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: The photo catalytic nature of TiO_2 finds applications in medicinal field to kill cancer cells, bacteria and viruses under mild ultraviolet illumination and the antibacterial characteristic of Ag makes the composition Ag-TiO_2 applicable for various purposes. It can also be used in other engineering appliances and industries such as humidity sensor, coolants and in footwear industry. Hence, this study deals with the analysis of the effects of Magnetic field, thermal radiation and quartic autocatalysis of heterogeneous-homogeneous reaction in an electrically conducting Ag-TiO_2-H_2 O hybrid nanofluid. Furthermore, the gyrotactic microorganisms are used as active mixers to prevent agglomeration and sedimentation of TiO_2 that occurs due to its hydrophobic nature. The Mathematical model takes the form of partial differential equations with viscosity and thermal conductivity being the functions of volume fraction. These equations are converted to ordinary differential equations by using similarity transformation and are solved by RKF-45 method with the aid of shooting method. It is observed that the increase in the size of the needle enhances the overall performance of the hybrid nanofluid. Furthermore, the temperature of the hybrid nanofluid increases with the increase in volume fraction. It is observed that the friction produced by the Lorentz force increases the temperature of the nanofluid. It is further observed that the heterogeneous reaction parameter has more significant effect on the concentration of bulk fluid than the homogeneous reaction parameter.

In this article, the flow of ternary nanofluid is analysed past a stretching sheet subjected to Thomson and Troian slip condition along with the temperature jump. The ternary nanofluid is formed by suspending three different types of nanoparticles namely $$\text{TiO}_{2}, \text{Cu}$$ TiO 2 , Cu and $$\text{Ag}$$ Ag into water which acts as a base fluid and leads to the motion of nanoparticles. The high thermal conductivity and chemical stability of silver was the main cause for its suspension as the third nanoparticle into the hybrid nanofluid $$\text{Cu-TiO}_{2}/\text{H}_{2} \text{O}$$ Cu-TiO 2 / H 2 O . Thus, forming the ternary nanofluid $$\text{Ag-Cu-TiO}_{2}/\text{H}_{2} \text{O}$$ Ag-Cu-TiO 2 / H 2 O . The sheet is assumed to be vertically stretching where the gravitational force will have its impact in the form of free convection. Furthermore, the presence of radiation and heat source/sink is assumed so that the energy equation thus formed will be similar to most of the real life applications. The assumption mentioned here leads to the mathematical model framed using partial differential equations (PDE) which are further transformed to ordinary differential equations (ODE) using suitable similarity transformations. Thus, obtained system of equations is solved by incorporating the RKF-45 numerical technique. The results indicated that the increase in the suspension of silver nanoparticles enhanced the temperature and due to density, the velocity of the flow is reduced. The slip in the velocity decreased the flow speed while the temperature of the nanofluid was observed to be increasing.

The impact of chemical reaction and activation energy plays a vital role in the analysis of fluid dynamics and its thermal properties. The application of the flow of fluid is significantly considered in nuclear reactors, automobiles, manufacturing setups, electronic appliances etc. This study explores the impacts of activation energy and chemical reaction on the magnetohydrodynamic Darcy–Forchheimer squeezed Casson fluid flow through a porous material across the horizontal channel where the two parallel plates are assumed to be in motion. By using similarity variables, partial differential equations are converted to ordinary differential equations. Numerical method is applied using MATLAB to solve the problems and acquire the data for velocity field, thermal distribution, and concentration distribution. The graphs indicate that fluid velocity and temperature increases as the plates are brought closer. In addition, there was a correlation between a rise in the Hartmann number and a decrease in the fluid's velocity because of the existence of strong Lorentz forces. The temperature and the concentration of the liquid will increase due to the Brownian motion. When the Darcy–Forchheimer and activation energy parameters are both increased, the velocity and concentration decreases.

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