Peristaltic flow of Herschel Bulkley nanofluid through a non-Darcy porous medium with heat transfer under slip condition

In this work, we focused on the peristaltic unsteady flow of non-Newtonian nanofluid with heat transfer through a non-uniform vertical duct. The flow obeys Herschel Bulkley model through a non-Darcy porous medium under the effects of mixed convection and thermal diffusion. Moreover, the effects of thermal radiation, heat generation, Ohmic dissipation, chemical reaction and uniform external magnetic field are investigated. The derived equations that describe the velocity, temperature and nanoparticles concentration are simplified under the assumptions of long wave length and low Reynolds number. These equations have been solved by using a numerical technique with the help of shooting method. The obtained solutions are functions of the physical parameters entering the problem. The effects of these parameters and the obtained solutions are explained and discussed through a set of graphs. It is found that the increment in Prandtl number or Thermophoresis parameter reduces the spread of the nanoparticles (concentration increased) within the fluid along with the thermal diffusivity through the fluid layers. Also the non-Darcy effect supports the inertial forces, and in order to maintain Reynolds number, the viscous forces are motivated and the axial velocity is damped. Moreover, for the validation of the current methodology, this model is reduced to power law model (no yield stress) and compared with the work of Eldabe et al. [16].