Computation of magnetized Couette–Poiseuille thermal flow of couple stress between two analogous plate with variable viscosity suspending the hafnium particles

Aims: In the presence of a magnetic field, the Couette–Poiseuille flow of a pair stress fluid between two parallel plates was thoroughly examined. The flow was caused by uniform motion of the top plate and an axial pressure gradient. The effect of Hafnium particles, both in spherical and homogeneous form, was investigated by heating the wall. For this purpose, Reynolds' model was employed. Methodology: The modeled equations are highly nonlinear partial differential equation which are transformed to convectional differential equation using the similarity transformation. The resulting non-linear system of equations was solved by recourse to the efficient bvph2 scheme along with homotopy analysis method (HAM). Novelty: The innovative fragment of the present study is to scrutinize the magnetized the Couette–Poiseuille nanofluid flow of a pair stress fluid between two parallel plates is thoroughly examined with variable viscosity, still not has been elaborated in the available works to date. Consequently, in the restrictive sense, the existing work is associated with available work reported by Makinde and Onyejekwe [39] and originated in exceptional agreement. Findings and conclutions: An inverse relation was found to exist between velocity and Hartman number. The reason behind this is that the increase in temperature enfeebles the viscous forces which, consequently, results in reduction of velocity. However, it was noticed that temperature profile is adversely affected by raising the viscosity parameters and consequently the velocity is enhanced. Future suggestion: It is possible to investigate diphase flows in various geometries using inertial particles suspended in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids, which might be one of the proposed model's future uses.