In this paper, the steady electrically conducting hybrid nanofluid (CuO-Cu/blood) laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms is considered. Additionally, hybrid nanofluid flow over a horizontal porous stretching sheet along with an induced magnetic field and external magnetic field effects that can be used in biomedical fields, such as in drug delivery and the flow dynamics of the microcirculatory system. This investigation can also deliver a perfect view about the mass and heat transfer behavior of blood flow in a circulatory system and various hyperthermia treatments such as the treatment of cancer. The simple partial differential equations (PDEs) are converted into a series of dimensional ordinary differential equations (ODEs), which are determined using appropriate similarities variables (HAM). The influence of the suction or injection parameter, mixed convection, Prandtl number, buoyancy ratio parameter, permeability parameter, magnetic parameter, reciprocal magnetic prandtl number, bioconvection Rayleigh number, coupled stress parameter, thermophoretic parameter, Schmidt number, inertial parameter, heat source parameter, and Brownian motion parameter on the concentration, motile microorganisms, velocity, and temperature is outlined, and we study the physical importance of the present problem graphically.

The key purpose of this article is to discuss the magnetohydrodynamic mixed convection flow for a Maxwell nanofluid past a stretching and permeable sheet. Variable thermal conductivity and Dufour and Soret effects are also taken into consideration. The modeled equations are transformed into a set of non-linear ordinary differential equations by employing similar transformable variables. The renovated system of equations is interpreted by Homotopy Analysis Method (HAM). The results determined by HAM have been compared with numerical solutions, and a good agreement has been noticed in both solutions. The main outcomes of this investigation are that velocity slows down with augmentation in Maxwell and magnetic parameters, temperature increases with radiation and thermophoretic parameters and reduces with growing values of Prandtl number and Brownian motion parameters, and furthermore, the motile micro-organism is a dropping function of Peclect and bio-convection Lewis numbers and bio-convection concentration difference parameters.

In this research article, the investigation of the three-dimensional Casson nanofluid flow in two rotating parallel plates has been presented. The nanofluid has been considered in steady state. The rotating plates have been considered porous. The heat equation is considered to study the magnetic field, joule heating, and viscous dissipation impacts. The nonlinear ordinary system of equations has been solved analytically and numerically. For skin friction and Nusslt number, numerical results are tabulated. It is found that velocity declines for higher values of magnetic and porosity parameter while it is heightened through squeezing parameter. Temperature is an enhancing function for Eckert number and nanoparticles volume fraction. Entropy generation is augmented with radiation parameter, Prandtl, and Eckert numbers. The Casson, porosity, magnetic field, and rotation parameters were reduced while the squeezing and suction parameters increased the velocity profile along x-direction. The porosity parameter increased the Bejan number while the Eckert and Prandtl numbers decreased the Bejan number. Skin friction was enhanced with increasing the Casson, porosity, and magnetic parameters while it decreased with enhancing rotation and squeezing parameters. All these impacts have been shown via graphs. The influences by fluid flow parameters over skin friction and Nusselt number are accessible through tables.

In this research article, the unsteady nanofluid flow between two horizontal plates is discussed. The main focus of this study is on the explanation of the relative study of water-based nanofluids with four different types of nanoparticles. The nanoparticles selected for this specific research article are copper oxide $(\mathrm{CuO})$ , aluminum oxide $(\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)$ , copper $(\mathrm{Cu})$ , and silver $(\mathrm{Ag})$ . The upper plate is moving downward with time-dependent velocity while the lower plate is stretching horizontally. Also the lower plate is made up of porous medium. The stream in permeable region is characterized by Darcy–Forchheimer relation. Cattaneo–Christov heat flux model is used for heat transfer phenomena. Viscous dissipation effect is taken in account. Skin friction and Nusselt number are numerically calculated. Total entropy generation is also discussed for squeezing system. Transformation technique is applied to transform the model from partial differential equations to ordinary differential equations. Homotopy techniques are applied to solve the problem. The influence of important parameters on velocity, temperature, and entropy profiles have been shown graphically and discussed in detail.

In this article, MHD flow of silver/water nanofluid past a stretched cylinder under the impact of thermal radiation with chemical reaction and slip condition is studied. The impact of Soret and Dufour effect is also analyzed during this flow. The uniqueness of the given problem is enlarged with the insertion of variable magnetic field, free stream velocity, thermal slip condition, and nonlinear thermal radiation. The PDEs are converted to ODEs by using suitable similarity transformation. The nonlinear system of ODEs is solved by applying convergent homotopy analysis method (HAM). The velocity, temperature, and concentration profiles for the free stream and at the plate are discussed through graphs and numerical tables. It is found that velocity field reduces, while the temperature profile rises for the increasing values of magnetic parameter. It is examined that effects of curvature on frication factor are increasing. Furthermore, temperature profile increases for greater Brownian motion and thermophoresis parameters. Transfer of heat enhances decreasing the radius of the cylinder also with heat generation parameter. The skin friction can be reduced by enhancing free stream and wall stretching velocities ratio. Velocity profile of the flow can be controlled by enhancing velocity slip and magnetic field.

In the current article, the augmentation of heat transmission for non-Newtonian Casson nanoparticles is investigated with motile gyrotactic microorganisms, magnetohydrodynamic (MHD), and thermal radiation upon a stretched sheet. An extended Darcy-Forchheimer model along with convective boundary conditions is also applied to the flow system. To convert these coupled nonlinear fluid flow expressions into ordinary differential expression, the concept of similarity transformation is employed. The modified coupled nonlinear set of differential expression is solved analytically by employing the HAM technique. The mathematical program Mathematica is used to manage the complexities of computations. It is established in this study that the velocity distribution is reducing the function of the inertial, porosity, and magnetic parameters. Additionally, the motile density of microorganisms displays diminishing conduct for developing estimations of bioconvection Lewis and Peclet numbers. It is further established in this study that there is an augmentation in Nusselt number and skin friction coefficient with a corresponding increase in nonlinear radiation and magnetic parameters. In order to ensure the validity of the HAM solution, we have determined numerical solutions for modeled equations with the help of boundary conditions by using ND-Solve in Mathematica-10. It is established that there is pretty fine concurrence between both solutions that ensure the validity of our solution by HAM.