations on a fine mesh grid, thereby increasing the order accuracy. After only one single correction step on a fine mesh grid, the hybrid two-grid algorithm achieves accuracy equivalent to that of using a high-order finite element pair. The stability analysis and error estimates for the hybrid two-grid algorithm are given. Ultimately, numerical experiments are conducted to demonstrate its efficiency and effectiveness. What’s more, the relative error is comparable to that of the two-level and two-step methods. Notably, this algorithm requires only minor modifications to the two traditional methods. [ABSTRACT FROM AUTHOR]

The present study is aimed at inspecting magnetohydrodynamic (MHD) viscoelastic hybrid nanofluid flow over circular stretched cylinder. We consider here alumina and silver as nanoparticles with base fluid carboxymethyl cellulose solution. The effect of heat source, heat radiation, and activation energy are taken into account. Moreover, with small Reynolds number, the induced magnetic field has no noticeable effect. The leading dimensional equations are converted to dimension-free form by employing similarity transformations. The converted equations are calculated by using MATLAB bvp4c numerical method. Graphs and tables are used to analyze velocity, skin friction, temperature, heat-mass transport rate, and concentration for numerous physical factors. Observation reflects that viscoelastic and curvature parameters enhance velocity profile. Moreover, heat source enhances fluid temperature. It is clearly reflected that volume fraction parameter for alumina and silver enhances the heat transport's rate. The mass transport's rate reduces for Arrhenius energy parameter. The present work compares to prior work without considering the newly added effects and finds consistent findings. [ABSTRACT FROM AUTHOR]

Significance of magnetohydrodynamic effect on a viscous (temperature‐dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter S $S$ lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are θr ${\theta }_{r}$ [0.0, 1.0], Nr $Nr$ [0.0, 2.0], Pr $Pr$ [0.8, 1.5], Sc $Sc$ [0.5, 2.0], B* ${B}^{* }$ [0.0, 1.0], k1 ${k}_{1}$ [0.2, 3.0], fw ${f}_{w}$ [1.0, 2.0], M $M$ [0.0, 3.0], Du $Du$ [0.4, 1.0], and Sr $Sr$ [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement. [ABSTRACT FROM AUTHOR]

This review reports a critical study on the effect of magnetic fields on the precipitation process of calcium carbonate scale from hard water. Indeed, the harmful consequences of the water scaling phenomenon urged researchers to find effective solutions. One of the interesting antiscaling processes is the magnetic treatment of water, which triggers a reduction in the precipitation of calcium carbonate on the walls when in contact with hard water. In the present review, we discuss selected examples related to this process in a combined analysis of the latest advances and the mechanism of action of the magnetic field. Despite the diversity of studies investigating this phenomenon, the effectiveness of this treatment remains a controversial issue, and it is not possible to obtain a clear explanation of the phenomenon. This review proposes, finally, interesting hypotheses which can effectively explain the effect of magnetic treatment on the behavior of hard waters and the precipitation of calcium carbonate, which include magnetohydrodynamics and the hydration effect. [ABSTRACT FROM AUTHOR]

The current work analyzes the role of various thermophysical variables in examining the Jeffrey model bioconvection phenomena in a stretched Darcy-Forchheimer medium. The non-Newtonian Jeffrey fluid model is significant because of its enormous applicability in the production of industrial fields, such as paints, oils, gels, and adhesives. Continuing measurements of the non-Newtonian model's flow dynamics and heat transfer shows complex fluctuations in the mass and heat flux rates. These observations, made under various physical conditions, help to clarify what its actual behavior is. The governing equations are converted to nonlinear ordinary differential equations utilizing a similarity transform and then solving analytically using the BVPh2.0 tool designed for optimal homotopic procedure in Mathematica. The temperature, velocity, concentration, and bioconvection microorganism analytical findings are generated and visually shown. Our investigation found that fluid velocity increased in the case of Jeffrey's fluid increase. Collisions between fluid particles produce Brownian motion, which increases fluid kinetic energy and nanoparticle activity and raises temperature; an increased Nt increases thermophoretic force, which pushes tiny particles far from the heated surface and produces a counter flow. By increasing the values of β and the velocity profile increases. The profile of velocity is greater for the boundary layer with thickness η = 0 without dimensions and then sharply decreases along the stretching sheet to zero. In the absence of magnetic fields, the profile of velocity is maximum, and in the presence of magnetic fields, it drops. By using the Jefferey model to investigate bioconvection in Darcy-medium, this work has practical implications that go beyond theoretical domains. These include groundwater management in environmental engineering and bioreactor optimization in biotechnology. Heat exchangers, distillation towers, cancer therapy, magnetic field-assisted wound healing, MHD Jeffrey fluid with porous media, and hyperthermia are just some of this fluid's industrial and medicinal uses. [ABSTRACT FROM AUTHOR]

