Magnetic Field Dependent Viscosity Research Articles

An Analytical Study on the influence of Magnetic Field-Dependent Viscosity on Viscous and Ohmic Dissipative Second-Grade Fluid Boundary Layers

Abstract The article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer, while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Influence of magnetic field-dependent viscosity on Casson-based nanofluid boundary layers: A comprehensive analysis using Lie group and spectral quasi-linearization method

This study examines the effects of magnetic-field-dependent (MFD) viscosity on the boundary layer flow of a non-Newtonian sodium alginate-based Fe3O4 nanofluid over an impermeable stretching surface. The non-Newtonian Casson and homogeneous nanofluid models are utilized to derive the governing flow and heat transfer equations. Applying Lie group transformations to dimensional partial differential equations yields nondimensional ordinary differential equations, which are then numerically solved using the spectral quasi-linearization technique. The analysis primarily focuses on the impacts of the MFD viscosity parameter, nanoparticle volume fraction of Fe3O4, and magnetic parameters on the flow and heat transfer characteristics. The local skin friction and heat transfer rate behaviors influenced by viscosity changes due to the magnetic field are discussed. It is found that MFD viscosity significantly impacts flow and thermal energies, enhancing skin friction coefficients and reducing Nusselt numbers in the boundary layer region.

Saturated Porous Ferroconvection in a Ferrofluid Layer with Viscosity as a Function of Magnetic Field: Focus on Convective Boundary Condition

The present work aims to examine the influence of magnetic field dependent (MFD) viscosity on the onset of ferroconvection (FC) in a horizontal porous layer saturated with a quiescent ferrofluid (FF) and subjected to a uniform vertical magnetic field. It is assumed that the porous boundaries at the bottom and top are rigid-paramagnetic. The thermal conditions consist of a constant heat flux at the lower surface and a convective boundary condition at the upper surface, encompassing fixed temperature and uniform heat flux cases. The application of the Galerkin technique to the resulting eigenvalue problem reveals that the stability region expands as the porous parameter, Biot number, MFD viscosity parameter and magnetic susceptibility increase in magnitude. Conversely, the stability region contracts as the magnetic number and non-linearity of magnetization increase. Furthermore, it is noted that under uniform heat flux boundary conditions, the criterion for the initiation of ferroconvection remains unaffected by the non-linearity of fluid magnetization.

Hydrothermal characteristics of ferrofluid in a wavy chamber with magnetic field-dependent viscosity: Effects of moving walls

The present investigation aims to scrutinize the role of different moving walls on the hydrothermal characteristics and thermal performance of a Fe3O4-H2O ferrofluid within a wavy chamber under mixed convection. Notably, the study also takes into consideration the effects of a magnetic field and internal heat generation or absorption phenomena. To achieve this, a numerical simulation employing a compact finite difference method is conducted, focusing on key factors such as the Richardson number (0.1≤Ri≤100), Hartmann number (0≤Ha≤30), magnetic orientation (00≤γ≤900), Grashof number (Gr=104), solid concentrations (0≤ϕnp≤0.04), magnetic number (0≤δ0≤1), Prandtl number (Pr=6.8377), and internal heat generation parameter (−2≤Q≤2). All of this is undertaken while carefully managing the ferromagnetic particle volume fraction. The primary aim is to assess how different types of moving walls affect the transport behavior of the ferrofluid and to determine the impacts of the magnetic field on the hydrothermal characteristics of the ferrofluid. The outcomes of this investigation reveal that the presence of moving walls leads to a non-uniform temperature distribution within the ferrofluid, significantly affecting the overall transport behavior. The addition of ferrofluid particles to the base fluid results in noteworthy enhancements in the average Nusselt numbers, signifying improved convective heat transfer efficiency. Specifically, Case-I experienced an increase of up to 3.21%, Case-II showed an improvement of 0.93%, Case-III exhibited a rise of 1.70%, and Case-IV demonstrated the highest enhancement of 20.71%. Furthermore, the inclusion of magnetic field-dependent viscosity and the internal heat generation coefficient significantly influences the behavior of the ferrofluid. The findings from this study hold paramount importance for the design and optimization of heat transfer systems that employ ferrofluids and have the potential to contribute to the development of novel technologies with a wide range of industrial applications.

