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The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al₂O₃/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here.

Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed.

Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid.

The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al₂O₃/water hybrid nanofluid.

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 analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.

The cavity inclination angle is fixed ω = 0 in case (I) and ω=π4 in case (II). The traditional fluid is water, and Fe3O4+MWCNT+Cu/H2O is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.

The average heat transfer rate is computed for four combinations of ternary nanofluids: Fe3O4(25%)+MWCNT(25%)+Cu(50%),Fe3O4(50%)+MWCNT(25%)+Cu(25%),Fe3O4(33.3%)+MWCNT(33.3%)+Cu(33.3%) and Fe3O4(25%)+MWCNT(50%)+Cu(25%) under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.

The purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.

The current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.

To the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective Fe3O4+MWCNT+Cu/H2O ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.

For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery.

Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field.

It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force.

The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

The purpose of this paper is to numerically analyze the stagnation point flow of Cu-Al2O3/water hybrid nanofluid with mixed convection past a flat plate and circular cylinder.

The similarity equations that reduced from the boundary layer and energy equations are solved using the bvp4c solver. The duality of solutions is observed within the specific range of the control parameters, namely, mixed convection parameter λ, curvature parameter γ and nanoparticles volumetric concentration ϕ1 for alumina, while for copper ϕ2. The stability analysis is also designed to justify the particular solutions’ stability. Additionally, the idea to obtain the solution for large value of λ and γ is also presented in this paper.

Two solutions exist in opposing and assisting flows up to a critical value λc where λc lies in the opposing region. An upsurge of the curvature parameter tends to extend the critical value (delay the separation process), whilst increase the heat transfer performance of the working fluid. Meanwhile, the application of hybrid Cu-Al2O3/water nanofluid also can decelerate the separation of laminar boundary layer flow and produce higher heat transfer rate than the Cu–water nanofluid and pure water.

The results are new and original. This study benefits to the other researchers, specifically in the observation of the fluid flow characteristics and heat transfer rate of the hybrid nanofluid. Also, this paper features with the mathematical formulation for the solution with large values of λ and γ.

This paper aims to examine the Cu-Al2O3/water hybrid nanofluid flow over a shrinking sheet in the presence of the magnetic field and dust particles.

The governing partial differential equations for the two-phase flow of the hybrid nanofluid and the dust particles are reduced to ordinary differential equations using a similarity transformation. Then, these equations are solved using bvp4c in MATLAB software. The bvp4c solver is a finite-difference code that implements the three-stage Lobatto IIIa formula. The numerical results are gained for several values of the physical parameters. The effects of these parameters on the flow and the thermal characteristics of the hybrid nanofluid and the dust particles are analyzed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

The outcome shows that the flow is unlikely to exist unless satisfactory suction strength is imposed on the shrinking sheet. Besides, the heat transfer rate on the shrinking sheet decreases with the increase of . However, the increase in and lead to enhance the heat transfer rate. Two solutions are found, where the domain of the solutions is expanded with the rising of, and. Consequently, the boundary layer separation on the surface is delayed in the presence of these parameters. Implementing the temporal stability analysis, it is found that only one of the solutions is stable as time evolves.

The dusty fluid problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the shrinking counterpart. Therefore, this study considers the problem of the dusty fluid flow over a shrinking sheet containing Cu-Al₂O₃/water hybrid nanofluid with the effect of the magnetic field. In fact, this is the first study to discover the dual solutions of the dusty hybrid nanofluid flow over a shrinking sheet. Also, further analysis shows that only one of the solutions is stable as time evolves.

This paper aims to investigate numerically the free convective heat transfer efficiency inside a rectotrapezoidal enclosure filled with Al₂O₃–Cu/water hybrid fluid. The bottom wall of the cavity is uniformly heated, the upper horizontal wall is insulated, and the remaining walls are considered cold. A new thermophysical relation determining the thermal conductivity of the hybrid nanofluid has been established, which produced results those match with experimental ones.

The governing partial differential equations are solved using the finite element method of Galerkin type. The simulated results in terms of streamlines, heat lines and isotherms are displayed for various values of the model parameters, which govern the flow.

The Nusselt number, friction factor and the thermal efficiency index are also determined for the pertinent parameters varying different ratios of the hybrid nanoparticles. The simulated results showed that thermal buoyancy significantly controls the heat transfer, friction factor and thermal efficiency index. The highest thermal efficiency is obtained for the lowest Rayleigh number.

