Magnetic Reynolds Number Research Articles

Thermal and magnetic evolution of an Earth-like planet with a basal magma ocean

Earth's geodynamo has operated for over 3.5 billion years. The magnetic field is currently powered by thermocompositional convection in the outer core, which involves the release of light elements and latent heat as the inner core solidifies. However, since the inner core nucleated no more than 1.5 billion years ago, the early dynamo could not rely on these buoyancy sources. Given recent estimates of the thermal conductivity of the outer core, an alternative mechanism may be required to sustain the geodynamo prior to nucleation of the inner core. One possibility is a silicate dynamo operating in a long-lived basal magma ocean. Here, we investigate the structural, thermal, buoyancy, and magnetic evolution of an Earth-like terrestrial planet. Using modern equations of state and melting curves, we include a time-dependent parameterization of the compositional evolution of an iron-rich basal magma ocean. We combine an internal structure integration of the planet with energy budgets in a coupled core, basal magma ocean, and mantle system. We determine the thermocompositional convective stability of the core and the basal magma ocean, and assess their respective dynamo activity using entropy budgets and magnetic Reynolds numbers. Our conservative nominal model predicts a transient basal magma ocean dynamo followed by a core dynamo after 1 billion years. The model is sensitive to several parameters, including the initial temperature of the core-mantle boundary, the parameterization of mantle convection, the composition of the basal magma ocean, the radiogenic content of the planet, as well as convective velocity and magnetic scaling laws. We use the nominal model to constrain the range of basal magma ocean electrical conductivity and core thermal conductivity that sustain a dynamo. This highlights the importance of constraining the parameters and transport properties that influence planetary evolution using experiments and simulations conducted at pressure, temperature, and composition conditions found in planetary interior, in order to reduce model degeneracies.

Identifying the mixed and forced convection flow with transverse magnetic field

AbstractOptimal control of the steady, laminar, magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid is considered under the effect of the transverse magnetic field in a square duct. The viscous and Joule dissipations are included and the flow is driven by a constant pressure gradient. The triple nonlinear set of momentum, induction, and energy equations are solved in dimensionless form by using the mixed finite element method (FEM) with the implementation of Newton's method for nonlinearity with the discretize‐then‐linearize approach. Accordingly, FEM solutions are obtained for various values of the problem parameters to ensure the efficiency of the underlying scheme. This study aims to investigate the problem of controlling the steady flow by using the physically significant parameters of the problem as control variables in the case of a mixed convection flow. In this respect, classification of the type of convection, forced or free, is achieved by controlling the Grashof number (Gr). Besides, single and pairwise controls with Hartmann number (M), Prandtl number (Pr), and magnetic Reynolds number (Rm) are also used to regain the prescribed fluid behaviors and required magnetic field. Control simulations are conducted with the sequential‐least‐squares‐programming (SLSQP) algorithm in the optimization.

Numerical Simulation and Neural Network Model for Hydromagnetic Nanofluid Convection in a Porous Wavy Channel with Thermal Non-Equilibrium Model

Abstract The present study aims to analyze the nonfluid MHD convective heat transfer in a porous wavy channel with a local thermal non-equilibrium (LTNE) model. Such a model finds applications related to enhancement in thermal performance, increasing the heat transfer coefficient in the compact design of heat exchangers for the aerospace and automotive industries and elevation in the efficiency of the solar collector. A sinusoidal porous wavy LTNE channel containing nanofluid and subjected to the induced and applied magnetic fields is considered. A uniform magnetic field is applied orthogonal to the channel and the induced magnetic field effects are considered due to the large magnetic Reynolds number. The momentum, continuity, energy, and nanoparticle volume fraction equations constitute the coupled nonlinear system of differential equations and are solved using the Galerkin finite element method. The reliability of the technique is assessed by comparing the proposed procedure with the results from earlier sources. A detailed analysis is presented to determine the effects of different physical parameters arising in the system on temperature, nanoparticle concentration, and velocity profiles. As an illustration, the findings exhibit that increasing the modified diffusivity ratio increases the values of the nanoparticle volume fraction whereas, reducing the modified diffusivity ratio enhances the temperature distribution. A higher value of thermal Rayleigh number presents a significant involvement of buoyancy forces, potentially resulting in the development of convective currents. A higher Nield number indicates more effective heat transport from the solid surface to the nanofluid. Consequently, there is a minimal thermal difference between the solid surface and the bulk nanofluid. Effective heat transmission enhances the nanofluid ability to absorb heat and generates a more consistent dispersion of temperature inside the fluid. The performance of the designed algorithms of the artificial neural network, namely, the Levenberg – Marquardt algorithm, in the problem under consideration is evaluated and the methodology is found reasonably precise with the matching of order around 6 to 7 decimal places of accuracy.

