This analysis is interested in the dynamic flow of incompressible triple diffusive fluid flowing through a linear stretched surface. The current study simulates when Boussinesq approximation and MHD are significant. As for originality, a comparative study of all the results for opposing and assisting flow cases is provided. Lie-group transformation is utilized to determine symmetry depletions of partial differential equations. The transformed system of ordinary differential equations is solved using the Runge-Kutta shooting technique. The impacts of magnetic parameter, buoyancy ratio parameter of temperature and concentration, and Lewis number on velocity, temperature, and concentration are depicted through graphs. We observed that the magnetic field parameter decelerates in velocity distribution for both fluid flow cases. Additionally, the same phenomenon was noticed with the buoyancy ratio parameters on both salt concentration distributions. Finally, the influence of heat and mass transfer rates decreases for both fluid flow cases with an increase in Lewis number.

In the context of bioconvection, bacteria are swimming microorganisms. Actually, a microorganism’s species is related to a focused swimming cell in the convection model. Unsteady chemically reactive (Water–Copper ( $Cu$)–Ferrous Oxide ( $F{e}_3{O}_4$)) hybrid nanofluid dynamics between two stretchable rotating disks at varied Lorentz force and viscous dissipation are unknown when the suspension of gyrotactic micro-organisms is taken into account. The paper’s novelty is addressing this gap, which is to examine the impact of chemical reactions on the unsteady bioconvective hybrid nanofluid flow between two stretchable rotating disks with viscous dissipation and the magnetic field. The use of Von-Karman similarity transformations allows for the conversion of governing equations into nonlinear ordinary differential equations. Based on the combination of Runge–Kutta fourth order and shooting methods, the final equations are calculated. A major finding of this study is Reynolds number escalates both axial and radial velocities but decreases the tangential velocity. The temperature increases with the rise in both Eckert number and heat source parameters. The concentration decreases with the rise in Schmidt number and chemical reaction parameter.

Right now, numerous nanoparticles are available in literature amidst these Copper, Aluminium and their alloys are sole feature nanoparticles with high physical, thermal and chemical possessions. These are enormously utilized in aircraft parts, generating space crafts and production of rocket climbing frames etc. This paper describes the steady and two-dimensional magnetohydrodynamic boundary layer flow of a hybrid nanofluid past a moving slandering needle. Copper (Cu) and Alumina Alloy (AA7072) are used as hybrid nanoparticles by considering water, a base fluid. The fundamental partial differential equations are transfigured to a set of nonlinear ordinary differential equations, then numerically solved with the help of MATLAB solver (bvp4c). The profiles of velocity, temperature and physical variables like skin friction coefficient and the local Nusselt number are displayed through figures for various parameters. The results are explored with nanofluid (Water + AA7072, Water + Cu) and hybrid nanofluid (Water + Cu + AA7072). The highest heat transfer rate can perceive in the case of Copper nanoparticles than AA7072 and hybrid cases (Water + Cu + AA7072) whereas skin friction is more in the case of Water + AA7072.

This work aims to study the combined effects of concentration and thermal radiation on a steady flow of Jeffrey nanofluid under the Darcy-Forchheimer relation over a flat nonlinear stretching sheet of variable thickness. A varying magnetic field influences normal to the flow movement is considered to strengthen the Jeffery nanofluid conductivity. However, a little effect of the magnetic Reynolds number is assumed to eliminate the impact of the magnetic field range. The higher-order nonlinear partial differential equations (PDEs) and convective boundary conditions are transformed into nonlinear ordinary differential equations (ODEs) by applying corresponding transformations. Then the ODEs are numerically solved with Runge-Kutta method via shooting technique. This process is applied for convergent relations of nanoparticle temperature, concentration, and velocity distributions. The influence of different fluid parameters like thermophoresis, melting param-eter, Deborah number, chemical reaction parameter, Brownian motion parameter, inertia parameter and Darcy number on the flow profiles is explained through graphical analysis. Thermal radiation is emitted by accelerated charged particles, and the enhanced particle motion at higher temperatures causes a more significant discharge of radiation. Also, it was concluded that the heat generation parameter enhances the momentum boundary layer thickness and reduces the thermal and solutal boundary layer thickness over a Jeffrey nanofluid.