The introduction of hybrid nanofluids is an important concept in various engineering and industrial applications. It is used prominently in various engineering applications, such as wider absorption range, low-pressure drop, generator cooling, nuclear system cooling, good thermal conductivity, heat exchangers, etc. In this article, the impact of variable magnetic field on the flow field of hybrid nano-fluid for the improvement of heat and mass transmission is investigated. The main objective of this study is to see the impact of hybrid nano-fluid (ferrous oxide water and carbon nanotubes) CNTs-$F{e}_3{O}_4$, $H_{2}O$ between two parallel plates with variable magnetic field. The governing momentum equation, energy equation, and the magnetic field equation have been reduced into a system of highly nonlinear ODEs by using similarity transformations. The parametric continuation method (PCM) has been utilized for the solution of the derived system of equations. For the validity of the model by PCM, the proposed model has also been solved via the shooting method. The numerical outcomes of the important flow properties such as velocity profile, temperature profile and variable magnetic field for the hybrid nanofluid are displayed quantitatively through various graphs and tables. It has been noticed that the increase in the volume friction of the nano-material significantly fluctuates the velocity profile near the channel wall due to an increase in the fluid density. In addition, single-wall nanotubes have a greater effect on temperature than multi-wall carbon nanotubes. Statistical analysis shows that the thermal flow rate of ($F{e}_3{O}_4$-SWCNTs-water) and ($F{e}_3{O}_4$-MWCNTs-water) rises from 1.6336 percent to 6.9519 percent, and 1.7614 percent to 7.4413 percent, respectively when the volume fraction of nanomaterial increases from 0.01 to 0.04. Furthermore, the body force accelerates near the wall of boundary layer because Lorentz force is small near the squeezing plate, as the current being almost parallel to the magnetic field.

In this article, the behavior of transient electroviscous fluid flow is investigated through squeezing plates containing hybrid nanoparticles. A hybrid nanofluid ${\mathrm{MoS}}_2+\mathrm{Au}$/${\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2-{\mathrm{H}}_2\mathrm{O}$ was formulated by dissolving the components of an inorganic substance such as molybdenum disulfide $\left({\mathrm{MoS}}_2\right)$ and gold (Au) in a base fluid of ethylene glycol/water. This hybrid non-liquid flow was modeled by various nonlinear mathematical fluid flow models and subsequently solved by numerical as well as analytical methods. For the numerical solution of nonlinear ODEs, a built-in function BVP4C was used in MATLAB, and the same problem was solved in MATHEMATICA by HAM. The result of the present problem related to the results obtained from the existing literature under certain conditions. The outcomes revealed that the concentration profiles were more sensitive to homogeneity diversity parameters. The simulation of the various physical parameters of the model indicated that the heat transfer through a mixture of hybrid nanofluids was greater than a simple nanofluid. In addition, the phenomenon of mixed convection was considered to improve the velocity of simple nanofluids and hybrid nanofluids, when both cases have low permeability. A rise in the volume fraction of the nanomaterials, $\Phi$, was associated with an increase in the heat transfer rate. It was observed that the heat transfer rate of the hybrid nanofluids ${\mathrm{MoS}}_2+{\mathrm{Au}/\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2-{\mathrm{H}}_2\mathrm{O}$ was higher than that of the single nanofluids ${\mathrm{MoS}}_2/{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2-{\mathrm{H}}_2\mathrm{O}$.

This article, investigates the behaviour of an ionized nanoliquid motion regarding heat transmission between two parallel discs. In the proposed model, the squeezing flow of Cu-water nanofluid with electrical potential force is analysed for studying the flow properties and an uniform magnetic field is applied to that fluid, by taking the surface of the bottom disc porous. We have also studied the effects of different nanomaterials on the transmission of heat through nanofluids. Furthermore, the influence of various physical parameters in the proposed model of nanofluids flow like volume fraction of nanomaterials, squeezing number, Hartmann number, Eckert number, and Prandtl number are analysed and discussed quantitatively through various tables and graphs. The system of nonlinear partial differential equations (PDE’s) has been used to formulate the proposed flow model and later converted to a set of nonlinear ODE’s by mean similarity transformation. Further, the reduced form of ODEs has been solved by Parametric Continuation Method (PCM), which is a stable numerical scheme. The outcomes obtained from the proposed model could also be used to analyse nanofluid flow in several fields, such as polymer processing, power transfer and hydraulic lifts.

The main purpose of the current article is to scrutinize the flow of hybrid nanoliquid (ferrous oxide water and carbon nanotubes) (CNTs + Fe${}_3$O${}_4$/H${}_2$O) in two parallel plates under variable magnetic fields with wall suction/injection. The flow is assumed to be laminar and steady. Under a changeable magnetic field, the flow of a hybrid nanofluid containing nanoparticles Fe${}_3$O${}_4$ and carbon nanotubes are investigated for mass and heat transmission enhancements. The governing equations of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential equations (PDEs) including momentum equation, energy equation, and the magnetic field equation. The proposed model was further reduced to nonlinear ordinary differential equations (ODEs) through similarity transformation. A rigorous numerical scheme in MATLAB known as the parametric continuation method (PCM) has been used for the solution of the reduced form of the proposed method. The numerical outcomes obtained from the solution of the model such as velocity profile, temperature profile, and variable magnetic field are displayed quantitatively by various graphs and tables. In addition, the impact of various emerging parameters of the hybrid nanofluid flow is analyzed regarding flow properties such as variable magnetic field, velocity profile, temperature profile, and nanomaterials volume fraction. The influence of skin friction and Nusselt number are also observed for the flow properties. These types of hybrid nanofluids (CNTs + Fe${}_3$O${}_4$/H${}_2$O) are frequently used in various medical applications. For the validity of the numerical scheme, the proposed model has been solved by another numerical scheme (BVP4C) in MATLAB.