Modelling and analysis of the unsteady flow and heat transfer of immiscible micropolar and Newtonian fluids through a pipe of circular cross section

Abstract

This study deals with the unsteady flow and heat transfer of micropolar and Newtonian fluids, flowing immiscibly through a circular pipe. The micropolar and Newtonian fluids occupy core and peripheral regions, respectively. Initially, the pipe and fluids in both regions are at rest; after an instant of time, a constant pressure gradient is applied to generate the flow. The equations governing the flow are time dependent, coupled and nonlinear. The solutions for velocity, microrotation and temperature are acquired numerically employing Crank–Nicolson finite difference approach. Volume flow rate is also obtained numerically and presented in tabular form. At fluid–fluid interface, continuity of velocities, shear stresses, temperatures and heat fluxes are considered. The results for velocity, microrotation and temperature are displayed graphically. It is seen that the fluid velocities, microrotation and temperatures are increasing with time and attain a steady state after a particular time level. The micropolarity parameter has a decreasing effect on the fluid velocities and temperatures.