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This paper aims to analyse numerically the unsteady stagnation-point flow of Cu-Al₂O₃/H₂O hybrid nanofluid towards a radially shrinking Riga surface with thermal radiation.

The governing partial differential equations are transformed into a set of ordinary (similar) differential equations by applying appropriate transformations. The numerical computation of these equations including the stability analysis is conducted using the bvp4c solver.

Two solutions are possible within the allocated interval: shrinking parameter, unsteadiness decelerating parameter, electro-magneto-hydrodynamics (EMHD) parameter, nanoparticles volumetric concentration, radiation parameter and width parameter, whereas the stability analysis certifies that the first (upper branch) solution, which fulfills the boundary conditions is the physical/real solution. The EMHD parameter generated from the application of Riga plate enhances the skin friction coefficient as well as the heat transfer process. The width parameter d is also one of the factors in the deterioration of the skin friction coefficient and heat transfer rate. It is crucial to control the width parameter of the magnets and electrodes to obtain the desired outcome. The radiation parameter is not affecting the boundary layer separation because the critical values are unchanged. However, the addition of radiation and unsteadiness decelerating parameters boosts the thermal rate.

The results are novel and contribute to the discovery of the flow and thermal performance of the hybrid nanofluid subjected to a radially shrinking Riga plate. Besides, this work is beneficial to the other researchers and general audience from industries regarding the factors which contribute to the thermal enhancement of the working fluid.

Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied.

The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail.

It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior.

The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement.

The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

The Central Electricity Research Laboratories (CERL) at Leatherhead is the largest and longest established of the research centres of the Central Electricity Generating Board. Its staff numbers about seven hundred, three hundred of whom are professional scientists, and their programmes cover research into generation of electricity by coal‐ and oil‐fired power stations, and into transmission and distribution. CERL's activities include those as diverse as magneto‐hydrodynamics and the microbiology of soils; the dispersion of plumes from high chimneys and the basic physics of brittle fracture in metals. Three quarters of its work and almost all the corrosion research relates to generating electricity, although it has some of the best facilities in the world for studying the transmission of electricity at very high voltages, and the first corrosion problem it tackled was on steel cored aluminium conductors.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH).

The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically.

It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH.

This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids.

Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production.

Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration.

The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

This study aims to enhance natural convection heat transfer for a porous thermal cavity. Multi-frequency sinusoidal heating is applied at the bottom of a porous square cavity, considering top wall adiabatic and cooling through the sidewalls. The different frequencies, amplitudes and phase angles of sinusoidal heating are investigated to understand their major impacts on the heat transfer characteristics.

The finite volume method is used to solve the governing equations in a two-dimensional cavity, considering incompressible laminar flow, Boussinesq approximation and Brinkman–Forchheimer–Darcy model. The mean-temperature constraint is applied for enhancement analysis.

The multi-frequency heating can markedly enhance natural convection heat transfer even in the presence of porous medium (enhancement up to ∼74 per cent). Only the positive phase angle offers heat transfer enhancement consistently in all frequencies (studied).

The present research idea can usefully be extended to other multi-physical areas (nanofluids, magneto-hydrodynamics, etc.).

The findings are useful for devices working on natural convection.

The enhancement using multi-frequency heating is estimated under different parametric conditions. The effect of different frequencies of sinusoidal heating, along with the uniform heating, is collectively discussed from the fundamental point of view using the average and local Nusselt number, thermal and hydrodynamic boundary layers and heatlines.

This paper aims to examine the squeezing flow of hybrid nanofluid within the two parallel disks. The 50:50% water–ethylene glycol mixture is used as a base fluid to prepare Ag–Fe_3O_4 hybrid nanofluid. Entropy generation analysis is examined by using the second law of thermodynamics, and Darcy’s modal involves estimating the behavior of a porous medium. The influences of Viscous dissipation, Joule heating and thermal radiation in modeling are further exerted into concern.

For converting partial differential systems to ordinary systems, a transformation technique is used. For the validation part, the numerical solution is computed by embracing a fourth-order exactness program (bvp4c) and compared with the analytical solution added by the homotopy analysis method (HAM). Graphical decisions expose the values of miscellaneous-arising parameters on the velocity, temperature and local-Nusselt numbers.

Hybrid nanofluid gives significant enhancement in the rate of heat transfer compared with nanofluid. The outcomes indicate that the average Nusselt number and entropy generation are increasing functions of the magnetic field, porosity and Brinkman number. When the thermal radiation rises, the average Nusselt number diminishes and the entropy generation advances. Furthermore, combining silver and magnetite nanoparticles into the water–ethylene glycol base fluid significantly enhances entropy generation performance.

Entropy generation analysis of the magneto-hydrodynamics (MHD) fluid squeezed between two parallel disks by considering Joule heating, viscous dissipation and thermal radiation for different nanoparticles is addressed. Furthermore, an appropriate agreement is obtained in comparing the numerical results with previously published and analytical results.

The Purpose of this study to examine the magneto hydrodynamics (MHD) using the analytical and numerical tool. In recent years, MHD growing tremendously due to the presence of multidisciplinary application in solving the tedious problems in the viscous flow.

The flows between the parallel plates under the steady inclined magneto hydrodynamic force were studied under the presence of different hall current and pressure gradient. The system was designed with the Darcian porous medium subjected to the incompressible flow. To analyse the flow reactions through stationary parallel plates, the governing equations were used using the integral transformation.

The velocity of the flows depends on the Hall parameter. As the intensity of the magnetic field increases the velocity of the flow is affected significantly. On the other hand, the radiation parameters also affect the flow of any medium through the porous medium.

Implementation of the Laplace and Fourier transform increases the reliability of the obtained results and further decreases the uncertainty during the measurement of the velocity of the flow without any restraints.

From the evident results, it is clear that the proposed MHD model can be applied to several operations of the fluid dynamic models. Further, the application of this technique will decrease the uncertainty in the results compared to the conventional computational models and other finite element and difference approaches.

The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring shooting technique and analytically via a new modified analytical technique called improved generalized Adomian decomposition method (improved-GDM).

It is well established that the generalized decomposition method (GDM) (Yong-Chang et al., 2008), which uses a new kind of decomposition strategy for the nonlinear function, has proved its efficiency and superiority when compared to the standard ADM method. In this investigation, based on the idea of improved-ADM method developed by Lina and Song (Song and Wang, 2013), the authors proposed a new analytical algorithm of computation named improved-GDM. Thereafter, the proposed algorithm is tested by solving the nonlinear problem of the hydro-magnetic boundary layer flow over a flat plate.

The proposed improved generalized decomposition method (I-GDM) introduces a convergence-control parameter “ω’’ into the GDM, which accelerates the convergence of solution and reduces considerably the computation time. In fact, the key of this method is mainly based on the best selection of the convergence-control parameter ω.

The paper presents a new efficient algorithm of computation that can be considered as an alternative for solving the nonlinear initial boundary layer value problems. Obtained results show clearly the accuracy of the proposed method.

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.