Lipid Concentration Effect on Blood Flow Through an Inclined Arterial Channel with Magnetic Field
Mathematical Modelling and Applications
Volume 5, Issue 3, September 2020, Pages: 129-137
Received: May 8, 2020;
Accepted: May 22, 2020;
Published: Jun. 4, 2020
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Kubugha Wilcox Bunonyo, Department of Mathematics and Statistics, Federal University Otuoke, Yenagoa, Nigeria
Emeka Amos, Department of Mathematics, Rivers State University, Port Harcourt, Nigeria
The purpose of this research is to formulate mathematical models to investigate lipid concentration effect on blood flow though an inclined arterial channel with magnetic field. The formulated coupled partial differential equations were made dimensionless and reduced to ordinary differential equation using a perturbation technique, the nonlinear ordinary differential equations were solved analytically for the blood velocity and lipid concentration profiles respectively with some resultant pertinent parameters. Numerical simulations were carried out using Mathematica codes developed by the authors for the flow profiles by carefully varying the pertinent parameters to study the effect of each of the parameters on velocity and concentration profiles respectively. It is notice that the solutal Grashoff number, Darcy number, angle of inclination, time and the treatment parameters respectively causes the velocity profiles to increase, while the parameters such as the onset, length of stenosis, Schmidt number, magnetic field intensity, and pulse rate respectively decelerate the velocity profile. Secondly, the parameters such as length of stenosis, the pulse rate, Schmidt number and the treatment parameters decelerate the concentration profile while the onset parameter increases the concentration profile and the results were presented graphically. We can conclude that lipid concentration and some of the resulted pertinent parameters either increases or decreases the flow profiles and of great importance in studying blood velocity in arterial channel.
Kubugha Wilcox Bunonyo,
Lipid Concentration Effect on Blood Flow Through an Inclined Arterial Channel with Magnetic Field, Mathematical Modelling and Applications.
Vol. 5, No. 3,
2020, pp. 129-137.
Bunonyo, K. W., Israel-Cookey, C., & Amos, E. (2018). Modeling of Blood Flow through Stenosed Artery with Heat in the Presence of Magnetic Field. Asian Research Journal of Mathematics, 1-14.
Shanthi, M., Pekka, P. and Norrving, B. (2011) Global Atlas on Cardiovascular DiseasesPrevention and Control. World Health Organization in collaboration with world Heart Federation and World Stroke Organisation, 3-18.
Li, J. and Huang, H. (2010) Effect of Magnetic Field on Blood Flow and Heat Transfer through a Stenosed Artery. Proceedings of 3rd International Conference on Biomedical Engineering and Informatics, Yantai, 16-18 October 2010, 028-2032. https://doi.org/10.1109/BMEI.2010.5639654.
Alshare, A. Tashtoush, B. and Elkhali, H. H. (2013) Computational Modelling of Non-Newtonina Blood Flow through Stenosed Arteries in the Presence of Magnetic Field. Journal of Biochemical Engineering, 135, 5-15.
Habibi, M. R. and Ghasemi, M. (2011) Numerical Study of Magnetic Nanoparticles Concentration in Biofluid (Blood) under Influence of High Gradient Magnetic Field. Journal of Magnetism and Magnetic Materials, 321, 32-38. https://doi.org/10.1016/j.jmmm.2010.08.023.
Mekheimer, K. S., Haroun, M. H. and Elkot, M. A (2012) Influence of Heat and Chemical Reactions on Blood Flow through an Isotropically Tapered Elastic Arterieswith Overlapping Stenosis. Applied Mathematics, 6, 281-292.
Sharma, P. R., Sazid, A. and Katiyar, V. K. (2011) Mathematical Modelling of Heat Transfer in Blood Flow through Stenosed Artery. Journal of Applied Sciences Research, 7, 68-78.
Srinivas, S., Vijayalakshmi, A. and Redely, A. S. (2017) Flow and Heat Transfer of Gold Blood Nanofluid in a Porous Channel with Moving/Stationary Wall. Journal of Mechanics, 33, 395-404.
Yadav, R. P., Harminder, S. and Bhoopal, S. (2008) Experimental Studies on Blood Flow in Stenosis Arteries in the Presence of Magnetic Field. Ultra Sciences, 20, 499-504.
