The effect of the chemical reaction and radiation absorption on the unsteady free convective flow of an incompressible viscous fluid through porous medium past a semi-infinite vertical permeable moving plate is studied. The system is stressed by a uniform transverse magnetic field. The system equations are derived for the flow over a vertical plate and the resulting nonlinear coupled differential equations are solved numerically by finite difference technique. Also, the case of the flow over a horizontal plate was studied analytically by using the perturbation technique. A comparison between the case of vertical and horizontal flow was illustrated graphically to access the accuracy of our numerical calculations, and the results show an excellent agreement. The effects of various parameters on the velocity, temperature and concentration profiles are presented graphically and the physical aspects of the problem are highlighted and discussed.

In this article, the magnetohydrodynamic (MHD) peristaltic transport of a nanofluid through porous medium is investigated. The effects of the slip conditions together with the wall properties are taken into account. The traveling wave technique is used to obtain the stream function distribution. Also, the homotopy perturbation method (HPM) is utilized to present the other distributions like; temperature and concentration. Finally, several diagrams are plotted to discuss and interpret the effects of various physical parameters of the considered problem. One of the important results of this paper is the behavior of the nanoparticle concentration with different values of Reynolds number, slip parameter, elasticity parameters, thermophoresis parameter, Hartman number and the Brownian motion parameter.