This study utilises mathematical modelling and computations to analyse the magnetohydrodynamic (MHD) effects on non-Newtonian Eyring–Powell fluid flow in an inclined non-uniform channel under long-wavelength, low Reynolds number conditions. The governing equations are solved by applying slip boundary conditions to determine the velocity, temperature, concentration, and streamline profiles. The key findings show that the magnetic parameter dampens the flow rate. The relationship between the variable viscosity, velocity, and temperature is nonlinear. The wall rigidity parameter and axial velocity are directly proportional until a threshold. Increasing inclination angles distorts streamlines. The magnetic field alters concentration contours and thermal transport. MATLAB parametric analysis explores MHD effects. This study enhances the understanding of inclined channel fluid dynamics, offering insights into variable viscosity, magnetic fields, wall properties, and impacts of inclination angles on non-Newtonian flow characteristics. This knowledge can optimise industrial MHD conduit/channel transport applications.

AbstractExamining the effects of varying transient magnetic fields and their orientations on boundary layers aids in understanding the flow in complex surface geometries, turbulence control, drag reduction, aircraft and ship design, groundwater management, and the study of construction and coastal engineering. The study introduces a novel dynamics of the boundary layer of a natural convective Jeffrey fluid flowing over an erect porous moving plate under the influence a non-uniform and transient magnetic field M˜ that grows exponentially over time with α as an accelerating parameter. The governing partial differential equations (PDEs) were non-dimensionalized using similarity variables and then solved analytically using the perturbation technique. The impact of various thermosphysical properties including chemical reactions, thermal source, Jeffrey fluid parameter and plate permeability on the fluid flow were presented graphically utilizing finite difference approximation(FDA) technique in MATLAB ODE15s solver. The study highlighted a notable decrease in shear stress (skin friction) by introducing M˜ to the vertical plate results in the reduction of momentum boundary layer, accompanied by an increment in thermal boundary layer. Also, the results shows that increasing the magnitude of α leads to decrease the velocity and increase the temperature distribution curve. Additionally, the concentration profile was also found to decrease with stronger chemical reactions. Furthermore, key parameters like heat and mass flux were estimated and discussed through comparison tables. Understanding the effects of unsteady and externally applied increasing magnetic field M˜ on viscous fluid flow have potential applications in biomedical engineering, such as the design of magnetic drug delivery systems and the analysis of blood flow in human body. [ABSTRACT FROM AUTHOR]

There are extensive range of applications related to nuclear industry, industrial manufacturing, science and engineering processing, in which the boundary layer hydromagnetic motion of Casson liquids perform vital role. Casson liquid is a useful liquid in the nuclear industry for optimizing the design and operation of nuclear reactors. Researchers have investigated transfer of heat in liquid motions with linear stratification, which is a phenomenon where the temperature varies linearly with height, affecting various fields such as medical equipment, glass fiber production, electronic devices, polymer sheets, paper production, filaments, and medicine. However, the most discussion of heat transfer problems is to get numerical solutions of a comprehensive Casson liquid model with heat generation described by the BVP4 via shooting method. In this study, a new velocity slip boundary condition is applied at the stretching or shrinking surface. These conditions are grounded in the previously established Buongiorno model, providing a more practical and realistic approach compared to previous study. The time independent Gov. Eqs. changed into a set of couple non-linear ODEs with help of suitable similarity conversions. The equations are evaluating via R-K-F by help of MATLAB software programming. [ABSTRACT FROM AUTHOR]

The mass‐transfer of oxygen in liquid phases (including in the bulk electrolyte and near the electrode surface) is a critical step to deliver oxygen to catalyst sites (especially immersed catalyst sites) and use the full capacity of oxygen reduction reaction (ORR). Despite the extensive efforts of optimizing the complex three‐phase reaction interfaces to enhance the gaseous oxygen transfer, strong limitations remain due to oxygen's poor solubility and slow diffusion in electrolytes. Herein, a magnetic method for boosting the directional hydrodynamic pumping of oxygen toward immersed catalyst sites is demonstrated which allows the ORR to reach otherwise inaccessible catalytic regions where high currents normally would have depleted oxygen. For Pt foil electrodes without forced oxygen saturation in KOH electrolytes, the mass‐transfer‐limited current densities can be improved by 60% under an external magnetic field of 435 mT due to the synergistic effect between bulk‐ and surface‐magnetohydrodynamic (MHD) flows induced by Lorentz forces. The residual magnetic fields are further used at the surface of magnetic materials (such as CoPt alloys and Pt/FeCo heterostructures) to enhance the surface‐MHD effect, which helps to retain part of the ORR enhancement permanently without applying external magnetic fields. [ABSTRACT FROM AUTHOR]

