In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angle with the fluid considered to be electrically conducting non-Newtonian elastic-viscous fluid. The momentum equation was transformed from dimensional form to dimensionless form with the Frobenius power series method used to solve the axially symmetric differential momentum equation with suitable boundary conditions. For clarity of the applicability of the study, results was shown graphically with behavior of the blood flow through the artery with stenosis shown for the velocity in the axial direction, blood acceleration, wall shear stress and volumetric flow rate. Results showed that, an increase in the body acceleration Go and pulsatile pressure Pl causes an increase in the blood flow, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the magnetic field M causes a decrease in the blood flow velocity, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the artery inclination ϕ results to an increase in the blood flow velocity, wall shear stress and the volumetric flow rate but an irregular behavior in the blood acceleration while the increase in slip velocity h at the wall decreases the velocity and blood acceleration, while the shear stress at the wall increases and the volumetric flow rate decreases.
Published in | International Journal of Theoretical and Applied Mathematics (Volume 8, Issue 1) |
DOI | 10.11648/j.ijtam.20220801.11 |
Page(s) | 1-13 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Magneto-hydrodynamic (MHD), Body Acceleration, Pulsatile Pressure, Slip Velocity, Permeability of the Porous Medium
[1] | P., D., Saffman, On the boundary conditions at the surface of a porous medium, Stud. Appl. Math., volume 50, pp. 93-101, (1971). |
[2] | G., S. Beaver and D., D. Joseph, Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, volume 30, pp. 197-207, (1967). |
[3] | D., A. McDonald, On steady blood flow through modelled vascular stenosis, Journal of Biochemistry, volume 12, pp 13-20, (1979). |
[4] | J., B. Shukla, R., S. Parihar and B., R., P. Rao, Effect of stenosis on non-Newtonian flow of blood in an artery, Bull. Math. Bio. volume 42, pp. 283 – 294, (1980). |
[5] | L., M. Srivastava, Flow of couple stress fluid through stenotic blood vessels, J. Biomech., volume. 1, pp. 479-485, (1985). |
[6] | J., C. Misra, M., K. Patra and S., C. Misra, A non-Newtonian model for blood flow through arteries under stenotic conditions, J. Biomech, volume 26, pp. 1129-1141, (1993). |
[7] | R. Ellahi, S., U. Rahman and S. Nadeem, Blood flow of Jeffery fluid in a catherized tapered artery with the suspension of Nano particles, Physics Letter A., Volume 378, number 40, pp. 2973-2980. |
[8] | R., N. Pralhad and D., H. Schultz, Modelling of arterial stenosis and its modelling to blood disease, Mathematical Bioscience, volume 190, number 2, pp. 203-220, (2004). |
[9] | N. Srivastava, Analysis of the flow characteristics of blood flowing through an inclined tapered porous artery with mild stenosis under the influence of an inclined magnetic field, Journal of Biophysics, (2014). |
[10] | Haik Y., Pai V, and Chen C. J. [1999]. Development of magnetic device for cell separation. Physics of fluids [1994-present], vol. 17, No. 7, 077103-077118. |
[11] | Eldesoky I. M. I. [2014]. 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, vol. 11, No. 11, pp. 901-922. |
[12] | Akbarzadeh P. Pulsatile magneto-hydrodynamic blood flows through porous blood vessels using a third grade non-Newtonian fluids model. Computer methods and programs in biomedicine, vol. 126, pp. 3-19, (2015). |
[13] | M. Gaur, and M., K. Gupta, unsteady slip flow of blood through constricted artery. Adv. Appl. Sci. Res., vol. 6, pp. 49-58, (2015). |
[14] | V., P. Rathod and S. Tanveer [2009]; pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field. Bull. Malaysian Math. Sci., vol. 32, pp. 245-259. |
[15] | S., U. Saddiqui, S., R. Shah and Geeta, Effect of body acceleration and slip velocity on the pulsatile flow through a casson fluid through stenosed artery, Adv. Appl. Sci. Res. Vol. 5, No. 3, pp. 213-225, (2014). |
[16] | Sinha, A., Shit, G. C. & Kundu, P. K. (2013). Slip Effect on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration. ISRN Biomedical Engineering, doi.org/10.1155/2013/925876. |
[17] | Nandal, J. & Kumari, S. (2019). The effect of slip velocity on unsteady peristalsis MHD blood flow through a constricted artery experiencing body acceleration. International Journal of Applied Mechanics and Engineering, Volume 24, No. 3, pp. 645-659. |
[18] | Bunonyo, W. K. & Amos, E. (2020). Blood flow through an inclined arterial channel with magnetic field. Mathematical Modelling and Applications, 5 (3), 129–137. |
[19] | Eldesoky, M. I. (2012). Slip Effects on Unsteady MHD Pulsatile Blood Flow through Porous Medium in an Artery under the Effect of Body Acceleration. International Journal of Mathematics and Mathematical Sciences, Volume 2012, ID 860239, doi: 10.1155/2012/860239. |
[20] | Kumar, A., Chandel, R. S., Shrivastava, R., Shrivastava, K. & Kumar, S. (2016). Mathematical Modelling of blood flow in an inclined tapered artery under MHD effect through porous medium. International Journal of Pure and Applied Mathematical Science, 9 (1), 75–88, ISSN 0972–9828, www.ripublication.com. |
[21] | Nadeem, S., Noreen, S. A., Hayat, T. & Awatif, A. H. (2012). Influence of Heat and Mass Transfer on Newtonian Bio magnetic Fluid of Blood Flow through a Tapered Porous Artery with Stenosis. Transport in Porous Medium, 91 (1): 81-100. |
[22] | Omamoke, E. & Amos, E. (2020). The Impact of Chemical Reaction and Heat source on MHD Free Convection Flow over an Inclined Porous Surface. International Journal of Scientific and Research Publications, Volume 10, Issue 5, ISSN 2250-3153, DOI: 10.29322/IJSRP.10.05.2020.p10103. |
[23] | Omamoke, E., Amos, E., & Jatari, E. (2020). Impact of Thermal Radiation and Heat Source on MHD Blood Flow with an Inclined Magnetic Field in Treating Tumor and Low Blood Pressure. Asian Research Journal of Mathematics, 16 (9), 77-87. https://doi.org/10.9734/arjom/2020/v16i930221. |
APA Style
Emeka Amos, Ekakitie Omamoke, Chinedu Nwaigwe. (2022). MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects. International Journal of Theoretical and Applied Mathematics, 8(1), 1-13. https://doi.org/10.11648/j.ijtam.20220801.11
ACS Style
Emeka Amos; Ekakitie Omamoke; Chinedu Nwaigwe. MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects. Int. J. Theor. Appl. Math. 2022, 8(1), 1-13. doi: 10.11648/j.ijtam.20220801.11
AMA Style
Emeka Amos, Ekakitie Omamoke, Chinedu Nwaigwe. MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects. Int J Theor Appl Math. 2022;8(1):1-13. doi: 10.11648/j.ijtam.20220801.11
@article{10.11648/j.ijtam.20220801.11, author = {Emeka Amos and Ekakitie Omamoke and Chinedu Nwaigwe}, title = {MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects}, journal = {International Journal of Theoretical and Applied Mathematics}, volume = {8}, number = {1}, pages = {1-13}, doi = {10.11648/j.ijtam.20220801.11}, url = {https://doi.org/10.11648/j.ijtam.20220801.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20220801.11}, abstract = {In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angle with the fluid considered to be electrically conducting non-Newtonian elastic-viscous fluid. The momentum equation was transformed from dimensional form to dimensionless form with the Frobenius power series method used to solve the axially symmetric differential momentum equation with suitable boundary conditions. For clarity of the applicability of the study, results was shown graphically with behavior of the blood flow through the artery with stenosis shown for the velocity in the axial direction, blood acceleration, wall shear stress and volumetric flow rate. Results showed that, an increase in the body acceleration Go and pulsatile pressure Pl causes an increase in the blood flow, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the magnetic field M causes a decrease in the blood flow velocity, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the artery inclination ϕ results to an increase in the blood flow velocity, wall shear stress and the volumetric flow rate but an irregular behavior in the blood acceleration while the increase in slip velocity h at the wall decreases the velocity and blood acceleration, while the shear stress at the wall increases and the volumetric flow rate decreases.}, year = {2022} }
TY - JOUR T1 - MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects AU - Emeka Amos AU - Ekakitie Omamoke AU - Chinedu Nwaigwe Y1 - 2022/02/09 PY - 2022 N1 - https://doi.org/10.11648/j.ijtam.20220801.11 DO - 10.11648/j.ijtam.20220801.11 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 1 EP - 13 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20220801.11 AB - In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angle with the fluid considered to be electrically conducting non-Newtonian elastic-viscous fluid. The momentum equation was transformed from dimensional form to dimensionless form with the Frobenius power series method used to solve the axially symmetric differential momentum equation with suitable boundary conditions. For clarity of the applicability of the study, results was shown graphically with behavior of the blood flow through the artery with stenosis shown for the velocity in the axial direction, blood acceleration, wall shear stress and volumetric flow rate. Results showed that, an increase in the body acceleration Go and pulsatile pressure Pl causes an increase in the blood flow, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the magnetic field M causes a decrease in the blood flow velocity, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the artery inclination ϕ results to an increase in the blood flow velocity, wall shear stress and the volumetric flow rate but an irregular behavior in the blood acceleration while the increase in slip velocity h at the wall decreases the velocity and blood acceleration, while the shear stress at the wall increases and the volumetric flow rate decreases. VL - 8 IS - 1 ER -