This theoretical study is significantly relevant to the applications of the hybrid nanofluids electronic devices cooled by fans, manufacturing process, renewable energies, nuclear reactors, electronic cooling, lubrication, refrigeration, combustion, medicine, thermal storage, etc.

The results showed that nanoparticle loading intensified the rate of heat transfer and thermal efficiency index at the expense of the higher friction factor or higher pumping power. The results further show that the heat transmission in Al₂O₃–Cu/water hybrid nanofluid at a fixed value of intensified $\phi_{hnf}$ compared to the Al₂O₃/water nanofluid when an amount of higher conductivity nanoparticles (Cu) added to it. Besides, the rate of heat transfer in Cu/water nanofluid declines when the lower thermal conductivity Al₂O₃ nanoparticles are added to the mixture.

This study aims to investigate the flow and heat transfer of a hybrid nanofluid through an exponentially stretching/shrinking sheet along with mixed convection and Joule heating. The nanoparticles alumina (Al₂O₃) and copper (Cu) are suspended into a base fluid (water) to form a new kind of hybrid nanofluid (Al₂O₃-Cu/water). Also, the effects of constant mixed convection parameter and Joule heating are considered.

The governing partial differential equations are transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The transformed nonlinear ODEs are solves using the bvp4c solver available in MATLAB software. A comparison of the present results shows a good agreement with the published results.

Dual solutions for hybrid nanofluid flow obtained for a specific range of the stretching/shrinking parameter values. The values of the skin friction coefficient increases but the local Nusselt number decreases for the first solution with the increasing of the magnetic parameter. Enhancing copper volume fraction and Eckert number reduces the surface temperature, which intimates the decrement of heat transfer rate for the first and second solutions for the stretching/shrinking sheet. In detail, the first solution results show that when the Eckert number increases as 0.1, 0.4 and 0.7 at λ = 1.5, the temperature variations reduced to 10.686840, 10.671419 and 10.655996. While in the second solution, keeping the same parameters temperature variation reduced to 9.750777, 9.557349 and 9.364489, respectively. On the other hand, the results indicate that the skin friction coefficient increases with copper volume fraction. This study shows that the thermal boundary layer thickness rises due to the rise in the solid volume fraction. It is also observed that the magnetic parameter, copper volume fraction and Eckert number widen the range of the stretching/shrinking parameter for which the solution exists.

In practice, the investigation on the flow and heat transfer of a hybrid nanofluid past an exponentially stretching/shrinking sheet with mixed convection and Joule heating is crucial and useful. The problems related to hybrid nanofluid have numerous real-life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical and drug reduction.

In specific, this study focuses on increasing thermal conductivity using a hybrid nanofluid mathematical model. The novelty of this study is the use of natural mixed convection and Joule heating in a hybrid nanofluid. This paper can obtain dual solutions. The authors declare that this study is new, and there is no previous published work similar to the present study.

The purpose of this paper is to study the comparative analysis between three hybrid nanofluids flow past a permeable stretching surface in a porous medium with thermal radiation. Uniform magnetic field is applied together with heat source and sink. Three set of different hybrid nanofluids with water as a base fluid having suspension of Copper-Aluminum Oxide (Cu−Al2O3), Silver-Aluminum Oxide (Ag−Al2O3) and Copper-Silver (Cu−Ag) nanoparticles are considered. The Marangoni boundary condition is applied.

The governing model of the flow is solved by Runga–Kutta fourth-order method with shooting technique, using appropriate similarity transformations. Temperature and velocity field are explained by the figures for many flow pertinent parameters.

Almost same behavior is observed for all the parameters presented in this analysis for the three set of hybrid nanofluids. For increased mass transfer wall parameter ( fw) and Prandtl Number (Pr), heat transfer rate cuts down for all three sets of hybrid nanofluids, and reverse effect is seen for radiation parameter (R), and heat source/sink parameter ( δ).

The thermal conductivity of hybrid nanofluids is much larger than the conventional fluids; thus, heat transfer efficiency can be improved with these fluids and its implications can be seen in the fields of biomedical, microelectronics, thin-film stretching, lubrication, refrigeration, etc.

The current analysis is to optimize heat transfer of three different radiative hybrid nanofluids ( Cu−Al2O3/H2O, Ag−Al2O3/H2O and Cu−Ag/H2O) over stretching surface after applying heat source/sink with Marangoni convection. To the best of the authors’ knowledge, this work is new and never published before.

This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects.

Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results.

It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al₂O₃/H₂O) is greater than the nanofluid (Cu/H₂O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists.

In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc.

In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.