Nonlinear Heat Transfer in a Two-Layer Flow With Nanofluids by OHAM

The problem of fully developed steady, laminar, incompressible flow in a vertical channel is studied analytically, one region is filled with water based copper nanofluid and the other region is filled with clear viscous fluid. The resulting coupled nonlinear ordinary differential equations (ODEs) are solved by optimal homotopy analysis method (OHAM). The convergence of our results is discussed by the so-called total average squared residual error. Analytical results are presented for different values of the physical parameters, such as the mixed convection parameters, the Brownian motion parameter, and thermophoresis parameter. Reversed flow is observed for sufficiently high buoyancy (mixed convection parameter). Further we investigate the effects of the Brownian motion parameter and thermophoresis parameter on the fluid flow and heat transfer at the interface of the two regions.