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The purpose of this paper is to analyze heat and mass transport mechanism of unsteady MHD thin film flow of aluminium–copper/water hybrid nanofluid influenced by thermophoresis, Brownian motion and radiation.

The authors initially altered the time dependent set of mathematical equations into dimensionless form of equations by using apposite transmutations. These equations are further solved numerically by deploying Runge–Kutta method along with shooting technique.

Plots and tables for skin friction coefficient, Nusselt number, Sherwood number along with velocity, temperature and concentration profiles against pertinent non-dimensional parameters are revealed. The study imparts that aluminium–copper hybrid nanoparticles facilitate higher heat transfer rate compared to mono nanoparticles. It is noteworthy to disclose that an uplift in thermophoresis and Brownian parameter depreciates heat transfer rate, while concentration profiles boost with an increase in thermophoretic parameter.

The current study targets to investigate heat transfer characteristics of an unsteady thin film radiative flow of water-based aluminium and copper hybrid nanofluid. The high thermal and electrical conductivities, low density and corrosion resistant features of aluminium and copper with their wide range of industrial applications like power generation, telecommunication, automobile manufacturing, mordants in leather tanning, etc., have prompted us to instil these particles in the present study.

The present study has many practical implications in the industrial and manufacturing processes working on the phenomena like heat transfer, magnetohydrodynamics, thermal radiation, nanofluids, hybrid nanofluids with special reference to aluminium and copper particles.

To the best extent of the authors’ belief so far no attempt is made to inspect the flow, thermal and mass transfer of water-based hybridized aluminium and copper nanoparticles with Brownian motion and thermophoresis.

Natural convection heat transfer analysis can be completed using entropy generation analysis. This study aims to accomplish both the natural convection heat transfer and entropy generation analyses for a hexagonal cavity loaded with Cu-H2O nanoliquid subjected to an oriented magnetic field.

Control volume-based finite element method is applied to solve the non-dimensional forms of governing equations and then, the entropy generation number is computed.

The results portray that both the average Nusselt and entropy generation numbers boost with increasing aspect ratio for each value of the undulation number, while both of them decrease with increasing the undulation number for each amplitude parameter. There is a maximum value for the entropy generation number at a specified value of Hartmann number. Also, there is a minimum value for the entropy generation number at a specified value of angle of the magnetic field. When the volume fraction of nanoparticles grows, the average Nusselt number increases and the entropy generation number declines. The entropy generation number attains to a maximum value at Ha = 14 for each value of aspect ratio. The average Nusselt number ascends 2.9 per cent and entropy generation number decreases 1.3 per cent for Ha = 0 when ϕ increases from 0 to 4 per cent.

A hexagonal enclosure (complex geometry), which has many industrial applications, is chosen in this study. Not only the characteristics of heat transfer are investigated but also entropy generation analysis is performed in this study. The ecological coefficient of performance for enclosures is calculated, too.

This paper aims to study the impacts of viscous dissipation, thermal radiation and Joule heating on squeezing flow current and the heat transfer mechanism for a magnetohydrodynamic (MHD) nanofluid flow in parallel disks during a suction/blowing process.

First, the governing momentum/energy equations are transformed into a non-dimensional form and then the obtained equations are solved by modified Adomian decomposition method (ADM), known as Duan–Rach approach (DRA).

The effect of the radiation parameter, suction/blowing parameter, magnetic parameter, squeezing number and nanoparticles concentration on the heat transfer and flow field are investigated in the results. The results show that the fluid velocity increases with increasing suction parameter, while the temperature profile decreases with increasing suction parameter.

A complete analysis of the MHD fluid squeezed between two parallel disks by considering Joule heating, thermal radiation and adding different nanoparticles using the novel method called DRA is addressed.

The purpose of this research is to describe the importance of the Cattaneo–Christov theory of heat conduction in a triangular enclosure with a semi-circular heater. Analysis subjected to Fe₃O₄-H₂O nanofluid is reported. Viscosity dependent on magnetic field is taken into consideration to simulate ferrofluid viscosity. Besides, heat generation and shape factor of nanoparticles are also considered.

The well-known control volume finite element method is used for simulations.

The outcomes reveal that the magnetic field can be introduced to the system as a controlling element.

No such analysis exists in the literature.

The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method.

The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method.

The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity.

The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

The purpose of this paper is to focus on the influence of multiple slips on MHD Williamson nanofluid flow embedded in porous medium towards a linearly stretching sheet that has been investigated numerically. The whole analysis has been carried out considering the presence of nth-order chemical reaction between base fluid and nanoparticles.