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate. [ABSTRACT FROM AUTHOR]

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration. [ABSTRACT FROM AUTHOR]

This study explores the effects of a first-order slip boundary condition on the magnetohydrodynamic flow and heat transfer in a Casson-based hybrid nanofluid containing copper oxide (CuO) and graphite oxide (GO) nanoparticles in methanol (CH 3 OH) . To address the critical need in advanced cooling and thermal management, the research delves into the complexities of thermal radiation, viscous dissipation, and Joule heating. To ensure comprehensive validation and robustness of the findings, we employed both the bvp4c and Keller–Box numerical methods, each chosen for its strengths in different aspects of the model problem. This dual-method approach, detailed in our comparative analysis section, enhances the scientific rigor of our results. Using an effective similarity transformation, complex governing equations are transformed into a manageable set of ordinary differential equations, which are then numerically solved. Our findings reveal that hybrid nanofluids offer enhanced thermal properties and flow adjustability compared to single-nanoparticle fluids, with significant impacts of radiation and magnetic field on the thermal boundary layer. These insights not only advance theoretical knowledge but also have substantial practical applications in fields such as medical sciences, opto- electronics, and energy systems, establishing a new benchmark in fluid dynamics and materials science for thermal management technologies. [ABSTRACT FROM AUTHOR]

The investigation of plasma waves and instabilities in the context of relativistic, anisotropic drifting astrophysical plasma is the focus of this study. Utilizing fluid equations in the linear regime, the research reveals the emergence of novel instabilities as a result of drift velocity. Furthermore, the study uncovers a modification in the condition for the mirror instability due to the drift velocity. These findings potentially hold significant implications for comprehending plasma behavior in space environments, particularly in regions like the solar wind or the interstellar medium. The study proposes the further development of the theory to directly apply to space plasma, which could enhance our understanding of the intricate astrophysical systems that are driven by plasma dynamics. [ABSTRACT FROM AUTHOR]

Understanding generalized Couette flow provides valuable insights into the behavior of fluids under various conditions, contributing to the advancement of more accurate models for real-world applications including tribology and lubrication, polymer and food processing, water conservation and oil exploration, microfluidics, biological fluid dynamics (blood flow in vessels), and electrohydrodynamic, and so on. The present study provided the exact asymptotic solution for the generalized Couette flow of a non-Newtonian Jeffrey fluid in a horizontal channel immersed in a saturated porous medium. The governing partial differential equations were transformed into a dimensionless form using the similarity technique and the resulting system of equations is solved by the Perturbation technique, as well as the method of the separation of variables, and computed on MATLAB (ode15s solver). The behavior of fluid velocity was investigated and presented through 2-D and 3-D graphs for two cases (i) when the implication of the magnetic field was strengthened and (ii) when the magnitude of the magnetic field was fixed but its degree of inclination was altered. The first-order chemical reactions and thermal radiation were also considered. Additionally, the effect of numerous emerging quantities on momentum, temperature, and concentration contours characterizing the fluid flow was depicted graphically and discussed. Furthermore, the skin friction (at different angles of inclination and magnetic strength), Nusselt number, and Sherwood number (at different time intervals) were evaluated at both boundaries and presented tabularly. The findings revealed that there was a decrease in the velocity profile with an increasing degree of inclination and strength of the magnetic field. Moreover, we observed an increment in thermal and mass flux when it was measured over time at both of the channels. Also, the outcomes predicted an oscillatory nature of shear stress at both of the boundries. [ABSTRACT FROM AUTHOR]

The current study pivoted on the numerical simulation of magnetohydrodynamic nanofluid flow through the irregular boundary over the Riga plate with heat radiation, suction/injection. The governing equations of continuity, momentum, and energy are constructed to be nonlinear in nature, based on the current problem. The combination of Quasilinear technique with finite difference method using irregular boundaries has been used to solve the governing equations. The velocity profile is enhanced for incremented values of Hartman number. The thermal radiation parameter due to Rosseland approximations is enhanced for temperature and concentration profiles whereas it declines the heat transfer and mass transfer profiles. Temperature, concentration, and heat transfer rates increase for augmented magnetic parameter values, but velocity and skin friction coefficient profiles show the opposite behaviour. The enhanced values of Biot number along with suction/injection parameter reduces the values of skin friction coefficient. The radiation parameter helps to drop the energy rate in the fluid flow as it reduced the skin friction coefficient values. The upsurged values of the thermal radiation parameter along with electromagnetic parameter decreases the values of the Nusselt number. [ABSTRACT FROM AUTHOR]

