MHD boundary layer flow of ternary hybrid nano-fluid (𝐓𝐢𝐨𝟐 - 𝐒𝐢𝐨𝟐, - 𝐀𝐥𝟐𝐨𝟑⁄𝐇𝟐𝐎 - 𝐂𝟐𝐇𝟔𝐎𝟐) A Numerical and analytical Investigations

Abstract In the present work, we explored the magneto hydrodynamic (MHD) flow in the pressure gradient across a flat plate. The effects of the magnetic field and the addition of ternary hybrid nano-fluid (i.e. a mixture of three nano particles for example ( \({Tio}_{2}, {Sio}_{2, } and {Al}_{2}{o}_{3}\)) in mixture base fluid ( \({H}_{2}O-{C}_{2}{H}_{6}{O}_{2}\) ) are also considered in this study. Basic partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations using similarity transformation. Then, this equation was treated numerically by the 4th–5th order of the Runge-Kutta-Fehlberg method with shooting approaches and analytically by a new method called the Daftardar-Jafari Method (DJM). The effect of various physical parameters namely the magnetic field (M), the volumetric fraction of the nanoparticles, the pressure gradient \(\left(m\right)\) on the velocity distribution, the type of the nanoparticles and the coefficient of friction \({\text{C}}_{\text{f}}\), of the theoretical results obtained confirm that the ternary hybrid nano-fluid has a better dynamic property than the hybrid nano-fluid, as well as the efficiency of the adopted DJM technique.