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The purpose of this study is to analyze the impact of inclined magnetohydrodynamics (MHD) and thermal radiation on the flow of a ternary micropolar nanofluid on a sheet that is expanding and contracting while applying mass transpiration and velocity slip conditions to the flow. The nanofluid, which is composed of Au, Ag and Cu nanoparticles dispersed in water as the base fluid, possesses critical properties for increasing the heat transfer rate and is frequently used in manufacturing and industrial establishments.

The set of governing nonlinear partial differential equations is transformed into a set of nonlinear ordinary differential equations. The outcome of this differential equation is solved and obtained the closed-form solution and energy equation in the form of hypergeometric functions.

The velocity, micro-rotation and temperature field are investigated versus a parametric variation. The physical domains of mass suction or injection and micropolar characteristics play an important role in specifying the presence, singleness and multiplanes of exact solutions. In addition, many nondimensional characteristics of the profiles of temperature, angular velocity and velocity profiles are graphically shown with substantial consequences. Furthermore, adding nanoparticles increases the heat transfer rate of the fluid used in manufacturing and industrial establishments. The current findings may be used for better oil recovery procedures, smart materials such as magnetorheological fluids, targeted medicine administration and increased heat transmission. Concerning environmental cleanup, nanomaterial fabrication and biomedical devices, demonstrate their potential influence in a variety of disciplines.

The originality of this paper is to analyze the impact of inclined MHD at an angle with the ternary nanofluid on a micropolar fluid over an expanding and contracting sheet with thermal radiation effect.

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

The purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the modified Buongiorno’s nanoliquid model.

On applying the appropriate similarity transformations, the governing partial differential equations were transformed into a set of ordinary differential equations. These equations have been then solved numerically using Runge–Kutta–Fehlberg method of fourth–fifth order programming in MAPLE software. Features of the velocity profiles, temperature distribution, reduced skin friction coefficient, reduced Nusselt number and microorganisms’ flux, for different values of the governing parameters were analyzed and discussed.

It was observed that as the needle thickness and solid volume fraction increase, the temperature rises, but the velocity field decreases. For a higher Peclet number, the motile microorganism curve increases, and for a higher Schmidt number, the concentration curve rises.

On applying the modified Buongiorno’s model, the present results are original and new for the study of HNF flow and heat transfer past a permeable thin needle.

This paper aims to present the analytical investigation on an unsteady magneto-convective rotation of an electrically conducting non-Newtonian Casson hybrid nanoliquid past a vertical porous plate. The effects of thermal radiation, heat source/sink and hydrodynamic slip phenomenon are also taken into account. Ethylene glycol (EG) is adopted as a base Casson fluid. The Casson fluid model is accounted for to describe the rheological characteristics of non-Newtonian fluid. EG with copper and alumina nanoparticles is envisaged as a non-Newtonian Casson hybrid nanoliquid. The copper-alumina-ethylene glycol hybrid nanoliquid is considered as the regenerative coolant.

The perturbation method is implemented to develop the analytical solution of the modeled equations. Acquired solutions are used to calculate the shear stresses and the rate of heat transfer in terms of amplitudes and phase angles. Numerical results are figured out and tabled to inspect the physical insights of various emerging parameters on the pertinent flow characteristics.

This exploration discloses that the velocity profiles are strongly diminished by the slip parameter. Centrifugal and Coriolis forces caused by the plate rotation are found to significantly change the entire flow regime. The supplementation of nanoparticles is to lessen the amplitude of the heat transfer rate. A comparative study is carried out to understand the improvement of heat transfer characteristics of Casson hybrid nanoliquid and Casson nanoliquid. However, the Casson hybrid nanoliquid exhibits a lower rate of heat transfer than the usual Casson nanoliquid.

This proposed model would be pertinent in oceanography, meteorology, atmospheric science, power engineering, power and propulsion generation, solar energy transformation, thermoelectric and sensing material processing, tumbler in polymer manufacturing, etc. Motivated by such practical implications, the proposed study has been unfolded.

The novelty of this paper is to examine the simultaneous effects of the magnetic field, Coriolis force, suction/injection, slip condition and thermal radiation on non-Newtonian Casson hybrid nanoliquid flow past an oscillating vertical plate subject to periodically heating in a rotating frame of reference. A numerical comparison is also made with the existing published results under some limiting cases and it is found that the results are in good agreement with them. An in-depth review of the literature and the author’s best understanding find that such aspects of the problem have so far remained unexplored.

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 paper is to design a parallel finite element (FE) algorithm based on fully overlapping domain decomposition for solving the nonstationary incompressible magnetohydrodynamics (MHD).

The fully discrete Euler implicit/explicit FE subproblems, which are defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain, are solved in parallel. In each subproblem, the linear term is treated by implicit scheme and the nonlinear term is solved by explicit one.

For the algorithm, the almost unconditional convergence with optimal orders is validated by numerical tests. Some interesting phenomena are presented.

The proposed algorithm is effective, easy to realize with low communication costs and preferred for solving the strong nonlinear MHD system.

The purpose of this study is research and development of the magnetohydrodynamics (MHD)-vortex technology.

The main instruments of research are mathematical modeling. For mathematical modeling used numerical and analytical both methods. For verification was made small copy of facility with forming of vortex in rotating magnetic field.

The design and manufacture of the industrial unit for melting small metal waste in a gas-fired smelt furnace has been completed.

Here shows new algorithm for engineering calculation of arc induction systems with take into account longitudinal edge effect and discrete distribution of current layers. Also shows verification of numerical results. Presented new MHD-technology for forming vortex in electromagnetic field.

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 analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper.

With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems.

The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer.

The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.