Tiari, S., Ahmadpour, M., Tafazzoli-Shadpour, M. and Sadeghi, M. R. (2011) An Experimental Study of Blood Flow in a Model of Coronary Artery with Single and Double Stenosis. Proceedings of the 18th Iranian Conference on Biomedical Engineering, Tehran, 14-16 December 2011, 33-36.
Aiman, A. and Bourhan, T. (2016) Simulation of MHD in Stenosed Arteries in Diabetic or Anaemic Model. Computational and Mathematical Methods in Medicine, 2016, Article ID: 8123930.
Misra, J. C. and Shit, G. C. (2007) Role of Slip Velocity in Blood Flow through Stenosed Arteries: A Non-Newtonian Model. Journal of Mechanical in Medicine and Biology, 7, 337-353. https://doi.org/10.1142/S0219519407002303.
Ponalgusamy, R. (2007) Blood Flow through an Artery with Stenosis. A TwoLayered Model, Different Shape of Stenosis and Slip Velocity at the Wall. Journal of Applied Sciences, 7, 1071-1077. https://doi.org/10.3923/jas.2007.1071.1077.
Verma, N. K., Siddiqui, S. U., Gupta, R. S. and Mishra, S. (2011) Effect of Slip Velocity on Blood Flow through a Catheterized Artery. Applied Mathematics, 2, 764-770. https://doi.org/10.4236/am.2011.26102.
Guar, M. and Gupta, M. K. (2014) Steady Slip Blood Flow through a Stenosed Porous Artery. Advanced in Applied Sciences Research, 5, 249-259.
Srikanth, D. S., Ramana, R. S. and Jain, A. K. (2015) Unsteady Polar Fluid Model of Blood Flow through Tapered X-Shape Stenosed Artery. Effect of Catheter and Velocity Slip. Ain Shams Engineering Journal, 6, 1093-1104.https://doi.org/10.1016/j.asej.2015.01.003.
Arun, K. M. (2016) Multiple Stenotic Effect of Blood Flow Characteristic in the Presence of Slip Velocity. American Journal of Applied Mathematics and Statistics, 4, 154-198.
Geeta, A. and Siddique, S. U. (2016) Analysis of Unsteady Blood Flow through Stenosed Artery with Slip Effect. International Journal of Bio-Science and Bio-Technology, 8, 43-54.
Sanjeev, K. and Chandraahekhar, D. (2015) Hematocrit Effect of the Axisymmetric Blood Flow through an Artery with Stenosed Arteries. International Journal of Mathematics Trends and Technology, 4, 91-96.
Verma, N. K. and Parihar, R. S. (2010) Mathematical Model of Blood Flow through a Tapered Artery with Mild Stenosed and Hematocrit. Journal of Applied Mathematics and Computer, 1, 30-46.
Shit, G. C. and Screeparma, M. (2015) Pulsatile Flow of Blood and Heat Transfer with Variable Viscosity under Magnetic and Vibration Environment. Journal of Magnetism and Magnetic Materials, 388, 106-115. https://doi.org/10.1016/j.jmmm.2015.04.026.
Singh, J. and Rathee, R. (2010) Analytical Solution of Two Dimensional Model of Blood Flow with Variable Viscosity through an Indented Artery Due to LDL Effect in the Presence of Magnetic Field. International Journal of Physical Sciences, 5, 1851-1868.
Chitra, M. and Karthikeya, D. (2017) Oscillatory Flow of Blood in Porous Vessel of a Stenosed Artery with Variable Viscosity under the Influence of Magnetic Field. International Journal of Innovative Research in Advanced Engineering, 4, 52-60.
Jagdish, S. and Rajbala, R. (2010) Analytical Solution of Two Dimensional Model of Blood Flow with Varible Viscosity through an Indented Artery due to LDL Effect in the Presence of Magnetic Field. International Journal of Physical Sciences, 5, 1857-1868.
Bunonyo, K. W., & Amos, E. (2020)."Investigation of the Treatment and Radiation Effects on Oscillatory Blood Flow through a Stenosed Artery.”American Journal of Engineering Research (AJER), vol. 9 (04), pp. 253-259.