A similarity transformation technique has been adopted to convert non-linear governing partial differential equations into ordinary ones and then they are solved by using both the RK-4 method and Laplace transform homotopy perturbation method. The consequences of multiple slip parameters on dimensionless velocity, temperature and concentration and heat and mass transfer rates have been demonstrated using tabular and graphical outline.

The investigation explores that the Nusselt number reduces for escalating behaviour of velocity slip and thermal slip parameter. Fluid’s temperature rises in the presence of generative reaction parameter.

A fine conformity of the current results has been achieved after comparing with previous literature studies. Considering destructive chemical reaction, reduced Nusselt number is found to decrease, but reverse consequence has been noticed in the case of generative chemical reaction. Mass transport diminishes when the order of chemical reaction amplifies for both destructive and generative reactions.

The purpose of this study is to simulate the natural convection of a heated square shape embedded in a circular enclosure filled with nanofluid using an incompressible smoothed particle hydrodynamics (ISPH) method.

In the ISPH method, the evaluated pressure was stabilized by using a modified source term in solving the pressure Poisson equation. The divergence of the velocity was corrected, and the dummy particles were used to treat the rigid boundary. Dummy wall particles were initially settled in outer layers of the circular enclosure for preventing particle penetration and reducing the error of truncated kernel. The circular enclosure was partially filled with a porous medium near to the outer region. The single-phase model was used for the nanofluid, and the Brinkman–Forchheimer-extended Darcy model was used for the porous medium. Dummy wall particles were initially settled in outer layers of circular enclosure for preventing particle penetration and reducing error from the truncated kernel on the boundary.

The length of the inner square shape plays an important role in enhancing the heat transfer and reducing the fluid flow inside a circular enclosure. The porous layer represents a resistance force for the fluid flow and heat transfer, and, consequently, the velocity field and temperature distributions are reduced at the outer region of the circular cylinder. Then, the radius of the inner square shape, Darcy parameter and radius of the porous layer were considered the main factors for controlling the fluid flow and heat transfer inside a circular enclosure. The average Nusselt number decreases as the inner square length, radius of the porous layer and solid volume fraction increase.

The stabilized ISPH method is corrected for simulating the natural convection from an inner hot square inside a nanofluid-filled circular enclosure saturated with a partial layer of a porous medium.

The aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media saturated with Cu–Al₂O₃/water hybrid nanofluid and heated at the left wavy wall. The thermophysical phenomena are explored thoroughly by varying the amplitude (λ) and undulation (n) of the wavy wall and the inclination of the enclosure (γ) along with other pertinent physical parameters. Darcy–Rayleigh number (Ra_m), Darcy number (Da), Hartmann number (Ha) and nanoparticle volumetric fraction (ϕ). The effect of all parameters has been analyzed and represented by using heatlines, isotherms, streamlines, average Nusselt number and local Nusselt number.

The finite volume method is used to work out the transport equations coupled with velocity, pressure and temperature subjected to non-uniform staggered grid structure after grid-sensitivity analysis by an indigenous computing code and the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The solution process is initiated following an iterative approach through the alternate direction implicit sweep technique and the tridiagonal matrix algorithm (TDMA) algorithm. The iterative process is continued until successive minimization of the residuals (<1e-8) for the governing equations.

This study reveals that the increase in the heating surface area does not always favor heat transfer. An increase in the undulation amplitude enhances the heat transfer; however, there is an optimum value of undulation of the wavy wall for this. The heat transfer enhancement because of the wall curvature is revealed at higher Ra_m, lower Da and Ha and lower volume fraction of nanoparticles. In general, this augmentation is optimum for four undulations of the wavy wall with an amplitude of λ = 0.3. The heat transfer enhancement can be more at the cavity inclination   γ = 45°.

The technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc.

This study is to address MHD thermo-fluid phenomena of Cu–Al₂O₃/water-based hybrid nanofluid flow through a non-Darcian porous wavy cavity at different inclinations. The amplitude and number of undulations of the wavy wall, permeability of the porous medium, magnetic field intensity, nanoparticle volumetric fraction and inclinations of the enclosure play a significant role in the heat transfer process. This analysis and the findings of this work can be useful for the design and control of similar thermal systems/devices.

Many researchers have examined the problem of buoyancy-induced free convection in a wavy-porous cavity packed with regular fluids or nanofluids. However, the effect of magnetic fields along with the amplitude (λ) at different undulations (n) of the heated wavy wall of an inclined enclosure is not attended so far to understand the transport mechanisms. Most often, the evolutions of the thermo-fluid phenomena in such complex geometries invoking different multiphysics are very intricate. Numerical implementations for simulations and subsequent post-processing of the results are also challenging.

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.

This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach.

The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B₀ has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid.

The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease.

The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.