Dual Solutions for MHD Jeffery–Hamel Nano-Fluid Flow in Non-parallel Walls Using Predictor Homotopy Analysis Method

Abstract

The main purpose of this study is to present dual solutions for the problem of magneto-hydrodynamic Jeffery–Hamel nano-fluid flow in non-parallel walls. To do so, we employ a new analytical technique, Predictor Homotopy Analysis Method (PHAM). This effective method is capable to calculate all branches of the multiple solutions simultaneously. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge-Kutta integration method illustrates the high accuracy for this technique. For the current problem, it is found that the multiple (dual) solutions exist for some values of governing parameters especially for the convergent channel cases (α = -1). The fluid in the non-parallel walls, divergent and convergent channels, is the drinking water containing different nanoparticles; Copper oxide (CuO), Copper (Cu) and Silver (Ag). The effects of nanoparticle volume fraction parameter (φ), Reynolds number (Re), magnetic parameter (Mn), and angle of the channel (α) as well as different types of nanoparticles on the flow characteristics are discussed.