Unsteady Two-Dimensional Drift of a Viscoelastic Fluid with Magnetic and Thermal Effects: A Perturbation Approach

This study explores the unsteady, two-dimensional flow of an electrically conductive, viscoelastic, and incompressible fluid past a uniformly moving, infinite, non-conducting vertical plate, in the presence of a uniform first-order chemical process involving mass and heat transfer. A uniform magnetic field is applied perpendicular to the flow, with the magnetic Reynolds number assumed small to neglect the induced magnetic field. The governing equations are solved using a regular perturbation method, yielding approximate solutions for concentration, velocity, temperature, and shear stress at the plate. Additionally, mass and heat transfer rates are determined, with the influence of viscoelasticity and other physical parameters emphasized. Where applicable, results are graphically represented.

Comparative study of magnetic field effect on fast plasma flow of heavy and light species investigated by spectroscopic measurement

To understand the effects of magnetic fields on the propagating plasma flows of heavy and light ion species, a laboratory-scale experiment was conducted using a pulsed-power discharge. The plasma drift velocity and electron temperature were estimated by time-of-flight and line-pair methods, respectively, using spectroscopic measurements. Ion current waveforms were measured using an ion collector. When a magnetic field was applied, the plasma drift velocity decreased and the electron temperature increased in both heavy and light plasmas. The magnetic Reynolds number, pressure balance between the plasma and magnetic field, and ion current waveforms show that heavy plasma has a high possibility of deforming the magnetic field and generating accelerated ions through interaction with the magnetic field.

Vorticity and magnetic dynamo from subsonic expansion waves. II. Dependence on the magnetic Prandtl number, forcing scale, and cooling time

The amplification of astrophysical magnetic fields takes place via dynamo instability in turbulent environments. Vorticity is usually present in any dynamo, but its role is not yet fully understood. This work is an extension of previous research on the effect of an irrotational subsonic forcing on a magnetized medium in the presence of rotation or a differential velocity profile. We aim to explore a wider parameter space in terms of Reynolds numbers, the magnetic Prandtl number, the forcing scale, and the cooling timescale in a Newtonian cooling. We studied the effect of imposing that either the acceleration or the velocity forcing function be curl-free and evaluated the terms responsible for the evolution vorticity. We used direct numerical simulations to solve the fully compressible, resistive magnetohydrodynamic equations with the Pencil Code. We studied both isothermal and non-isothermal regimes and addressed the relative importance of different vorticity source terms. We report no small-scale dynamo for the models that do not include shear. We find a hydro instability, followed by a magnetic one, when a shearing velocity profile is applied. The vorticity production is found to be numerical in the purely irrotational acceleration case. Non-isothermality, rotation, shear, and density-dependent forcing, when included, contribute to increasing the vorticity. As in our previous study, we find that turbulence driven by subsonic expansion waves can amplify the vorticity and magnetic field only in the presence of a background shearing profile. The presence of a cooling function makes the instability occur on a shorter timescale. We estimate critical Reynolds and magnetic Reynolds numbers of 40 and 20, respectively.

