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The steady laminar quasi-3D fully developed magnetohydrodynamic (MHD) flow of a liquid metal in a curved annular channel is studied in order to determine the effect of the magnetic field on the velocity distribution. The paper aims to discuss this issue.

Due to the fluid motion under the effect of the applied transverse external magnetic field, an additional magnetic field and an electric current density are induced. A hybrid formulation is used for the induced electric current density, implementing for its axial component the Ohm’s law and for its transverse components the Ampere’s law. The suggested formulation (denominated h-formulation) is combined with the extended Continuity Vorticity Pressure numerical variational method for MHD flows.

Results are obtained for different values of curvature ratios and Hartmann numbers. It is proved that as the strength of the magnetic field increases, two side regions of velocity jets are formulated in the right and in the left half sides of the inner cylinder in a direction parallel to the external magnetic field. The magnitude of the axial velocity at each region is determined by the balance of the centrifugal and the electromagnetic forces. The results help to better understand the MHD flow in toroidal ducts.

The results aim to help to a better understanding of the MHD flow in curved ducts.

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally.

Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions.

This work was supported by the NSF of China (No. 11971152).

This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.

Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.

A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.

To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.

The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field.

The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials.

The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems.

In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda.

This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids.

This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems.

Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study.

The purpose of this study is to investigate the enhancement and suppression of heat transfer for hybrid nanofluids (Cu–Al2O3/water) in a square enclosure containing a thermal-conductive cylinder when the Lorentz force is applied to the hybrid nanofluids.

Since the inner conductive cylinder in present research has a complex geometry, an in-house meshless method, namely, the local radial basis function (LRBF) method, is applied to solve the 2 dimensional (2D) incompressible Navier–Stokes equation in the fluid domain and Fourier heat conduction equation in solid domain. The solid–fluid interface remains the physical continuity of temperature and heat flux. Only the Lorentz force is considered for the presence of the magnetic field. The conjugate natural convection is assumed to be steady, thus only fully developed heat exchange from the nanofluids to solid or vice versa is comprehensively investigated.

It can be concluded that Lorentz force plays a more significant role than hybrid nanofluids in enhancing/suppressing heat transfer when the orientation of magnetic field is the same to the x direction. The thermal conductivity ratio can dramatically change the isotherms and streamlines as well as the mean value of the Nusselt number, resulting in totally different heat transfer phenomena. The included angle of magnetic field also has a significant effect on the heat transfer rate when it changes from horizontal to vertical.

The constant thermo-physical properties of incompressible fluid and the 2D steady flow are considered in this study.

The conjugate MHD natural convection of hybrid nanofluids is numerically investigated by an in-house meshless LRBF method. The enhancement and suppression of heat transfer under the combined influence of the volume fraction of nanoparticles, Hartmann number and the thermal conductivity ratio are comprehensively investigated.

The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.

The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem.

The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations.

The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Numerical method is applied to find the results.

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

This paper aims to demonstrate the impact of interstellar (IS) magnetic field on stellar shocks existence, shape and size in the stellar wind (SW) vs interstellar medium (ISM) numerical models.

Comparison of hydrodynamics (HD) and magnetohydrodynamic (MHD) models results with or without ISM magnetic field, its intensity and ISM parameters.

ISM magnetic field facilitates formation and stabilises bow shocks around all astrophysical objects. ISM magnetic field may also be one of the reasons for a bow shock existence around the Sun.

ISM magnetic field should be implemented in MHD and future kinetic numerical models of the SW interaction with ISM plasma.

This paper presents the results of HD and MHD models of bow shocks and the importance of ISM magnetic field implementation, according to astronomical bow shock observations. The study also presents a review of the most important papers showing the numerical results of bow shock formation.