Thermogravitational Convection in a Multiple Baffled Enclosure Filled with Magneto-Hybrid Nanofluid Subjected to Magnetic Field Dependent Viscosity

This study explores the significant impacts of thin baffles and magnetic field dependent viscosity on magnetohydrodynamic (MHD) thermogravitational convection of Cu-Al2O3 (50%–50%) water hybrid nanoliquid in a cavity. Considering different arrangements of baffle sticks on both the vertical walls, four geometrical configurations (Case-I, Case-II, Case-III and Case-IV) have been analyzed. Numerical simulation has been performed for the governing Navier-Stokes (N-S) equations in streamfunction - vorticity form having energy equation. These coupled equations are solved by proposing a higher-order compact finite difference method. The combination of five important aspects (hybrid nanofluid, multiple baffles, magnetic field dependent viscosity (MFDV), magnetic field and compact computation) signifies the novelty of this work. Fluid flow and transportation of thermal energy within the stipulated domain are presented for various flow pertinent parameters. The outcomes show that the increase in number of baffles diminishes the average Nusselt number values. It is concluded here that an increase in Hartmann number from 0 to 90 leads to a decrease in average Nusselt number up to 23.7% for Case-I, 23.8% for Case-II, 21.2% for Case-III and 28% for Case-IV in presence of MFDV effects.

Analysis of Jenkins Model Ferro Flow for Magnetic Field Dependent Viscosity with Porosity

Analysis of Jenkins Model Ferro Flow for Magnetic Field Dependent Viscosity with Porosity

Lattice Boltzmann simulation of natural convection of ethylene glycol-alumina nanofluid in a C-shaped enclosure with MFD viscosity through a parallel computing platform and quantitative parametric assessment

There has been a strong interest to design and optimise thermally efficient heating and cooling equipment. The conventional fluids such as oil and water have limited thermal efficiency. Therefore, researchers have been seeking alternatives to the conventional fluids to improve the efficacy of heat exchanging and electronic cooling devices and nanofluid has been identified as a great option in this regard. Although nanofluid is a great alternative, certain specifications, geometries, and pertinent parameters need to be thoroughly investigated for a comprehensive understanding with the aid of robust computational technique. The aim of this study was to investigate the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to numerically analyse the effects of magnetic field dependent (MFD) viscosity on the natural convection of ethylene glycol (C2H6O2)-alumina (Al2O3) nanofluid in a side heated two-dimensional C-shaped enclosure using graphics processing unit (GPU) by a computing unified device architecture (CUDA) C parallel computing platform. Numerical simulations were performed at multifarious Rayleigh numbers, Hartmann numbers, and the different magnetic field inclination angles to study the heat transfer and various flow patterns under magnetic field-dependent (MFD) viscosity, solutions were presented by varying volume fraction of nanoparticles, Rayleigh numbers, viscous parameters, magnetic inclination angles, and Hartman numbers on streamlines, isotherms, local and average Nusselt number and temperature. Further correlation developments were conducted through Levenberg-Marquardt data-driven algorithm to investigate the influence of all the parameters on average Nusselt numbers, entropy generation, and fluid irreversibility parameter. The findings demonstrated that as the Rayleigh numbers augmented, the average Nusselt number increased significantly due to the influence of buoyancy, whereas under the influence of Hartmann numbers, average Nusselt numbers decreased due to the dominance of magnetic field strength and Lorentz force. However, the heat transfer continued to improve if the concentration of the nanoparticles increased, thus showcasing the importance of hybrid nanofluid. In addition, the entropy generation impact across the cavity for the ethylene glycol-alumina nanofluid was greatly enhanced by a stronger buoyancy influence.

Simulation of magneto mixed convective flow and thermal behavior of hybrid nanofluid in a partially heated wavy cavity

This study is an attempt to address numerically the thermal performance of magneto mixed convection in a wavy cavity filled with Cu-Al2O3(50%–50%) hybrid nanoparticles suspended in water under the influence of magnetic field dependent viscosity. A focus is made on the nonuniform partial heating from the left. The role of geometric parameters on the thermal performance is scrutinized thoroughly by changing surface waviness of the right wall, heating location and the direction of motion of the top and bottom walls. Based on these lid motion, the analysis is conducted by considering four geometrical set up. The transformed governing Navier–Stokes equations in dimensionless form are written in stream function-vorticity and energy transport equations. These equations are solved by using an inhouse computing code written in the compact finite difference approach. This study encompasses the effects of different physical pertinent parameters such as Richardson number, Hartmann number, magnetic orientation, solid concentrations, magnetic number. Simulations show the significant enhancement of thermal performance with the increase of magnetic orientation, undulation of the waviness and solid concentration of nanoparticles while it decreases with the increase in magnetic intensity. It is also seen that Case-I (single wall motion) and Case-III (parallel wall motion) can be an optimal configuration to get the strongest heat transfer inside the partially heated wavy enclosure.