Magnetic field dragging in filamentary molecular clouds

Context. Maps of polarized dust emission of molecular clouds reveal the morphology of the magnetic field associated with star-forming regions. In particular, polarization maps of hub-filament systems show the distortion of magnetic field lines induced by gas flows onto and inside filaments. Aims. We aim to understand the relation between the curvature of magnetic field lines associated with filaments in hub-filament systems and the properties of the underlying gas flows. Methods. We consider steady-state models of gas with finite electrical resistivity flowing across a transverse magnetic field. We derive the relation between the bending of the field lines and the flow parameters represented by the Alfvén Mach number and the magnetic Reynolds number. Results. We find that, on the scale of the filaments, the relevant parameter for a gas of finite electrical resistivity is the magnetic Reynolds number, and we derive the relation between the deflection angle of the field from the initial direction (assumed perpendicular to the filament) and the value of the electrical resistivity, due to either Ohmic dissipation or ambipolar diffusion. Conclusions. Application of this model to specific observations of polarized dust emission in filamentary clouds shows that magnetic Reynolds numbers of a few tens are required to reproduce the data. Despite significant uncertainties in the observations (the flow speed, the geometry and orientation of the filament), and the idealization of the model, the specific cases considered show that ambipolar diffusion can provide the resistivity needed to maintain a steady state flow across magnetic fields of significant strength over realistic time scales.

A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.

New insights into MHD squeezing flows of reacting-radiating Maxwell nanofluids via Wakif's–Buongiorno point of view

AbstractThis work presents a computational investigation of a squeezing nanofluid flow under the influence of thermal radiation, magnetohydrodynamics (MHD), and chemical process in a constrained parallel-wall geometry. In this study, the non-Newtonian behavior of a rate-type (Maxwell) nanofluid is captured by rheological expressions that serve as the foundation for the flow formulation. This kind of thinking makes it possible to simulate the intricate nanofluid behavior that incorporates the elastic and viscous responses, which are useful in a variety of situations related to nanofluid dynamics, rheology, and materials science. Additionally, the transport equations are modeled properly using Wakif's–Buongiorno nanofluid model. The equations reflecting the dynamics of the nanofluid and heat-mass transport are developed based on admissible physical assumptions, such as the negligible viscous dissipation as well as the lower magnetic Reynolds number. After that, several similarity variables are introduced in these equations to get the dimensionless formulation form. Akbari–Ganji's method is used to carry out extensive computational simulations. Our results show that the increased squeezing parameters lead to larger horizontal and vertical velocities. On the other hand, the temperature showed a reverse relationship with the increasing squeezing parameters and exhibiting a cooling impact.

Improving the rheological behavior of magnetiz couple stress Buongiorno's nanofluid through resilient wavy channel with curvature effect: Nonlinear analysis

In biological systems, fluids with complex rheological behavior often encounter complex microenvironments. Couple stress fluids can be applied to model the flow of biological fluids in micro-vessels, capillaries, and other intricate structures. Couple stress fluids can be employed to model drug transport in microfluidic devices and capillaries, providing insights into the behavior of pharmaceuticals at small scales. Studying the couple stress fluids is crucial, particularly when considering the impact of particle viscosity in the existence of induced magnetic fields and nanoparticles that might enhance the characteristic motion. So, we studied the moderate and magnetic Reynold numbers and curvature effects of magnetized couple stress Buongiorno's nanofluid model through resilient wavy channel. The governing equations of this model are formed in non-dimensional form without any approximation, i.e., in the companionship of moderate Reynolds number and curvature effect, which aren't studied in this form. Using the Adomian decomposition approach, it is possible to obtain a solution of nonlinear system of partial differential equations analytically. The semi-analytical results are obtained and represented graphically for characteristic motion and bio-thermal properties for temperature and concentration, as well as magnetic features. Physically, by rising the magnetic Reynolds number, the magnetic permeability raises, so the ability of the couple stress fluid to form an internal magnetic field within itself with the impact of an applied magnetic field increases, which increases the magnetic force.

Finite element iterative algorithm based on Anderson acceleration technique for incompressible MHD equations

In this paper, an Anderson’s acceleration algorithm for the finite element Oseen iterative scheme of the steady incompressible magnetohydrodynamics (MHD) problem is designed and analyzed. The Anderson acceleration algorithm based on solving an optimization problem in each iteration receives great attention to accelerate linear and nonlinear iterations. We prove that the proposed algorithm has higher convergence rate than that of the Oseen iterative method for the steady incompressible MHD, and give the accelerating convergence theory under different acceleration depths m. Numerical experiments including the singular solution and benchmark problems are carried out to verify the correctness and effectiveness of the algorithm. The tests show the marked improvement in the high physical parameters (including the hydrodynamic and magnetic Reynolds numbers, and the coupling number) when the Oseen iteration fails to converge.

