Oscillatory Hartmann Flow in a Rotating Channel with Magnetized Walls

What is it about?

Oscillatory Hartmann flow of a viscous, incompressible and electrically conducting fluid in a rotating channel withmagnetized walls in the presence of a uniform transverse magnetic field is studied. Exact solution of the governing equations isobtained in closed form. Mathematical formulation of the problem contains four pertinent flow parameters, namely, magnetic parameter αm, Ekman number E, frequency parameter ω and magnetic Prandtl number Pm. Solutions in the limit of vanishing magnetic Prandtl number Pm and small finite magnetic Prandtl number Pm are also obtained. Asymptotic behavior of these solutions is analyzed for large values of frequency parameter ω to gain some physical insight into the flow pattern. Expressions for the shear stress at the plates due to primary and secondary flows and mass flow rates in the primary and secondary flow directions are also derived. The numerical values of the fluid velocity and induced magnetic field are displayed graphically whereas that of shear stress at the plates due to primary and secondary flows and mass flow rates in the primary and secondary flow directions are presented in tabular form for various values of α2m and ω.

Featured Image