Influence of magnetic dipole on ferrohydrodynamic thin film flow over an inclined spinning surface

This study investigates the three-dimensional problem of steady ferrofluid deposition on an inclined rotating surface in the presence of a magnetic dipole. A finite element procedure is used to solve normalized ordinary differential equations derived from momentum and energy equations. The current numerical model and its solution is compared and validated against previous numerical results. The velocity and temperature field variations are a representation of the effects of magnetic field-based viscosity, magnetic polarization force, Curie temperature, and Prandtl number. In addition, some common errors in the similarity transformation for inclined rotating disk flows are addressed in the present study. The results show that the magnetic field-dependent viscosity generated by the magnetic torque in the current flow reduces the velocity of the thin film liquid in all directions, including rotational flow (radial, tangential, and axial) and inclined flow (drainage and induced). Moreover, the local heat transfer between the fluid and the surface of the rotating disk increases with a rise in the ferromagnetic interaction number and Prandtl number. These findings imply that ferrofluids could be effective for cooling electronic devices in the presence of a magnetic dipole.

Hydrodynamic analysis of the magnetic field dependent viscous fluid flow and thermosolutal convection between rotating channels

According to research, exposing a person to a magnetic field enhances blood flow and minimizes their risk of suffering a heart attack. Ferrohydrodynamics is the study of fluid motion mechanics that is affected by strong magnetic polarisation forces (FHD). Ferrofluids may transmit heat in a variety of ways by using magnetic fluids. This behaviour is demonstrated by liquid-cooled speakers, which utilise less ferrofluid to prevent heat from reaching the speaker coil. This modification boosts the coil’s ability to expand, which enables the loudspeaker to create high-fidelity sound. It is investigated how the fluid dynamics of spinning, squeezing plates are affected by thermosolutal convection and a magnetic field dependent (MFD) viscosity. Standard differential equations are used to represent the equations of the modified form of Navier Stokes, Maxwell’s, and thermosolutal convection. The magnetic field, modified velocity field equations, and thermosolutal convection equations all yield suitable answers. Additionally computed and thoroughly detailed are the MHD torque and fluid pressure that are imparted to the top plate. To create a technique with quick and certain convergence, the resulting equations for uniform plates are solved using the Homotopy Analysis Method (HAM) with appropriate starting estimates and auxiliary parameters. The validity and reliability of the HAM outcomes are shown by comparing the HAM solutions with the BVP4c numerical solver programme. It has been found that a magnetic Reynolds number lowers the temperature of the fluid as well as the tangential and axial components of the velocity field. Additionally, when the fluid’s MFD viscosity rises, the axial and azimuthal components of the magnetic field behave in opposition to one another. This study has applications in the development of new aircraft take-off gear, magnetorheological airbags for automobiles, heating and cooling systems, bio-prosthetics, and biosensor systems.

Magneto-thermogravitational convection for hybrid nanofluid in a novel shaped enclosure

The proposed work exhibits a numerical simulation of steady thermogravitational convection of Cu–Al2O3(50%−50%) water hybrid magneto-nanofluid in a novel shaped enclosure regulated by magnetic field dependent (MFD) viscosity in presence of flush mounted variable heaters. Various cases (Case-I to Case-IV) have been considered depending on the location of the heaters on the bottom and left boundaries. Pertaining to this analysis, the streamfunction (ψ)- vorticity (ζ) form including the energy transport equation of coupled partial differential equations are evaluated with the help of an efficient higher order compact finite difference scheme. Results are exhibited in terms of streamlines, isotherms and Nusselt numbers to describe the transport phenomena obtained for different physical parametric values to this simulation. The influence of the physical parameters such as, Rayleigh number (104≤Ra≤106), Hartmann number (0≤Ha≤60), hybrid nanoparticles volume fraction (0≤ϕhnp≤0.04), orientation of magnetic field (00≤γ≤600) and magnetic number (0≤δ0≤1) on the hybrid nanofluid flow and energy transfer are analyzed. Obtained results indicate that the combinations of the heaters location and the shaped of the geometry have major impact on all the transport phenomena. Moreover, Cu–Al2O3 hybrid nanoparticles play an essential role to levitate the thermal transmission compared to other physical parameters. An addition of hybrid nanoparticles leads to an increase in the average Nusselt number up to 10.8% in Case-I, 12% in Case-II, 11.66% in Case-III and 11.65% in Case-IV. The novelty of the present work is to examine the rheological properties of hybrid nanoliquid in a novel shaped cavity subjected to magnetic field dependent viscosity (MFDV) along with flush mounted variable heaters.