Effect of magnetic field on viscous flow through porous wavy channel using boundary element method

AbstractThe study aims to investigate the effect of uniform inclined magnetic field on two‐dimensional flow of a steady, viscous incompressible fluid at low Reynolds number through a porous wavy channel. We consider a channel having sinusoidal walls filled with a fully saturated porous medium. The porous regime is assumed to be homogenous and isotropic. The viscous flow through a porous regime is governed by Brinkman equation, where the viscous forces are dominant. This allows us to assume the no‐slip boundary conditions at the walls of the wavy channel. Boundary element method (BEM) based on non‐primitive variables namely, stream function‐vorticity variables is used to solve the Brinkman equation. Further, we consider a very small magnetic Reynolds number to eliminate the magnetic‐induced equation. We analyzed that an increase in Hartman number, porosity, and reduction in inclination angle of magnetic field, wave amplitude, and Darcy number led to a reduction in horizontal velocity, whereas an increase in Hartman number, porosity, wave amplitude, and decrease in Darcy number and angle of inclination of magnetic field led to an increase in vertical velocity. Moreover, the flow reversal phenomena occur in the vicinity of the crest regime of the porous wavy channel for high wave amplitude and low Hartman number. The proposed investigation has widespread applications, such as drug delivery systems to target the drug precisely, magneto‐hydrodynamic pumps to regulate the blood flow in artificial hearts to reduce the risk of blood clotting, and so forth.

Effects of a spanwise magnetic field on the exact coherent states in a channel flow

The primary objective of this study is to examine the effect of a uniformly constant spanwise magnetic field on exact coherent states and their structures in channel flow. Exact coherent states represent nonlinear solutions to the Navier–Stokes equations, bearing significant importance in the prediction and control of flow with and without magnetic field. Despite the recent extensive research which have reported the influences of magnetic fields with respect to fluid dynamics, the specific effect of a spanwise magnetic field on the exact coherent states remain ambiguous. To investigate the influence of magnetic field on exact coherent states in channel flow, our study encompasses Reynolds numbers ranging from 3000 to 10 000, with variations in the size of computational domains. High-precision direct numerical simulations, coupled with a Fourier–Chebyshev spatial pseudospectra discretization, are employed to solve the governing equations under the assumption of low magnetic Reynolds number. Starting from laminar flow, we utilize a bisection method on the amplitude of perturbations to track the exact coherent states in the channel. In a smaller computational domain 2π × 2.4 × 2, the spanwise magnetic field expedites the self-sustaining process of exact coherent structures, accelerating the transition from streamwise vortices to streamwise streaks. In a larger computational domain, the exact coherent states are bifurcated from relative periodic orbit solutions to traveling wave solutions. Furthermore, as the spanwise computational domain expands, localization coherent structures persist and steadily propagate downstream in the channel.

Contributions of Jupiter's Deep‐Reaching Surface Winds to Magnetic Field Structure and Secular Variation

AbstractNASA's Juno mission delivered gravity data of exceptional quality. They indicate that the zonal winds, which rule the dynamics of Jupiter's cloud deck, must slow down significantly beyond a depth of about 3,000 km. Since the underlying inversion is highly non‐unique additional constraints on the flow properties at depth are required. These could potentially be provided by the magnetic field and its Secular Variation (SV) over time. However, the role of these zonal winds in Jupiter's magnetic field dynamics is little understood. Here we use numerical simulations to explore the impact of the zonal winds on the dynamo field produced at depth. We find that the main effect is an attenuation of the non‐axisymmetric field, which can be quantified by a modified magnetic Reynolds number Rm that combines flow amplitude and electrical conductivity profile. Values below Rm = 3 are required to retain a pronounced non‐axisymmetric feature like the Great Blue Spot (GBS), which seems characteristic for Jupiter's magnetic field. This allows for winds reaching as deep as 3,400 km. A SV pattern similar to the observation can only be found in some of our models. Its amplitude reflects the degree of cancellation between advection and diffusion rather than the zonal wind velocity at any depth. It is therefore not straightforward to make inferences on the deep structure of cloud‐level winds based on Jupiter's SV.

