Magnetohydrodynamic Blood Flow Modeling with Nanoparticle Dynamics

Magnetohydrodynamic blood flow modelling with nanoparticle dynamics combines principles of fluid mechanics, electromagnetism and particle transport to simulate how blood—which behaves as a conductive, often non-Newtonian fluid—interacts with magnetic fields and dispersed nanoparticles. Governing equations typically extend Navier–Stokes formulations to include Lorentz forces and coupling terms that describe nanoparticle motion, heat transfer and mass transport. Fractional derivatives or memory kernels are often introduced to capture viscoelastic and time-dependent responses. Numerical and analytical approaches, including spectral transforms, finite-difference schemes and homotopy methods, are employed to solve for velocity, pressure, temperature and particle concentration profiles. This interdisciplinary framework underpins advances in targeted drug delivery, hyperthermia-based tumour ablation and nano-cryosurgery by enabling precise control over particle trajectories, thermal deposition and local haemodynamics. Recent models address arterial geometries with stenoses or bifurcations, investigate the influence of slip and wall effects, and explore how parameters such as the Hartmann number, Grashof number and nanoparticle volume fraction modulate flow and thermal fields. Applications extend to non-invasive imaging, magnetically guided carriers and smart therapeutics, reflecting growing demand for personalised and minimally invasive treatments.

Research from Nature Portfolio

Recent studies have developed analytical solutions for unsteady convection of a Casson nanofluid laden with gold nanoparticles in a cylindrical vessel to emulate nano-cryosurgery. Using Laplace and Hankel transforms, these investigations revealed that increased nanoparticle fraction and thermal Grashof numbers enhance temperature rise, while blood velocity is sensitive to slip velocity and rheological parameters. Another work introduced a fractional-order magnetohydrodynamic model of blood flow in a cylindrical tube containing magnetic particles. By employing Caputo time-fractional derivatives and spectral transforms, the study quantified how magnetic field strength and particle mass parameter decelerate both the fluid and nanoparticle velocities. These findings inform optimised particle steering for minimally invasive diagnostics and regulated hyperthermia treatments.

Magnetohydrodynamic Blood Flow Modeling with Nanoparticle Dynamics publication trend

The graph below shows the total number of articles in magnetohydrodynamic blood flow modeling with nanoparticle dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Casson fluid: A non-Newtonian fluid model describing shear-thinning behaviour with a yield stress, often used for blood rheology.

Hartmann number: A dimensionless parameter measuring the ratio of magnetic to viscous forces in an electrically conducting fluid.

Caputo fractional derivative: A generalised derivative operator capturing memory and hereditary effects in time-dependent processes.

Lorentz force: The force exerted on charged particles or conducting fluids in the presence of electric and magnetic fields.

Homotopy asymptotic method: An analytical perturbation technique for obtaining approximate solutions of nonlinear differential equations.

Electro-osmotic parameter: A dimensionless measure of fluid motion induced by an applied electric field across charged surfaces.

References

1. Unsteady natural convection flow of blood Casson nanofluid (Au) in a cylinder: nano-cryosurgery applications. Scientific Reports (2023).
2. Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles. Scientific Reports (2022).
3. The dynamic flow of ternary nanofluids with magnetic nanoparticles in an inclined artery exposed to thermal radiation and magnetic fields. Alexandria Engineering Journal (2025).
4. Fractional model for blood flow under MHD influence in porous and non-porous media. An International Journal of Optimization and Control Theories & Applications (IJOCTA) (2024).
5. Performance Analysis of Magnetic Nanoparticles during Targeted Drug Delivery: Application of OHAM. Computer Modeling in Engineering & Sciences (2021).