In this paper, the peristaltic motion of nano-coupled stress fluid through non-Darcy porous medium is investigated, and the heat transfer is taken into account. The system is stressed by an external magnetic field. The Ohmic and viscous couple stress dissipations, heat generation and chemical reaction are considered. This motion is modulated mathematically by a system of non-linear partial differential equations, which describe the fluid velocity, temperature and nanoparticles’ concentration. These equations are transformed to non-dimensional form with the associated appropriate boundary conditions. The homotopy perturbation method is used to find the solutions of these equations as a function of the physical parameters of the problem. The effects of the parameters on the obtained solutions are discussed numerically and illustrated graphically. It is found that these parameters play an important role to control the solutions. Significant outcomes from graphical elucidation envisage that the inclusion of more magnetic field strength increases the resistance of the fluid motion. Intensification of the couple stress parameter attenuates the temperature values, while it increases with increasing thermophoresis parameter.

The magnetohydrodynamic stability criterion of self-gravitating streaming fluid cylinder under the combined effect of self-gravitating, magnetic, and capillary forces has been derived. The results are discussed analytically and some data are verified numerically for different parameters of the problem. The magnetic and capillary forces are stabilizing, but the streaming is destabilizing while the self-gravitating is stabilizing or destabilizing according to restrictions. The stable and unstable domains are identified and, moreover, the influences of the magnetic and capillary forces on the self-gravitating instability of the model have been examined. Including the magnetic force together with self-gravitating force improves the instability of the model. However, the self-gravitating instability will never be suppressed whatever the effects of the MHD force stabilizing effects are.