There are extensive range of applications related to nuclear industry, industrial manufacturing, science and engineering processing, in which the boundary layer hydromagnetic motion of Casson liquids perform vital role. Casson liquid is a useful liquid in the nuclear industry for optimizing the design and operation of nuclear reactors. Researchers have investigated transfer of heat in liquid motions with linear stratification, which is a phenomenon where the temperature varies linearly with height, affecting various fields such as medical equipment, glass fiber production, electronic devices, polymer sheets, paper production, filaments, and medicine. However, the most discussion of heat transfer problems is to get numerical solutions of a comprehensive Casson liquid model with heat generation described by the BVP4 via shooting method. In this study, a new velocity slip boundary condition is applied at the stretching or shrinking surface. These conditions are grounded in the previously established Buongiorno model, providing a more practical and realistic approach compared to previous study. The time independent Gov. Eqs. changed into a set of couple non-linear ODEs with help of suitable similarity conversions. The equations are evaluating via R-K-F by help of MATLAB software programming.

This research presents an unsteady free convection magnetohydrodynamics (MHD) dusty fluid flow over a vertical cone enclosed inside a porous medium. The Crank–Nicolson approach is used to get the numerical solutions for these non-linear partial differential equations (PDEs). The velocity and temperature distributions are graphed numerically for a wide range of physical parameters to highlight important characteristics of the solutions. The results showed that increasing the porosity parameter leads to a rise in the velocity profile for the fluid and dust phases, while doing the reverse with the rise of the magnetic parameter, fluid-particle interaction parameter, and mass concentration of the particle phase parameter. Additionally, it is shown that the temperature profile rises as the magnetic parameter and the mass concentration of particle phase parameter grow, whereas the fluid-particle interaction parameter and porosity parameter show the opposite tendency.

This study explores the effect of theoretical MHD on curved circular and flat plates using non-Newtonian lubricant. Lower flat plate is porous and rough. The Stokes theory has been used to incorporate the couple stress effects. Furthermore, Darcy law is taken into account for porous medium. Average pressure, load support and squeeze film time are determined from Christensen theory. The numerical results for bearing characteristics such as pressure, load carrying capacity and squeeze film time are plotted graphically to study the influence of curved circular and flat plate. This investigation shows that the squeeze film characteristics are higher in azimuthal roughness patterns and lower in radial patterns due to roughness parameter. In addition, MHD and couple stress boost the pressure, load support and squeezing time compared to Newtonian and non-magnetic cases. The effect of permeability of the porous layer is to decrease the load carrying capacity as it gives an easy path for the lubricant to pass through.

Understanding generalized Couette flow provides valuable insights into the behavior of fluids under various conditions, contributing to the advancement of more accurate models for real-world applications including tribology and lubrication, polymer and food processing, water conservation and oil exploration, microfluidics, biological fluid dynamics (blood flow in vessels), and electrohydrodynamic, and so on. The present study provided the exact asymptotic solution for the generalized Couette flow of a non-Newtonian Jeffrey fluid in a horizontal channel immersed in a saturated porous medium.The governing partial differential equations were transformed into a dimensionless form using the similarity technique and the resulting system of equations is solved by the Perturbation technique, as well as the method of the separation of variables, and computed on MATLAB (ode15s solver).The behavior of fluid velocity was investigated and presented through 2-D and 3-D graphs for two cases (ⅰ) when the implication of the magnetic field was strengthened and (ⅱ) when the magnitude of the magnetic field was fixed but its degree of inclination was altered. The first-order chemical reactions and thermal radiation were also considered. Additionally, the effect of numerous emerging quantities on momentum, temperature, and concentration contours characterizing the fluid flow was depicted graphically and discussed. Furthermore, the skin friction (at different angles of inclination and magnetic strength), Nusselt number, and Sherwood number (at different time intervals) were evaluated at both boundaries and presented tabularly. The findings revealed that there was a decrease in the velocity profile with an increasing degree of inclination and strength of the magnetic field. Moreover, we observed an increment in thermal and mass flux when it was measured over time at both of the channels. Also, the outcomes predicted an oscillatory nature of shear stress at both of the boundries.