Numerical study on the dispersion of hybrid nanoparticles complex rheological liquid media subjected to thermal transport using Carreau-Yasuda model

This study explores the impact of various factors on entropy generation (EG) in non-Newtonian rheological fluid characterized by the Carreau-Yasuda (CY) constitutive model. Methanol is taken as base fluid with shear rate-dependent viscosity. Two types of nanoparticles (NPs) GO and are considered to disperse in methanol. The flow of the mixture over a heated circular pipe is subjected to a radial magnetic field. Mathematical equations are formulated and solved numerically using the finite element method (FEM). The computed solutions are utilized to explore the impact of single-type (), two types of NP (GO and ), magnetic field, Joule heating, and shear rate dependent viscosity on the EG. It is noticed from calculations that in methanol with GO and generates less entropy relative to that generated by methanol with single type NPs (). However, monotonic behavior in the EG in both fluids (GO/methanol and GO–/methanol) versus curvature parameter is noted. Power law index in the constitutive model plays a remarkable role in controling the viscous region in the flow near the vicinity of the pipe.

Effect Of MFD Viscosity On Ferroconvection In A Fluid Saturated Porous Medium With Variable Gravity

<p>Convective instability of a horizontal ferromagnetic fluid saturated porous layer with magnetic field dependent (MFD) viscosity subjected to gravity field varying with distance in the layer is investigated. The fluid motion is described by the Brinkman model. The method of small perturbation is applied and the resulting eigenvalue problem is solved using the higher order Galerkin technique. The stationary instability is shown to be the preferred mode of instability and the resulting eigenvalue problem is solved by taking into account the realistic rigidrigid- isothermal boundary conditions. The study reveals that the effect of MFD viscosity is to delay the onset of ferroconvection and the stabilizing effect of MFD viscosity is reduced when the magnetic Rayleigh number is sufficiently large. In the presence of variable gravity, the effect of magnetic and non-magnetic parameters on ferroconvective instability is also discussed.</p>

Exploration of energy‐based volumetric heating on ferrothermal porous convection: Effects of MFD viscosity and boundary conditions

AbstractThe impact of energy‐based volumetric internal heating and magnetic field‐dependent (MFD) viscosity on the onset of ferrothermal porous convection for different types of boundary conditions is investigated. The lower and upper boundaries are considered to be either rigid or stress‐free. The lower boundary is insulating, while at the upper boundary a Robin type of thermal condition is applied. Besides this, a general type of boundary conditions is invoked on the magnetic potential. The stability eigenvalue problem is solved numerically using the Galerkin‐type of weighted residuals technique with the Rayleigh number, as the eigenvalue. The results obtained for different boundary combinations are found to be qualitatively similar though not quantitatively. The effect of Biot number, MFD viscosity, and porous parameters is to hinder, while the influence of internal heat source strength, magnetic number, and the nonlinearity of fluid magnetization is to advance the onset of convection. The rigid and conducting boundaries offer a more stabilizing influence on the onset when compared to stress‐free and insulating boundaries. The convection cells get contracted the most when the boundaries are rigid and also when the upper boundary is conducting. The results delineated under the limiting cases are found to be in good agreement with those available in the literature.

PENETRATIVE THERMO-GRAVITATIONAL AND SURFACE-TENSION DRIVEN CONVECTION IN A FERROFLUID LAYER THROUGH VOLUMETRIC INTERNAL HEATING WITH VARIABLE VISCOSITY

This work pertaining to analytical and numerical studies on FTC in a FF layer with impact of coupled buoyancy-gravitational and surface-tension forces through the strength of internal heat source on the system subjected to the magnetic field dependent (MFD) viscosity effect. The lower boundary is considered to be rigid at either conducting or insulating to temperature perturbations, while upper boundary free open to the atmosphere is flat and subject to a Robin-type of thermal boundary condition. The Rayleigh-Ritz method with Chebyshev polynomials of the second kind as trial functions is employed to extract the critical stability parameters numerically. The onset of FTC is delayed with an increase in MFD (  ) parameter and Biot number ( Bi ) but opposite is the case with an increase in Rayleigh number( M1 ), non-linearity of fluid magnetization ( M 3 ) and strength of internal heat source ( Ns ). Their effects are complementary in the sense that the critical Mac and Rmc decrease with an increase in Rt .

