The Analytical Improvement of q-Homotopy Analysis Method for Magneto-hydrodynamic (MHD) Jeffrey Hamel Nanofluid Flow

Abstract

The present study analyzes the velocity distribution for magneto-hydrodynamic (MHD) Jeffrey Hamel nanofluid with nanoparticles between two non-parallel planar walls divergent and convergent channels the governing equations for this problem are reduced to an ordinary differential equation. This is demonstrated through the use of a new analytical method called q-homotopy analysis (q-HAM). This new technique is based on combining the q-HAM method with the Laplace transform (LT) and the EL-Zaki transform (ZT) in the presence of convolution theory in this research. The results proved that the improved solutions obtained from this problem were proven to be highly accurate by comparing them using Bvp4c, a Maple built-in function. As wall as the impact of emerging parameters such as Reynolds number, Hartmann number and open angle is discussed for three material Al₂O₃, TiO₂ and Cu. The results show that the increment in velocity distribution occurs through growing Hartmann number for both channels, While the opposite of the case occurs, which shows a reduce in the velocity distribution with a rise in the Reynolds number.