Modern heat transport processes such as fuel cells, hybrid engines, microelectronics, refrigerators, heat exchangers, grinding, coolers, machining, and pharmaceutical operations may benefit from the unique properties of nanoliquids. By considering Al2O3{{\rm{Al}}}_{2}{{\rm{O}}}_{3} nanoparticles as a solo model and Al2O3–Cu{{\rm{Al}}}_{2}{{\rm{O}}}_{3}{\rm{\mbox{--}}}{\rm{Cu}} as hybrid nanocomposites in a hyperbolic tangent fluid, numerical simulations for heat and mass transfer have been established. To compare the thermal acts of the nanofluid and hybrid nanofluid, bvp4c computes the solution for the created mathematical equations with the help of MATLAB software. The impacts of thermal radiation, such as altering thermal conductivity and cross-diffusion, as well as flow and thermal facts, including a stretchy surface with hydromagnetic, and Joule heating, were also included. Furthermore, the hybrid nanofluid generates heat faster than a nanofluid. The temperature and concentration profiles increase with the Dufour and the Soret numbers, respectively. The upsurge permeability and Weissenberg parameter decline to the velocity. An upsurge variable of the thermal conductivity grows to the temperature profile. Compared to the nanofluids, the hybrid nanofluids have higher thermal efficiency, making them a more effective working fluid. The magnetic field strength significantly reduces the movement and has a striking effect on the width of the momentum boundary layer.

An investigation of the impacts of magnetic field, heat generation/absorption and thermal radiation on unsteady free convection dusty fluid flow over a non-isothermal vertical cone enclosed inside a porous medium is explored. The Crank–Nicolson approach is used to get the numerical solutions for these nonlinear, coupled partial differential equations (PDEs). The interaction of physical parameter range on temperature and velocity distribution is calculated and graphically presented. The results demonstrate that when the porosity, heat generation/absorption, and thermal radiation parameters are increased, the velocities rise, whereas the magnetic and mass concentration of particle phase parameters have an opposite effect. Furthermore, raising the fluid-particle interaction parameter causes a rise in dust phase velocity but a reduction in fluid phase velocity. [ABSTRACT FROM AUTHOR]

The investigation focuses on the hydrodynamic instability of a fully developed pressure-driven flow within a bidisperse porous medium containing an electrically conducting fluid. The study explores this phenomenon using the Darcy theory for micropores and the Brinkman theory for macropores. The system involves an incompressible fluid under isothermal conditions confined in an infinite channel with a constant pressure gradient along its length. The fluid moves in a laminar fashion along the pressure gradient, resulting in a time-independent parabolic velocity profile. Two Chebyshev collocation techniques are employed to address the eigenvalue system, producing numerical results for evaluating instability. Our findings indicate that enhancing the values of the Hartmann numbers, permeability ratio, porous parameter, and interaction parameter contributes to an enhanced stability of the system. The spectral behavior of eigenvalues in the Orr-Sommerfeld problem for Poiseuille flow demonstrates noteworthy sensitivity, influenced by various factors, including the mathematical characteristics of the problem and the specific numerical techniques employed for approximation. [ABSTRACT FROM AUTHOR]

High-precision surface of 201 stainless steel obtained by electrochemical micro-machining without or with magnetic field-assisted was studied by combining experiments and simulations. The results demonstrated that the surface roughness of the samples was reduced to 0.40 μm after 18 min electrochemical micro-machining. Besides, the introduction of the magnetic field further improved the surface accuracy and reduced it to 0.20 μm. At the same machining time, the magnetic field-assisted electrochemical micro-machining provided lower surface roughness, which indicated that the magnetic field had a favorable impact on the improvement of machining efficiency. Additionally, the distribution characteristics of magnetic induction lines in the machining gap were also discussed. When the magnetic induction lines were approximately parallel to the anode surface and perpendicular to the electric field, the processing efficiency was further improved. The simulation results showed that the current density on the anode surface and the mass transfer rate of the electrolyte were enhanced by the existence of the magnetic field, which accelerated the electrochemical reaction behavior. The external permanent magnet contributed magnetohydrodynamic force during electrochemical micro-machining promoting the occurrence of magnetohydrodynamic convection. Consequently, the charge and the mass transfer in electrolyte was expedited, indicating the improvement of processing efficiency. [ABSTRACT FROM AUTHOR]

