The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects are examined here. The empirical relations for nanoparticle materials associated with thermophysical properties are expressed as partial differential equations, which are then interpreted into ordinary differential expressions using appropriate variables. The initial shooting method converts the boundary condition into the initial condition with an appropriate guess and finally finds out an accurate numerical solution by using the Runge–Kutta method with numerical stability. Variations in nanoparticle volume fraction at the lower and upper walls of porous surfaces, as well as the heat transfer rate measurements, are computed using the controlling physical factors. The effects of the flow-related variables on the axial velocity, radial velocity, temperature, and concentration profile dispersion are also investigated. The Permeable Reynolds number is directly proportional to the regression parameter. The injection/suction phenomenon associated with the expanding/contracting cases, respectively, have been described with engineering parameters. The hybrid nanoparticle volume fraction (1–5%) has a significant effect on the thermal system and radial velocity.

The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of biological fluids flows with the effect of TiO₂ and Ag hybrid nanoparticles was developed. Further, we explain the engineering phenomena of biological fluids and the role of hybrid nanoparticles in the blood vessel system. The improvement of drug delivery systems by using low seepage Reynolds number was associated with expansion/contraction and was discussed in detail through the rectangular domain. Using similarity transformation, the governing equations were converted into non-linear ordinary differential equations, and the mathematical problem was solved by employing the numerical shooting method. Plots of momentum, temperature, skin friction coefficient, as well as the Nusselt number on different non-dimensionless parameters are displayed via lower/upper porous walls of the channel. It was analyzed that the walls of the channel showed different results on magnetized physical parameters. Values of thermophoresis and the Brownian motion flow of the heat transfer rate gradually increased on the upper wall and decreased on the lower wall of the channel. The important thing is that the hybrid nanoparticles, rather than nano, were more useful for improving thermal conductivity, heat transfer rate, and the nano-layer.

Currently, pagination clearly explains the increase in the thermophysical attributes of viscous hybrid nanofluid flow by varying morphological aspects of inducted triadic magnetic nanoparticles between two coaxially rotating disks. Copper metallic nanoparticles are inserted with three different types of metallic oxide nanoparticles: Al₂O₃, Ti₂O, and Fe₃O₄. Single-phase simulation has been designed for the triadic hybrid nanofluids flow. The achieved expressions are transmuted by the obliging transformation technique because of dimensionless ordinary differential equations (ODEs). Runge–Kutta in collaboration with shooting procedure are implemented to achieve the solution of ODEs. The consequences of pertinent variables on associated distributions and related quantities of physical interest are elaborated in detail. It is inferred from the analysis that Cu-Al₂O₃ metallic type hybrid nanofluids flow shows significant results as compared with the other hybrid nanoparticles. The injection phenomenon on hybrid nanofluids gives remarkable results regarding shear stress and heat flux with the induction of hybridized metallic nanoparticles. Shape and size factors have also been applied to physical quantities. The morphology of any hybrid nanoparticles is directly proportional to the thermal conductance of nanofluids. Peclet number has a significant effect on the temperature profile.

The current work investigated the mass and heat transfer of the MHD hybrid nanofluid flow subject to the impact of activation energy and cluster interfacial nanolayer. The heat transport processes related to the interfacial nanolayer between nanoparticles and base fluids enhanced the base fluid’s thermal conductivity. The tiny particles of $F{e}_3{O}_4$ and $PPy$ were considered due to the extraordinary thermal conductivity which is of remarkable significance in nanotechnology, electronic devices, and modern shaped heat exchangers. Using the similarity approach, the governing higher-order nonlinear coupled partial differential equation was reduced to a system of ordinary differential equations (ODEs). Fe₃O₄–PPy hybrid nanoparticles have a considerable influence on thermal performance, and when compared to non-interfacial nanolayer thermal conductivity, the interfacial nanolayer thermal conductivity model produced substantial findings. The increase in nanolayer thickness from level 1 to level 5 had a significant influence on thermal performance improvement. Further, the heat and mass transfer rate was enhanced with higher input values of interfacial nanolayer thickness.

In this article, we study the novel features of morphological effects for hybrid nanofluid flow subject to expanding/contracting geometry. The nanoparticles are incorporated due to their extraordinary thermal conductivity and innovative work for hybrid nanofluids, which are assembled of aluminum oxides, Al₂O₃ metallic oxides, and metallic copper Cu. Cu nanoparticles demonstrate very strong catalytic activity, while Al₂O₃ nanoparticles perform well as an electrical insulator. The governing partial differential equations of the elaborated model are transformed into a system of nonlinear ordinary differential equations with the use of similarity variables, and these equations are numerically solved through a shooting technique based on the Runge–Kutta method. We develop a hybrid correlation for thermophysical properties based on a single-phase approach. A favorable comparison between shape and size factors for metallic and metallic-oxide nanoparticles is discussed via tables and figures. Moreover, the effect of embedding flow factors on concentration, velocity, and temperature is shaped in line with parametric studies, such as the permeable Reynolds number, nanoparticle volume fractions, and expansion/contraction parameters. The fluid velocity, temperature, and concentration are demonstrated in the presence of hybrid nanoparticles and are discussed in detail, while physical parameters such as the shear stress, flow of heat, and mass transfer at the lower and upper disks are demonstrated in a table. The hybrid nanoparticles show significant results as compared to the nanofluids. If we increase the nanoparticle volume fraction, this increases the thermal performance for an injection/suction case as well. The above collaborative research provides a strong foundation in the field of biomedical equipment and for the development of nanotechnology-oriented computers.