Convective Fluid Flow through a Sclerotic Oscillatory Artery in the Presence of Radiative Heat and a Magnetic Field
K.W. Bunonyo *
MMDARG, Department of Mathematics and Statistics, Federal University Otuoke, Nigeria.
G. D. Eli
Department of Petroleum and Gas Engineering, Federal University Otuoke, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this study, convective fluid flow through a sclerotic oscillatory artery in the presence of radiative heat and a magnetic field was conceived and formulated as a partial differential equation subject to a no-slip boundary condition. The magnetic field is assumed to be constant and perpendicular to the flow of blood in an artery, where the blood is assumed to be a viscous, incompressible, electrically conducting fluid. The system of partial differential equations was scaled to be a dimensionless system and was further reduced to a system of ordinary differential equations using the perturbation method, where we obtained some governing parameters involved. The Laplace method was used to obtain the analytical solution to the governing models. Analytical and explicit expressions of the axial velocity, temperature profile, and lipid concentration profile are obtained and numerical simulation is carried out using Wolfram Mathematica in order to demonstrate the effect of the obtained pertinent parameters on the flow profiles and to show the applicability of the formulated mathematical models. The results showed that the axial velocity is maximum at the centre of the sclerotic artery where the radius is zero; however, the velocity begins to decrease as the wall thickness increases for different wall temperatures and lipid concentrations. The aforementioned behavior was seen for Schmidt number, chemical reaction parameter, thermal Grashof number, the lipid concentration growth rate, and stenotic height increase, but the velocity profile showed a reversing flow when there is an increase in radiation absorption, magnetic field due to Lorentz force, and systolic pressure parameter. Secondly, it is seen that an increase in wall temperature increases blood temperature. This is because the additional temperature increases the fluid convection; the lipid growth rate also increases the fluid temperature. However, the temperature of the fluid decreases for an increase in Prandtl number, radiation absorption parameter, oscillatory frequency. Thirdly, the investigation involved the role played by the lipid concentration on the fluid; it is seen that wall lipid concentration, growth rate, and stenotic height increase in turn increase the lipid concentration profile, but the concentration profile decreases for an increase in Schmidt number, chemical reaction, and oscillatory frequency parameter. This research has shown that blood flow through a sclerotic artery can be modeled and is useful in understanding blood flow problems. This could lead to more cardiovascular issues and, as such, is a useful guide for mathematicians and scientists who would be interested in understanding and proffering solutions to blood flow problems.
Keywords: Oscillatory, concentration, sclerotic artery, magnetic field, radiative heat, lipoprotein, atherosclerosis, magneto-hydrodynamics, blood
How to Cite
Downloads
References
Bunonyo KW, Amos E. Theoretical investigation of the role of perfusion rate and haematocrit on blood flow and its impact on radiation behavior of tissue for tumor treatment; 2020.
Kollin A. Electromagnetic flow meter: principle of method and its application to blood flow measurement. Proceedings of the Society for Experimental Biology and Medicine. 1936;35:53–56.
Korchevskii E, Marochnik L. Magnetohydrodynamic version of movement of blood. Biophysics. 1965;10(2):411–414.
Chakraborty D, Gnann MV, Rings D, Glaser J, Otto F, Cichos F, Kroy K. Generalised Einstein relation for hot Brownian motion. EPL (Europhysics Letters). 2011;96(6):60009.
Gupta CP. Role of iron (Fe) in body. IOSR Journal of Applied Chemistry. 2014;7(11):38-46.
Perktold K, Hilbert D. Numerical simulation of pulsatile flow in a carotid bifurcation model. Journal of Biomedical Engineering. 1986;8(3):193-199.
Formaggia L, Lamponi D, Quarteroni A. One-dimensional models for blood flow in arteries. Journal of Engineering Mathematics. 2003;47(3-4):251-276.
Iqbal J, Hussain MM. Intestinal lipid absorption. American Journal of Physiology-Endocrinology and Metabolism. 2009;296(6):E1183-E1194.
Ros E. Intestinal absorption of triglyceride and cholesterol. Dietary and pharmacological inhibition to reduce cardiovascular risk. Atherosclerosis. 2000;151(2):357-379.
Durrington P. Dyslipidaemia. The Lancet. 2003;362(9385):717-731.
Bunonyo KW, Amos E. Mathematical Modeling of Mixed LDL-C and Blood Flow through an inclined Channel with Heat in the presence of Magnetic Field. In 9th (Online) International Conference on Applied Analysis and Mathematical Modeling (ICAAMM21). 2021;Istanbul-Turkey 143.
Lubrano V, Ballardin M, Longo V, Paolini M, Scarpato R. Hydroperoxides and cytokines as biomarkers in detecting atherosclerosis predisposition in cigarette smokers. Modern Research in Inflammation. 2012;1(01):11.
Prakash O, Singh S, Kumar D. A study of effects of heat source on mhd blood flow through bifurcated arteries. AIP Advances. 2011;1(4):042128.
Cobbold CA, Sherratt JA, Maxwell SRJ. Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach. Bulletin of mathematical biology. 2002;64(1):65-95.
Bowry VW, Stocker R. Tocopherol-mediated peroxidation. The prooxidant effect of vitamin E on the radical-initiated oxidation of human low-density lipoprotein. Journal of the American Chemical Society. 1993;115(14):6029-6044.
Francis GA. High density lipoprotein oxidation: in vitro susceptibility and potential in vivo consequences. Biochimica et Biophysica Acta (BBA)-Molecular and Cell Biology of Lipids. 2000;1483(2):217-235.
Habash RWY, Bansal R, Krewski D, Alhafid HT. Thermal Therapy, Part 2: Hyperthermia Techniques, Critical Reviews in Biomedical Engineering. 2006;34:491–542.
Denardo GL, Denardo SJ. Turning the heat on cancer. Cancer Biother. Radiopharm. 2008;23:671–680.
Sharma S, Singh U, Katiyar VK. Magnetic field effect on flow parameters of blood along with magnetic particles in a cylindrical tube, Journal of Magnetism and Magnetic Materials. 2015;377: 395–401.
Kotaka T, Kimura S, Kashiwayanagi M, Iwamoto J. Camphor induces cold and warm sensations with increases in skin and muscle blood flow in human. Biological and Pharmaceutical Bulletin. 2014;37(12):1913-1918.
Das SK, Roberts SB. Energy metabolism in fasting, fed, exercise, and re-feeding states. Present knowledge in Nutrition. 2012;58.
Ross R. Atherosclerosis – an inflammatory disease. Massachussets Medical Society. 1999;340(2): 115–126.
Tortora GJ, Derrickson BH. Principles of anatomy and physiology. John Wiley & Sons; 2018.
Venkatesan J, Sankar DS, Hemalatha K, Yatim Y. Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries. Journal of Applied Mathematics. 2013;11.
Article ID: 583809.
Bunonyo KW, Amos E, Eli IC. Unsteady oscillatory couette flow between vertical parallel plates with constant radiative heat flux. Asian Research Journal of Mathematics. 2018;1-11.
Bunonyo KW, Israel-Cookey C, Amos E. Modeling of Blood Flow through Stenosed Artery with Heat in the Presence of Magnetic Field. Asian Research Journal of Mathematics. 2018;1-14.