Simulating small-scale dynamo action in cool main-sequence stars

Context. The origin of the ubiquitous small-scale magnetic field observed on the solar surface can be attributed to the presence of a small-scale dynamo (SSD) operating in the sub-surface layers of the Sun. It is expected that a similar process could self-sustain a considerable amount of magnetic energy also in the near-surface layers of cool main-sequence stars other than the Sun. Aims. In this paper the properties of the magnetic field resulting from SSD action operating in the near-surface layers of four cool main-sequence stars and its self-organization into magnetic flux concentrations are investigated numerically. Methods. Three-dimensional radiative magnetohydrodynamic simulations of SSD action in the near-surface layers of four cool main-sequence stars of spectral types K8V, K2V, G2V, and F5V are carried out with the CO5BOLD code. The simulations are set up to have approximately the same Reynolds and magnetic Reynolds numbers, and to disentangle the impact of the effective temperature and the surface gravity on the SSD action from numerical effects. Results. It is found that the SSD growth rates in SI units differ for the four stellar models; the highest and lowest growth rate is for the K2V and F5V model, respectively. This is due to the different turnover times in the four simulations. Even so, the SSD field strengths reached in the saturation phases are similar in all models, with the same amount of kinetic energy converted into magnetic energy. If the magnetic energy that is pumped out from the computational domain across the bottom boundary is partially replenished from outside of the computational domain, we find that the SSD action leads to a sufficient reduction in the convective velocities to reduce the convective horizontal length scales in the convection zone by 5–10%, vanishing towards the optical depth unity level. In this case, strong kilogauss magnetic flux concentrations emerge at the surface, leading to magnetic bright features, which are more numerous and conspicuous for the K2V and G2V models than for the K8V and F5V models. Their vertical magnetic field component on the surface of optical depth unity increases from 1 kG to 1.6 kG with decreasing effective temperature from F5V to K8V. However, more than 90% of the magnetic flux through any of these stellar surfaces has a field strength of less than 1 kG.

The detrimental effect of thermal exposure and thermophoresis on MHD flow with combined mass and heat transmission employing permeability

We look at the viscous free-convective transitional magnetohydrodynamic thermal and mass flow over a plate that is always perforated and standing upright through permeable media while thermal radiation, a thermal source, and a chemical reaction are all going on. There is additional consideration for the Soret effect. The plate receives a normal application of a transversely consistent magnetic field. The magnetic Reynolds number is considerably lower considering the axial applied magnetic field instead of the induced magnetic field. The models that control mass, heat, and fluid flow are turned into two-dimensional shapes, and the answers are found by running numerical simulations using the MATLAB algorithm bvp4c. In realistic circumstances, the outcomes have been illustrated graphically. Several fluid properties have been found to have an impact on velocity, temperature, and concentration profiles. There is noticeable increase in velocity along with the growth of the permeability parameter and Soret number. Other dimensionless parameters have a significant impact on the fluid velocity. Likewise, the temperature profile diminishes as the radiation parameter has increased. The concentration distribution falls as the heat source parameter expands. Also, the analysis is encompassed in tabular form for the shearing stress, Nusselt number, and Sherwood number. The combined knowledge of heat and mass moving through viscous flows can be used to make a wide range of mechanisms and processes. These include biological reactors, therapeutic delivery systems, methods of splitting, aerodynamic aircraft design, and modeling for sustainability. It also optimizes automotive radiators and engine efficiency, and it improves cooling systems.

Time dependent magnetic field effects on the MHD flow and heat transfer in a rectangular duct

AbstractWe consider the effect of time dependent magnetic field on the natural convection magnetohydrodynamic flow in a rectangular duct. The flow is two‐dimensional, unsteady, laminar and the fluid is electrically conducting and incompressible. The heat transfer is taken into account using the Boussinesq approximation and the buoyancy force is included in the momentum equations for the thermal coupling. The flow is considered at low magnetic Reynolds number setting and hence, the induced magnetic field is neglected. The proposed model in which the governing equations are given in terms of stream function, vorticity and temperature, is approximated by using a Chebyshev spectral collocation method for the spatial discretisation coupled with a backward difference scheme that is unconditionally stable for the temporal integration. The flow and heat transfer characteristic are analysed for several definitions of applied time varying magnetic field. Increase of the Hartmann number and the time variation of the applied magnetic field, changes the flow behaviour, especially at transient time levels and at the steady‐state.

