Abstract
The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds’ model was utilized. The Runge–Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model.
Highlights
Diverse forms of flow paths appear when fluid flow is diverted by debris blocking streams
The multiphase flows have attracted the attention of scientists and engineers due to the frequently arising issues in industrial and mechanical problems
Couple stress fluid flow under the influence of heat between two parallel walls was examined by Farooq et al [1]
Summary
Diverse forms of flow paths appear when fluid flow is diverted by debris blocking streams. Ellahi et al [17] have considered two different viscosity models for their investigations of heated flow. They chose third-grade nanofluid flow through coaxial cylinders. Ellahi et al [20] studied the thermally charged couple stress fluid suspended with spherically homogenous metallic Hafnium particles for bi-phase flow along slippery walls. We aim to study the magnetized multiphase Couette-Poiseuille flow of non-Newtonian couple stress fluid suspended by metallic particles of Hafnium with temperature dependent viscosity. The viscosity of the base fluid is exponentially decreasing due to the heating effects at the lower wall of the channel which is at rest. The humble effort will speak about the mechanical and industrial multi-phase flows but would fill the gap yet not available in the existing literature on the topic under consideration
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