Effect of Throughflow on Marangoni Convection in Ferromagnetic Liquids with Variable Viscosity

The effect of surface tension and vertical throughflow in magnetic field and temperature sensitive liquid of Newtonian ferromagnetic type is examined. Combining shooting and Galerkin techniques the stationary critical eigenvalues are computed. On the ferroconvection onset, M3, non-buoyancy magnetic parameter and Pr (>1), Prandtl number have no influence. For upward or downward directions dual effect of destabilizing or stabilizing the system is observed in the presence of vertical throughflow. Throughflow effect studied through Pe, Peclet number delays ferroconvection onset and is observed to be independent to flow direction. M1, the magnetic buoyancy number, and V, the variable viscosity parameters have destabilizing influences on the system. Ferrofluids being fascinating materials are used as constant agents for magnetic resonance imaging (MRI). The great variety of magnetic fluids are tailored for technological, biological, medical and material science applications. Key words: Ferroconvection, throughflow, surface tension, temperature dependent viscosity, magnetic field dependent viscosity.

Numerical evaluation of the ferrofluid behaviour under the influence of three-dimensional non-uniform magnetic field

Ferrofluids have always been the centre of interest for a broad range of applications where the flow manipulation is achieved using different types of magnetic fields. In the present work, a Finite Volume Method based numerical study is performed to investigate the ferrofluid behaviour in the laminar flow regime using the complete set of Ferrohydrodynamics equations. Four distinct single layer finite solenoids of different Ls/Ds (length to diameter ratio) are considered to replicate a 3D (three-dimensional) non-uniform magnetic field, and a twofold validation is also reported to authenticate the generated field distributions. Moreover, a magnetic field dependent viscosity model is used to take into account the variation of ferrofluid viscosity in the presence of a non-uniform magnetic field. To accommodate the varying particle size distribution of ferrofluid, an effective relaxation time constant is used that can accurately predict the magnetization using Debye relaxation mechanism. The obtained flow characteristics are then further discussed and compared along with the case of stationary ferrofluid for all solenoid configurations. New insights about the flow structures are provided using the λ2 criteria of vortex identification technique and the critical point theory analysis. It is observed that each solenoid arrangement have a distinct magnetic field distribution which leads to the occurrence of unique vortex structures and fluid deformations. Also, different flow trajectories are noticed within the fluid domain owing to the peculiar distribution of Kelvin force density. Results from the present work have direct implications in all ferrofluid based momentum transport devices and can be effectively used to further improve our understanding about their performances.

Publisher's Note: “On the analysis of magnetohydrodynamics and magnetic field-dependent viscosity effects on thermogravitational convection of hybrid nanofluid in an enclosure with curved walls” [Phys. Fluids 33, 102010 (2021)

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On the analysis of magnetohydrodynamics and magnetic field-dependent viscosity effects on thermogravitational convection of hybrid nanofluid in an enclosure with curved walls

This work deals with the impact of magnetic field-dependent viscosity and magnetohydrodynamics on the natural convection heat transfer of Ag–MgO (50%–50%) water hybrid nanoliquid in a complicated enclosure. The considered cavity with concave or convex horizontal boundaries has been differentially heated and cooled by multiple heat sources and heat sinks. The governing equations (Navier–Stokes equations) constituting stream function (ψ)-vorticity (ζ) formulation with energy equation are solved by adopting a compact finite difference scheme. Meanwhile, the flow domain that is influenced by several factors including Hartmann number (0≤Ha≤60), hybrid nanoparticles volume fraction (0≤ϕhnp≤0.02), Rayleigh number (103≤Ra≤106), orientation angle of magnetic field (00≤γ≤900), magnetic number (0≤δ0≤1), different cases (Case-I to III), and internal heat generation or absorption (−2≤Q≤2) is analyzed generously. Experimentally based correlations for thermal conductivity and dynamic viscosity have been used throughout the study. The outcomes show that the geometric parameters can be used as an excellent controller of the thermal performance inside the wavy chamber.

A numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

PurposeThe effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.Design/methodology/approachThe thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained.FindingsThe conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number Ta is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number Ta leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.Originality/valueThis research paper is new and original.