Computation of viscous channel flow in a rotating magnetohydrodynamic energy generator configuration with oscillatory effects

Beg, OA; Beg, TA; El Gendy, M; Kadir, A; Leonard, HJ

Abstract

With the desire for a green economy in the 21st century, considerable resurgence in renewable energy systems has been
witnessed. Among the most promising and least environmentally damaging systems is the MHD (magnetohydrodynamic)
energy generator. The MHD generator can be considered to be a fluid dynamo, which is similar to a mechanical dynamo in
which the motion of a metal conductor through a magnetic field creates a current in the conductor. However, in the MHD
generator the metal conductor is replaced by a conducting gaseous plasma or liquid e.g. seeded potassium, liquid metal,
ionized hydrogen, ionized air etc. Pioneered in the USA, Japan, France and Russia in the 1960s, interest in deploying large
scale MHD in the energy industry has rekindled in recent years. Motivated by providing a deeper insight into the intricate
fluid dynamics of such systems, in the present work we examine resonant hydromagnetic flow in a rotating MHD generator
using a viscous, unsteady model comprising parallel plates under the action of an inclined, uniform magnetic field, Bo. A
generalized angular velocity function is included allowing rotation to be simulated about different axes in the system. The
governing equations are normalized with appropriate transformations. Both closed-form and variational finite element
numerical solutions are obtained for the dimensionless primary (u) and secondary (v) velocities. The effects of rotation
parameter (K2
), Hartmann magnetohydrodynamic number squared (M2
), angular velocity colatitudes (*), angular
frequency (), pressure gradient parameter (R) and time (T) on the spatial velocity distributions (u,v) are studied in detail.
It is also shown that the inertial frequency,

, satisfies the condition
cos (16 cos * sin ) .
2
1 2
1
4 2 4 4  = T K  − M 
and
is valid for a slowly rotating system (weak Coriolis effect i.e. low K2 values) with reference to solar and terrestrial contexts.
The excitation frequency
( )
2
1
4 2 4 4
cos 16 cos * sin
2
1
  T K  −M 
therefore responds over the resonant level when
a forced oscillation is taken into account. A number of special cases are also described including the case where the plates
and channel rotate in unison with same constant angular velocity  (
o * = 0
), one dimensional MHD flow without
rotation (*=/2), resonant angular frequency case (T =/2), steady MHD flow in a rotating environment in the presence
of an inclined magnetic field (

= 0 in addition to
0 * =0
). The present study provides a solid foundation for
hydromagnetic flows under a forced oscillation in rotating frames of reference with colatitudes, *, and is relevant to
dynamics of MHD energy generators under different orientations.

Citation

Beg, O., Beg, T., El Gendy, M., Kadir, A., & Leonard, H. (2021, January). Computation of viscous channel flow in a rotating magnetohydrodynamic energy generator configuration with oscillatory effects. Presented at ICETP 2021: 15th International Conference on Energy and Thermal Physics, Rome, Italy

• Presentation Conference Type: Other
• Conference Name: ICETP 2021: 15th International Conference on Energy and Thermal Physics
• Conference Location: Rome, Italy
• Start Date: Jan 18, 2021
• End Date: Jan 19, 2021
• Acceptance Date: Apr 13, 2020
• Publication Date: Jan 19, 2021
• Deposit Date: Apr 18, 2020
• Publisher URL: https://waset.org/energy-and-thermal-physics-conference-in-january-2021-in-rome
• Additional Information: Event Type : Conference