THERMAL SCIENCE

International Scientific Journal

Maasoomah Sadaf

,

Ayesha Khan

,

Zahida Perveen

,

Ghazala Akram

,

Muhammad Abbas

EFFECT OF FRACTIONAL ORDER ON UNSTEADY MAGNETOHYDRODYNAMICS PULSATILE FLOWOF BLOOD INSIDE AN ARTERY

ABSTRACT
This manuscript aims to investigate the velocity profile for the blood flow through an artery subject to magnetic field. It has been investigated how periodic acceleration of the body and slip conditions affect the irregular pulsatile blood flow across a porous media inside an artery if a magnetic field is present, under the assumption that blood is an incompressible electrically conducting fluid. A mathematical formulation involving Caputo fractional derivative serves as the basis of study. An analytical solution for fluid velocity is developed with the help of finite Hankel and Laplace transforms. The influence of fractional order on the fluid velocity is illustrated with the help of graphical simulations. The obtained results will be helpful in future research for the treatment of stenosis and other cardiovascular diseases.
KEYWORDS
MHD, blood flow, magnetic field, stenosis, Caputo time-fractional derivative
PAPER SUBMITTED: 2022-05-01
PAPER REVISED: 2022-05-14
PAPER ACCEPTED: 2022-06-17
PUBLISHED ONLINE: 2023-05-20
DOI REFERENCE: https://doi.org/10.2298/TSCI2302727S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 2, PAGES [1727 - 1734]
REFERENCES
  1. Eldesoky, I. M., Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source, World Journal of Mechanics, 2 (2012), 3, pp. 131-137
  2. Latha, R., Kumar, B. R., Mass Transfer Effects on Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source and Radiation, Journal of Applied Environmental and Biological Science, 6 (2016), 5, pp. 96-106
  3. Ali, M., et al., Analytical Solution of Unsteady MHD Blood Flow and Heat Transfer through Parallel Plates when Lower Plate Stretches Exponentially, Journal of Applied Environmental and Biological Sciences, 5 (2015), 3, pp. 1-8
  4. Kumar, S., Diwakar, C., A Mathematical Model of Power Law Fluid with an Application of Blood Flow through an Artery with Stenosis, Advances in Applied Mathematically BioSciences, 4 (2013), 2, pp. 51-61
  5. Sharma, M. K., et al., Pulsatile MHD Arterial Blood Flow in the Presence of Double Stenoses, Journal of Applied Fluid Mechanics, 6 (2013), 3, pp. 331-338
  6. Eldesoky, I. M., Unsteady MHD Pulsatile Blood Flow through Porous Medium in Stenotic Channel with Slip at Permeable Walls Subjected to Time Dependent Velocity (Injection/Suction), Walailak Journal of Science and Technology, 11 (2014), 11, pp. 901-922
  7. Misra, J. C., Sinha, A., Effect of Thermal Radiation on MHD Flow of Blood and Heat Transfer in a Permeable Capillary in Stretching Motion, Heat and Mass Transfer, 49 (2013), 5, pp. 617-628
  8. Nallapu, S., Radhakrishnamacharya, G., Jeffrey Fluid-Flow through a Narrow Tubes in the Presence of a Magnetic Field, Procedia Engineering, 127 (2015), Dec., pp. 185-192
  9. Agarwal, R., Varshney, N. K., Effect f of Permeability of Porous Medium on MHD Flow of Blood in Very Narrow Capillaries, Research and Reviews in BioSciences, 6 (2012), 8, pp. 204-209
  10. Verma, N. K., et al., Pulsatile Flow of Blood in Mild Stenosis, Journal of Science and Technology, 5 (2011), 6, pp. 61-76
  11. Rabby, M. G., et al., Pulsatile Non-Newtonian Laminar Blood Flows through Arterial Double Stenoses, Journal of Fluids, 2014 (2014), 757902
  12. Kumar, S., Diwakar, C., Hematocrit Effects of the Axisymmetric Blood Flow through an Artery with Stenosis Arteries, International Journal of Mathematics Trends and Technology, 4 (2013), 6, pp. 91-96
  13. Kamel, M. H., et al., Slip Effects on Peristaltic Transport of a Particle-Fluid Suspension in a Planar Channel, Appl. Bionics Biomech, 2015 (2015), ID703574
  14. Alimohamadi, H., Imani, M., Finite Element Simulation of 2-D Pulsatile Blood Flow through a Stenosed Artery in the Presence of External Magnetic Field, International Journal for Computational Methods in Engineering Science and Mechanics, 15 (2014), 4, pp. 390-400
  15. Mathur, P., Jain, S., Pulsatile Flow of Blood through a Stenosed Tube: Effect of Periodic Body Acceleration and a Magnetic Field, Journal of biorheology, 25 (2011), 1-2, pp. 71-77
  16. Shah, N. A., et al., Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Non-local Shear Stress, Advances in Mathematical Physics, 2021 (2021), ID5546701
  17. Abro, K. A., Atangana, A., Porous Effects on the Fractional Modelling of Magnetohydrodynamic Pulsatile Flow: An Analytic Study Via Strong Kernels, Journal of Thermal Analysis and Calorimetry, 146 (2021), 2, pp. 689-698
  18. Anwar, T., et al., Generalized Thermal Investigation of Unsteady MHD Flow of Oldroyd-B Fluid with Slip Effects and Newtonian Heating, A Caputo-Fabrizio Fractional Model, Alexandria Engineering Journal, 61 (2022), 3, pp. 2188-2202
  19. Misra, J. C., et al., Mathematical Modelling of Blood Flow in a Porous Vessel Having Double Stenoses in the Presence of an External Magnetic Field, International Journal of Biomathematics, 4 (2011), 2, pp. 207-225
  20. Caputo, M., Linear Models of Dissipation Whose Q is Almost Frequency Independent II, Geophysical Journal International, 13 (1967), 5, pp. 529-539
  21. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherland, 2006
  22. Everitt, W. N., Kalf, H., The Bessel Differential Equation and the Hankel Transform, Journal of Computational and Applied Mathematics, 208 (2007), 1, pp. 3-19
  23. Li, X. J., On the Hankel Transformation of Order Zero, Journal of Mathematical Analysis and Applications, 335 (2007), 2, pp. 935-940
PDF VERSION [DOWNLOAD]
Effect of fractional order on unsteady magnetohydrodynamics pulsatile flowof blood inside an artery

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence