Unsteady electromagnetohydrodynamic flow of couple stress fluid through a microchannel: A theoretical analysis

Abstract

In this work, we investigate the transient electromagnetohydrodynamic (EMHD) flow of non-Newtonian fluid in a narrow/micro-fluidic channel. We consider the couple stress fluid (CSF) model to characterize non-Newtonian behaviour. We present an analytical solution for electric potential and temporal EMHD flow velocity by applying the standard Laplace transform method using physically relevant boundary conditions. We demonstrate the excellent agreement between the present analytical solution for fluid flow with the CSF model and previously reported results for a Newtonian fluid. We analyse the transient flow velocity and volume flow rate for a wide range of flow governing parameters. We notice that the steady-state flow velocity magnitude is higher for magnetic parameter/ Hartmann number values than for the couple stress parameter values, which characterizes the flow’s viscous resistance. We demonstrate that the contribution of couple stresses in the fluid medium is prominent in the combined pressure, magnetic and electroosmotic force to increase the volume flow rate, which contrasts with the EMHD flow of Newtonian fluid. We observe that the critical Hartmann number attains a fixed value (about 1.3) for higher values of the couple stress parameter due to the transverse electric field effect. The present work hold the key towards explaining non-Newtonian behaviour impersonating bio-fluid transport in the narrow/micro-fluidic channel under the combined effect of electromagnetic force and pressure gradient. The results anticipated from the present attempt are useful to develop efficient electro-magneto-mechanical and micro-bio-fluidic devices.