A couple stress fluid modeling on free convection oscillatory hydromagnetic flow in an inclined rotating channel

Abstract

This study focuses analytically on the oscillatory hydromagnetic flow of a viscous, incompressible, electrically-conducting, non-Newtonian fluid in an inclined, rotating channel with non-conducting walls, incorporating couple stress effects. The model is then non-dimensionalized with appropriate variables and shown to be controlled by the inverse Ekman number (K2 = 1/Ek), the hydromagnetic body force parameter (M), channel inclination (α), Grashof number (Gr), Prandtl number (Pr), oscillation frequency (ω) and time variable (ωT). Analytical solutions are derived using complex variables. Excellent agreement is obtained between both previous and present work. The influence of the governing parameters on the primary velocity, secondary velocity, temperature (θ), primary and secondary flow discharges per unit depth in the channel, and frictional shear stresses due to primary and secondary flow, is studied graphically and using tables. Applications of the study arise in the simulation of the manufacture of electrically-conducting polymeric liquids and hydromagnetic energy systems exploiting rheological working fluids.

Keywords

• Ekman number
• Couple stresses
• Oscillatory flow
• Magnetohydrodynamics
• Inclination
• Electro-conductive polymer processing