In this study, we have investigated magnetohydrodynamic Couette flow across a deformable porous regime with entropy generation having equal suction and injection velocities. The aim of this work is to analyze the novel impact of thermophoresis deposition, activation energy, and magnetic effect by considering viscosity and thermal conductivity as dependent on temperature in a deformable porous regime. The dimensional equations are turned into nonlinear ordinary differential equations (ODEs) through proper similarity variables. To solve these ODEs, we utilized the MATLAB bvp4c approach. Graphs are used to study the behavior of many physical parameters such as skin friction, Bejan number, velocity, displacement, entropy generation, concentration, and temperature. It is found that the viscosity parameter reduces the solid displacement, whereas it enhances the fluid concentration. Due to the impact of suction/injection and drag parameters, fluid velocity becomes reduced. The thermal conductivity parameter raises entropy generation and temperature, but it decays the Bejan number. The volume fraction parameter plays an interesting behavior in skin friction. Moreover, the current work is compared with prior research work while neglecting the newly introduced effects, and the results remain consistent. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze a second order unconditionally convergent mixed finite element method for solving incompressible magnetohydrodynamic problem based on magnetic vector potential. We utilize the second-order backward difference formula within the framework of the mixed finite element method and linearize the nonlinear terms by using the extrapolated technique. The finite element approximation is proposed with the fluid equations are discretized by Taylor–Hood type elements and the magnetic vector potential equation by edge elements. As a result, the divergence-free condition on the magnetic induction preserves exactly on the discrete level. Unconditional error estimates for the velocity and magnetic vector potential are established in the sense that no any restrictions are imposed on the relationship between the time-step size and the spatial size. Finally, several three-dimensional numerical simulations are carried out to illustrate the developed scheme, including convergence tests and some benchmark problems, such as the driven cavity problems and hydromagnetic Kelvin–Helmholtz instability [ABSTRACT FROM AUTHOR]

This study explores the effect of theoretical MHD on curved circular and flat plates using non-Newtonian lubricant. Lower flat plate is porous and rough. The Stokes theory has been used to incorporate the couple stress effects. Furthermore, Darcy law is taken into account for porous medium. Average pressure, load support and squeeze film time are determined from Christensen theory. The numerical results for bearing characteristics such as pressure, load carrying capacity and squeeze film time are plotted graphically to study the influence of curved circular and flat plate. This investigation shows that the squeeze film characteristics are higher in azimuthal roughness patterns and lower in radial patterns due to roughness parameter. In addition, MHD and couple stress boost the pressure, load support and squeezing time compared to Newtonian and non-magnetic cases. The effect of permeability of the porous layer is to decrease the load carrying capacity as it gives an easy path for the lubricant to pass through. [ABSTRACT FROM AUTHOR]

In this study, magnetohydrodynamic cross fluid model is used to formulate the 2D boundary layer equations of fluid moving on the parabolic surface. The surface is assumed to be in vertical shape due to the convection. The underlying effects of viscous dissipation and chemical reaction are modeled to observe the transportation of heat and mass rate. To understand fluid behavior, the thermophysical properties are considered as variable because they have huge influence in food processing, viscometers, lubricants and various industrial works. The assumed geometry of fluid flows is similar in shape of bullet, submarine, aircraft and car's bonnet, namely paraboloid surface. The modeled equations of cross fluid with mentioned effects are obtained in form of PDEs and then converted these equations in form of ODEs by assuming set of scaling transformations. For the sake of numerical and graphical outcomes, the resulting equations are solved numerically on Matlab software via BVP4c method. Results achieved across velocity indicate that the decay happens by numerous values of Weissenberg number, power law index, viscosity parameter and Hartmann number. The temperature and concentration fields attained increasing influence by thermal conductivity coefficient, Eckert number and thermal diffusivity parameter. [ABSTRACT FROM AUTHOR]

AbstractThis study examines the phenomenon of uniform magnetohydrodynamic mixed convective flow in a cavity filled with nanofluid. The research focuses on analyzing the mixed convection induced by a uniformly heated lid-driven cavity with diagonal motion. The fluid and heat transport equations are solved using the finite volume method. Numerical simulations are conducted for various parameters including Richardson number (Ri) ranging as 0.1, 1 & 10, Hartmann number (Ha) 0, 10, 25 & 50, angle of inclination (γ) 0°, 30°, 45°, 60° & 90°, and solid volume fraction from 0.0 to 0.05. The results are presented in terms of flow and thermal fields. It is observed that higher Hartmann numbers and inclination angles of the magnetic field lead to a suppression of convection, favoring a dominant conduction mode and reducing the overall heat transfer rate. Specifically, the study highlights a significant enhancement in the heat transfer rate in a nanofluid-filled cavity with a diagonally moving wall. The movement’s of diagonal wall has significant power consumption, the tool may be used in an industrial process that improves heat transfer, offers flexibility, and raises the quality of the finished product. Additionally, the correlations that were found are a useful tool for heat exchanger design. [ABSTRACT FROM AUTHOR]

