Simulation of Biomagnetic Fluid Flow
in a Lid-Driven Cavity Under Steady
Localized Magnetic Field
Sumanta Banerjee and Ranjan Ganguly
Abstract The simulation study of steady, laminar, incompressible, and isothermal
biomagnetic fluid flow within a lid-driven cavity is presented, under the influence of
a time-independent localized external magnetic field. The mathematical model used
for the problem formulation is consistent with the principles of FHD and MHD and
therefore considers both the magnetic Kelvin force and the Lorentz force as body
forces. The biomagnetic fluid is modeled as a homogeneous Newtonian continuum,
which dually exhibits magnetization and its electrical conductivity. The numerical
solution of the problem, described by a system of coupled, nonlinear system of PDEs
with appropriate boundary conditions, is carried out using the SIMPLER algorithm.
The solution is obtained by the finite volume method on a staggered grid. The results
of the simulation, as visualized through the stream function plots, indicate the field–
fluid interactions in laminar flow regimes.
Keywords Ferrohydrodynamics (FHD) · Magnetohydrodynamics (MHD) ·
Biomagnetic fluid · Lid-driven cavity · Magnetic number
1 Introduction
Biomagnetic Fluid Dynamics (BFD) investigates the dynamic behavior of magnetically susceptible biological fluids in the presence of magnetic fields. In simplified
models, the biological fluids are considered as isothermal, Newtonian, and electrically nonconducting (Bashtovoy et al. 1988). These models, in line with the principles
of Ferrohydrodynamics (FHD), attribute the driving Kelvin body force (KBF) in the
flow field solely to fluid magnetization (Bashtovoy et al. 1988; Rosensweig 1985).
S. Banerjee (B)
Mechanical Engineering Department, Heritage Institute of Technology, Kolkata 700107, India
e-mail: sumanta.banerjee@heritageit.edu
R. Ganguly
Power Engineering Department, Jadavpur University, Kolkata 700098, India
e-mail: rgangu2@yahoo.com
© Springer Nature Singapore Pte Ltd. 2021
D. Ramkrishna et al. (eds.), Advances in Bioprocess Engineering and Technology,
Lecture Notes in Bioengineering,
https://doi.org/10.1007/978-981-15-7409-2_42
423
in a Lid-Driven Cavity Under Steady
Localized Magnetic Field
Sumanta Banerjee and Ranjan Ganguly
Abstract The simulation study of steady, laminar, incompressible, and isothermal
biomagnetic fluid flow within a lid-driven cavity is presented, under the influence of
a time-independent localized external magnetic field. The mathematical model used
for the problem formulation is consistent with the principles of FHD and MHD and
therefore considers both the magnetic Kelvin force and the Lorentz force as body
forces. The biomagnetic fluid is modeled as a homogeneous Newtonian continuum,
which dually exhibits magnetization and its electrical conductivity. The numerical
solution of the problem, described by a system of coupled, nonlinear system of PDEs
with appropriate boundary conditions, is carried out using the SIMPLER algorithm.
The solution is obtained by the finite volume method on a staggered grid. The results
of the simulation, as visualized through the stream function plots, indicate the field–
fluid interactions in laminar flow regimes.
Keywords Ferrohydrodynamics (FHD) · Magnetohydrodynamics (MHD) ·
Biomagnetic fluid · Lid-driven cavity · Magnetic number
1 Introduction
Biomagnetic Fluid Dynamics (BFD) investigates the dynamic behavior of magnetically susceptible biological fluids in the presence of magnetic fields. In simplified
models, the biological fluids are considered as isothermal, Newtonian, and electrically nonconducting (Bashtovoy et al. 1988). These models, in line with the principles
of Ferrohydrodynamics (FHD), attribute the driving Kelvin body force (KBF) in the
flow field solely to fluid magnetization (Bashtovoy et al. 1988; Rosensweig 1985).
S. Banerjee (B)
Mechanical Engineering Department, Heritage Institute of Technology, Kolkata 700107, India
e-mail: sumanta.banerjee@heritageit.edu
R. Ganguly
Power Engineering Department, Jadavpur University, Kolkata 700098, India
e-mail: rgangu2@yahoo.com
© Springer Nature Singapore Pte Ltd. 2021
D. Ramkrishna et al. (eds.), Advances in Bioprocess Engineering and Technology,
Lecture Notes in Bioengineering,
https://doi.org/10.1007/978-981-15-7409-2_42
423