The use of nanoparticles, has become increasingly utilized for medical applications and is of great interest as an approach to killing or reducing the activity of numerous microorganisms. The motivation of the present study is to scrutinize the impacts of magnetic field, radiation and chemical reaction on non-Newtonian Prandtl fluid containing gyrotactic microorganisms and nanoparticles. The governing nonlinear partial differential equations are decreased to nonlinear ordinary differential equations using appropriate similarity transformation. Our system of equations are solved numerically by using Rung-Kutta-Merson method with Newton iteration in a shooting and matching technique. The impacts of various parameters on velocity, temperature, nanoparticles concentration and density of motile microorganisms for suction (f w > 0), injection (f w < 0) and the case of impermeable plate surface (f w = 0) have been made.

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We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable.

In the present examination, we have talked about the impacts of heat absorption, chemical reaction, and wall properties on the peristaltic stream of micropolar nanofluid through a permeable medium. The key conditions of the movement are first regulated and after that streamlined under the suspicions of long wavelength and low Reynolds number. The careful arrangements have been determined for the velocity and the microrotation velocity, while the administering conditions of energy and nanoparticle conditions are solved analytically utilizing the homotopy perturbation technique. At last, graphical outcomes are talked about to represent the impacts of different physical parameters of the issue on these dispersions.

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The reason for this work is to assess the impact of the peristaltic flow of Jeffery nanofluid containing motile gyrotactic microorganisms. This problem can be considered a numerical depiction of the fluid move through an endoscope or catheter tube. Where the catheter is covered with a blend of anti-infection agents and nanoparticles to oppose the formation of vital membranes. The effects of non-linear thermal radiation, viscous dissipation, and magnetic field are taken into consideration. Both inward and the external cylinders have sinusoidal waves traveling along their walls since there is a coupling between the occlusion of the external cylinder and the radius ratio. For long wavelength and low Reynolds number, a numerical study by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching technique is performed. The effect of physical implanted parameters is represented through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms, shear stress, pressure rise, and pressure gradient.

Our study intends to examine the combined effects of radiation, magnetic field, and chemical reaction on the peristaltic flow of a non‐Newtonian fluid containing gyrotactic microorganisms and nanoparticles. The system of our equations is understood numerically by using the Rung‐Kutta‐Merson method with Newton iteration in a shooting and matching procedure. The effect of physical implanted parameters is represented and discussed through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms. From this discussion, we notice that the motile microorganisms profile is affected by the arising with the Brownian motion parameter and radiation parameter but the thermophoresis parameter, traditional Lewis number, and bioconvection of Peclet number are decremented the motile microorganisms profile.

In this paper, the effects of slip velocity and Hall currents on peristaltic motion of a non-Newtonian fluid with heat and mass transfer through a porous medium inside a symmetric horizontal channel with flexible walls are studied. The fluid obeys Maxwell model, the ohmic and viscous dissipations are taken into account. Some of partial differential equations describe the fluid motion with the appropriate boundary conditions are written in dimensionless form and simplified by using the approximations of long wavelength and low Reynolds number. These equations are solved analytically, and the stream function, pressure rise, temperature, and concentration distributions are obtained as functions of physical parameters of the problem. The effects of the parameters of the problem on these solutions are discussed numerically and illustrated graphically through a set of figures. It is found that the physical parameters played important roles in controling the obtained solutions.