Methods for enhancing fluid dynamics and thermal mixing in 3D open flow were performed and evaluated numerically in the current study. The impacts of a grouping of active and passive techniques of enhancement, namely: nonuniform magnetic field, complex geometry and nanofluids, on hydrodynamic and thermal behaviors were assessed. Flow characteristics such as degree of mixing, Nusselt number, and secondary flow structure indices were evaluated for various enhancement protocols being considered. An external magnetic field was applied in this project in two ways: over the entire channel or on specific stretches of the complex duct. In addition, mentioned flow features are examined along the channel with the number of Hartmann (Ha) ranging between 0 and 50 and three angles of orientation of the magnetic field (0, π/4 and π/2). The results show that the optimal protocol to achieve good thermal mixing between hot and cold fluids with a degree of mixing exceeds the 90% is for a nonuniform use of magnetic force oriented by π/2 or π/4. Moreover, it was observed that by applying the same optimized protocol, the parietal heat transfer represented by the Nusselt number was increased by more than 45%. [ABSTRACT FROM AUTHOR]

In this research, the dynamics of MHD Casson fluid flow has been discussed in the presence of non-Darcy Forchheimer porous medium. The investigation is focused on how thermal radiation, Soret–Dufour, and chemical reactions affect the incompressible Casson flow in a non-Darcy Forchheimer porous medium, taking account of pressure force. The mathematical model of the system is solved using the finite difference scheme followed by the shooting technique with bvp4c tool in MATLAB. The effects of physical parameters on velocity and transport (heat and mass) profile are illustrated through graphs. From the results, it is observed that Soret effect reduces the thermal boundary layer thickness which leads to the asymptotic increase in heat dissipation. The findings of the study on MHD Casson fluid model considering the non-Darcy Forchheimer porous medium are useful in engineering and science areas such as chemical machinery systems, geophysics, etc. [ABSTRACT FROM AUTHOR]

AbstractHeat and mass transfer inside a partially porous medium is a complex coupling process in which the interface boundary conditions between free and porous space are critical for a wide range of engineering applications, including natural and engineered fractures in oil and gas extraction. In this study, we looked into the numerical simulation of magnetohydrodynamic mixed convection of nanofluid in an annular partially porous space between two coaxial cylinders with a permeable interface, in which we investigated the contribution of the interface in order to better understand the heat transfer processes. The inner cylinder is subjected to a discrete uniform heat flux, while the external cylinder is kept at a uniform cold temperature and moving at a constant speed. The base walls are designed to be impermeable and insulated. A finite difference-based vorticity-stream function method is used to solve the nonlinear coupled conservation equations using the Successive Over Relaxation approach (SOR). The acquired numerical results in terms of streamlines, isotherms, and Nusselt numbers are shown to demonstrate the effect of various control factors such as the Rayleigh number, Darcy number, Hartmann number, Reynold number, nanoparticle concentration, and the direction of the outer wall. The results of this numerical simulation show that the upward or downward direction of the wall under these control factors plays an important role in improving the rate of heat transfer or replacing the magnetic effect by limiting and controlling heat transfer [ABSTRACT FROM AUTHOR]

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the entropy generation in hydromagnetic mixed convection of a micropolar fluid flowing over a stretchable sheet, taking into account various influential factors such as nonlinear thermal radiation, Ohmic dissipation, uniform heat source/sink effects, chemical reaction, thermophoresis, and Brownian motion. The Spectral Quasilinearization Method (SQLM) is employed, which transforms nonlinear equations into a series of linearized ones, streamlining the solving process. Additionally, Lie group analysis is utilized to identify symmetries and derive similarity transformations crucial for converting partial differential equations into coupled ordinary differential equations, which are then solved numerically. A comprehensive sensitivity analysis is conducted on critical parameters, including the Darcy parameter, Biot number, Brinkman number, nonlinear convection parameter, and chemical reaction parameter. This analysis explores the impacts of these parameters on various flow profiles, such as velocity, temperature, microrotation, concentration, and entropy generation, enriching the depth and practical relevance of the findings. The results reveal that increasing the Brinkman and Reynolds numbers enhances entropy generation profiles while increasing the coupling parameter reduces them. The focus on entropy generation analysis provides valuable insights into energy utilization and system efficiency, particularly in micropolar fluid dynamics. Furthermore, the study underscores the practical implications of its findings by highlighting their relevance in evaluating the effectiveness of industrial processes, especially those related to energy conversion and heat transfer phenomena. [ABSTRACT FROM AUTHOR]

