Unsteady Pulsatile Hydromagnetic Counter-Current Flows of Cu–Water and CuO–Water Nanofluids Through Two Elastic Coaxial Pipes with Porous Blocks

Abstract

In the present work, we study pulsatile magnetohydrodynamic mixed convection counter-current flows of Cu–Water and CuO–Water nanofluids through two elastic coaxial pipes with wall-mounted porous blocks. A two-phase model that takes the effects of Brownian motion and thermophoresis into consideration is used to describe the transfer of heat and the transport of nanoparticles within each nanofluid. The mixed finite element method with $$P_{2}-P_{1}$$ Taylor-Hood elements is employed in order to numerically solve the governing equations with the associated initial and boundary conditions. This numerical solution is used to investigate the effects of porous block thickness, Darcy number, ratio of the radii of the inner and outer channels, Hartmann number and Grashof number on heat transfer, fluid flow, nanoparticle concentration and pressure drop.