Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel

•The two-layer boundary-layer flows of non-Newtonian nano-fluid are solved analytically.•A easy-to-use Mathematica package BVPh 2.0 is used to solve the corresponding coupled nonlinear ODEs.•The influence of physical parameters on the considered flows is investigated in details.

The heat and mass transfer of two-layer flows of non-Newtonian (third-grade) fluid in a vertical channel is investigated in details, when one layer of water is nano-fluid and the other is clear, with the viscous dissipation. In each layer, the boundary-layer flow is governed by coupled nonlinear ordinary differential equations (ODEs). The systems of coupled nonlinear ODEs are solved analytically by means of a Mathematica package BVPh 2.0 based on the homotopy analysis method (HAM), an analytic approximation method for highly nonlinear problems. The influence of the physical parameters is studied in detailed. It is found that the layer of nano-fluid has many different properties from that of clear fluid. This paper also illustrates the validity and power of the HAM-based Mathematica package BVPh 2.0 for some complicated boundary-layer flows.