AbstractIn the present work, the author used a multistep numerical approach, namely the Milne (Predictor and Corrector) method with the Runge-Kutta method, to discuss the synergistic impacts of magnetohydrodynamic (MHD) and stagnation point flow involving a tangent hyperbolic fluid on the surface of a stretched cylinder. The flow field study is constructed with the impact of heat source/sink, chemically reactive species, and the joule heating effect. The phenomenon of concentration and temperature stratification is also taken into account. The Soret and Dufour effects are used to determine the solutal and thermal performance. To create a mathematical model of a physical occurrence, momentum, energy, and concentration laws are employed. The appropriate transformations can be used to convert nonlinear partial differential equations into ordinary differential equations. The Milne (Predictor-Corrector) method along with the Runge-Kutta 4th order scheme is used to determine the numerical findings. The graphical and numerical findings are depicted to show how several parameters influence the respective fields. The finding indicates that the velocity of fluid reduces by making variation in the Hartmann number whereas the temperature region enhances due to Hartmann number. The movement of fluid increases when the stretching ratio parameter is higher but decreases when the Weissenberg number and curvature parameter are higher. The Soret number reduces the concentration region and Dufour number enhances the temperature profile. The temperature distribution rises with higher inputs of the heat source but declines for the heat sink constrain and thermal stratification coefficient. Similarly, the concentration region upsurges for the stretching ratio parameter, while it decreases for the chemical reaction rate and solutal stratification. [ABSTRACT FROM AUTHOR]

A computational analysis is performed to scrutinize the stimulus of an aligned magnetized force and radiative flux on the unsteady magneto-flow of ZnO + H2O nanoliquid across a varied thickness extending surface in the attendance of convective edge constraints. The prime motive of this exploration is to confer the best thermal transfer enactment nanomodel among Maxwell and Xue nanomodels. The arising system of PDE's are exercised by adopting suitable similarities to attain the no-dimension ODE's and the solutions are attained by implementing the built-in bvp5c MATLAB package. The energy equation is encompassed by Buongiorno slip mechanism, viscous dissipation, and radiative flux. Further, the flow, thermal, and concentration gradients are illustrated graphically. The major upshots imply that the radiative flux and thermal Biot number efficiently augment the Nusselt number in both situations. Also, the energy transport rate is noticeably 4% large in the Maxwell nanomodel when equated to Xue nanomodel. [ABSTRACT FROM AUTHOR]

In this article, we analyses electroosmosis augmented MHD peristaltic transport of SWCNTs suspension in porous media, the basic equations have been constructed under assumptions of low Reynolds number and long wave length. The exact solution by the regular perturbation technique are obtained and the flow qualities have been plotting by using MATHEMATICA software for all the figures. Series solution for stream function, pressure gradient and temperature distribution have been computed in the peristaltic transport in an asymmetric channel. [ABSTRACT FROM AUTHOR]

Kink oscillations, which are frequently observed in coronal loops and prominences, are often accompanied by extreme-ultraviolet (EUV) waves. However, much more needs to be explored regarding the causal relationships between kink oscillations and EUV waves. In this article, we report the simultaneous detection of kink oscillations and EUV waves that are both associated with an X2.1 flare on 2023 March 03 (SOL2023-03-03T17:39). The kink oscillations, which are almost perpendicular to the axes of loop-like structures, are observed in three coronal loops and one prominence. One short loop shows in-phase oscillation within the same period of 5.2 min at three positions. This oscillation could be triggered by the pushing of an expanding loop and interpreted as the standing kink wave. Time lags are found between the kink oscillations of the short loop and two long loops, suggesting that the kink wave travels in different loops. The kink oscillations of one long loop and the prominence are possibly driven by the disturbance of the coronal mass ejection (CME), and that of another long loop might be attributed to the interaction of the EUV wave. The onset time of the kink oscillation of the short loop is nearly same as the beginning of an EUV wave. This fact demonstrates that they are almost simultaneous. The EUV wave is most likely excited by the expanding loop structure and shows two components. The leading component is a fast coronal wave, and the trailing one could be due to the stretching magnetic field lines. [ABSTRACT FROM AUTHOR]