The effect of the induced magnetic field on the motion of Eyring-Powell nanofluid Al2O3, containing gyrotactic microorganisms through the boundary-layer is investigated. The viscoelastic dissipation is taken into consideration. The system is stressed by an external magnetic field. The continuity, momentum, induced magnetic field, temperature, concentration, and microorganisms equations that describe our problem are written in the form of 2-D non-linear differential equations. The system of non-linear PDE is transformed into ODE using appropriate similarity transformations with suitable boundary conditions and solved numerically by applying the NDSolve command in the MATHEMATICA program. The obtained numerical results for velocity, induced magnetic field, temperature, the nanoparticles concentration, and microorganisms are discussed and presented graphically through some figures. The physical parameters of the problem play an important role in the control of the obtained solutions. Moreover, it is obvious that as Grashof numbe increases, both the velocity, f ?, and the induced magnetic field, h?, increase, while, the reciprocal magnetic Prandtl number, A, works on decreasing both f ? and h?. As Eckert number increases the temperature increases, while it decreases as the velocity ratio B increases.

In this work we investigated the solution of the peristaltic motion of Bingham plastic nanofluid through a vertical symmetric channel. The system is stressed by an external strong magnetic field to produce a hall currents. Moreover, we involved effects of Joule heating, radiation, chemical reaction and couple stresses. Further, we considered Soret and Dufour effects. This phenomenon is represented mathematically by a system of non-linear equations which describe the problem. We used the approximation of low Reynolds number and long-wavelength approximation to simplify the governing equations. Then, we used Homotopy perturbation method (HPM) to solve the equations. We sketched a graph for the influence of various parameters on velocity, temperature and nanoparticles concentration profiles and then discussed them physically. Finding revealed that an increase of Bingham number and the regularization parameter of Bingham fluid decreases the velocity and increases the temperature, but radiation parameter has an opposite relative to them. Also, we found that increasing of chemical reaction parameter reduces the nanoparticles concentration, whereas the reverse is the case when the reaction order is increased.

The current analytical study is concerned with studying the impact of Cattaneo-Christov heat flux of an incompressible flow which obeys Carreau nanofluid inside a symmetric channel in the existence of the porous medium. The impacts of couple stress, heat generation absorption, joule heating, couple stress viscous dissipation with Soret as well as Dufour numbers are all presumed. Long wavelength and law Reynold’s number approximations are utilized for solving the governing system of equations. Furthermore, the traditional perturbation method together with the homotopy perturbation technique (HPM) are applied to obtain the resultant solutions of these equations. The different physical parameters on velocity, temperature and nanoparticles concentration distributions are illustrated through a set of graphs. It is found that the elevate in the slip velocity parameter dwindle the velocity. Meanwhile, the rise in the value of thermal relaxation time parameter led to decay the temperature of the fluid. Over and above, enhancing the nano Biot number value caused an enrichment in the concentration of nanofluid.

The theme of this study is to investigate the influence of the chemical reaction and activation energy on MHD peristaltic flow of Jeffery nanofluids in an inclined symmetric channel through a porous medium. Joule heating, radiation, viscous dissipation, heat generation/absorption, activation energy, and thermal diffusion and diffusion thermo effects are involved. The long wavelength and low Reynolds number approximations are used to simplify the non-linear equations that govern the flow. Then, the simplified equations are solved by using the homotopy perturbation method (HPM). We have depicted the velocity, temperature, solute concentration, and nanoparticles volume friction graphically. Physical explanations for the results are provided. The influence of interest parameters on entropy generation is also observed. Numerical results for the heat transfer coefficient, Nusselt number, and Sherwood number are presented. The results revealed that an increase in the value of the ratio of relaxation to retardation times of Jeffery nanofluid enhances the velocity distribution, while a reduction in the solute concentration distribution occurs by increasing the activation energy parameter and the temperature difference parameter . We also discovered that an increase of the chemical reaction parameter increases the temperature profile and decreases the velocity and solute concentration profiles. Furthermore, the velocity becomes lower along the normal axis y and ends up with the minimum value near the upper wall of the channel. Also, the maximum and minimum values of the velocity increase with an increase of the second order slip parameter , while they decrease as Darcy number increases