Thermally charged MHD bi-phase flow coatings with non-Newtonian nanofluid and Hafnium particles along slippery walls

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge-Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.