The significance of radiative heat and mass transfer through a vertical sheet with chemical reaction: Designing by artificial approach Levenberg-Marquardt

The present study examines the impact of incorporating soft computing algorithms during neural network training on the evaluation and prediction performance of artificial neural networks. The research centers on a magneto hydrodynamic flow model (RHMT-VSCR) that depicts the movement of rotating fluid along a vertical sheet in a permeable medium. Furthermore, the model considers the impact of heat source-sink interactions, thermal radiation, and reactive species in conjunction with the effects of Hall current on the enhancement of energy and solute profiles. Because the induced magnetic field has a negligible magnetic Reynolds number, it is disregarded. A set of governing nonlinear PDEs is converted to a system of ODEs by applying an appropriate postulate of similarity variables in order to analyze the system. The multilayer perceptron network utilizes a supervised Levenberg–Marquardt Backpropagation algorithm (LMLA-BPNN) to ascertain the ideal quantity of neurons to be included in the hidden layer of artificial neural networks intended for modeling purposes. The bvp4c numerical approach is utilized to establish a continuous neural network mapping, which produces datasets that are utilized for the purposes of authentication, training, and testing. The range i.e., 10−2−10−8 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks. After acquiring knowledge of neural network mapping, it is applied to approximate solutions for a wide range of scenarios through the manipulation of physical constraints, including suction/injection quantities, magnetic parameter, and porosity parameter, which influence the characteristics of flow, energy, and concentration.To assess the precision of the proposed method, statistical graphs based on regression, mean squared error analysis graphs, and error histogram graphs are employed. The results of the research demonstrate that the Levenberg-Marquardt Backpropagation neural network mappings' derivation, convergence, authentication, and stability were effectively validated.

Effects of MHD and thermal radiation on non-Newtonian fluid with Cattaneo–Christov heat over a stretching flow surface

In this study, we are investigating the flow of an incompressible Williamson fluid using a Cattaneo–Christov heat flux model, with consideration for a magnetic Reynolds number that is not high. This fluid flows over a linearly stretched 2-D surface and is affected by a magnetic field, thermal radiation-diffusion, and heat generation. To model the Williamson flow, we apply a boundary layer approximation and develop the ordinary differential equations. The system of differential equations is transformed into a system of ordinary differential equations using a suitable transformation. We utilize the Iterative Runge–Kutta fourth-order scheme to numerically solve the boundary conditions associated with the nonlinear, dimensionless ordinary differential equations. Graphical representations of the results are employed to analyze the impact of physical properties on velocity, temperature, and concentration, with the numerical results presented in tabular form. Upon comparing our findings with previously published results, we have found them to be in good agreement. The velocity decreases as the Williamson fluid factor gradually increases. Williamson fluids are recognized for their shear thinning behavior, wherein viscosity decreases as the shear rate increases. However, higher parameter values can lead to increased fluid viscosity, potentially reducing the degree of shear thinning. This phenomenon results in a more uniform viscosity profile across varying shear rates, contributing to a reduced velocity distribution within the fluid.

Thermal analysis of mixed convective peristaltic pumping of nanofluids in the occurrence of an induced magnetic field and variable viscosity

The present study investigates the heat and flow characteristics of mixed convective peristaltic transport of nanofluids containing magnetite γAl2O3 nanomaterials dispersed in conventional liquids, namely, ethylene glycol (C2H6O2) and water (H2O). The research provides a comprehensive analysis, considering various factors such as induced magnetic field, variable viscosity, buoyancy force, viscous dissipation, and porous media effects. The mathematical model is formulated based on a set of governing equations encompassing continuity, temperature, momentum, and induction, which are subsequently transformed into dimensionless form through appropriate scaling. A numerical method is employed to solve the resulting nonlinear differential equations. Results indicate that the velocity profile exhibits substantially higher magnitudes in the case of the γAl2O3-C2H6O2 nanoliquid when compared to the γAl2O3-H2O nanoliquid. Increasing the magnetic Reynolds number leads to a higher magnitude of the axial-induced magnetic field. An observed reduction in system entropy is associated with an increase in the permeability parameter.