Mathematical Modeling of an Oscillatory MHD Blood Flow through a Lipid Saturated Porous Channel with Metabolic Heat and Magnetic Field

Authors

  • Kubugha Wilcox Bunonyo Federal University Otuoke Yenogoa, Nigeria
  • Innocent C. Eli Federal University Otuoke Yenogoa, Nigeria

Keywords:

Blood, Lipid, Magnetic Field, Cardiovascular system, Heat transfer, ODE and PDE.

Abstract

Communication In Physical Sciences, 2020, 6(1): 783-792

Authors: K.W. Bunonyo* and I.C. Eli

Received 12 November 2020/Accepted 27 November 2020

This research investigates an oscillatory blood flow through a lipid saturated porous channel with metabolic heat and magnetic field. The study involves formulating mathematical model for blood momentum equation, the energy equation and the lipid concentration equation, and the coupled PDE were reduced to set of nonlinear ODE using the perturbation method. The set of ODEs are solved and the blood velocity, temperature and lipid concentration profiles were obtained, with some governing parameters. Numerical computation was carried out using Mathematica software to by varying the governing parameters within some specific range in order to the study the effects of the parameters on the flow profiles. The results revealed that the flow profiles were influenced with the varying pertinent parameters such as Prandtl number, radiation parameter, metabolic heat parameter, Hartmann number, Grashof number, solutal Grashof number, Schmidt number and the oscillatory frequency parameters respectively.

Downloads

Download data is not yet available.

Author Biographies

Kubugha Wilcox Bunonyo, Federal University Otuoke Yenogoa, Nigeria

Department of Mathematics and Statistics

Innocent C. Eli, Federal University Otuoke Yenogoa, Nigeria

Department of Mathematics and Statistics

References

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, 6,1, pp. 1-14.

Bunonyo, K.W. & Amos, E. (2020). Blood Flow through a Sine-Shaped Atherosclerotic Aorta with a Source Wall Temperature and Magnetic Field, American Journal of Computational and Applied Mathematics, 10, 2, pp. 21-38.

Craciunescu, O. I. & Clegg, S. T. (2001). Pulsatile blood flow effects on temperature distribution and transfer in rigid vessels. Journal of Biomechanical Engineering, 123, 5, pp. 500–505

Durrington, P. (2003). Dyslipidaemia. The Lancet, 362, 9385, pp. 717-731.

He, Y., Shirazaki, M., Liu, H., Himeno, R. & Sun, Z, (2006), A numerical coupling model to analyze the blood flow, temperature, and oxygen transport in human breast tumor under laser irradiation. Computers in Biology and Medicine, 36, pp. 1336–1350.

Horng, T. L., Lin, W. L., Liauh, C. T. & Shih, T. C. (2007). Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy. Medical Physics, 34, pp.1312-1320.

Inoue, S. & Kobaya, M. (1989). Biological activities caused by farinfrared radiation. International Journal of Biometerology, 33, pp. 145-150.

Kobu, Y. (1999). Effects of infrared radiation on intraosseous blood flow and oxygen tension in rat tibia. Kobe. Journal of Medical Sciences, 45, pp. 27-39.

Misra, J. C. & Shit, G. C. (2007). Role of slip velocity in blood flow through stenosed arteries: A non-Newtonian model. Journal of Mechanics and Medical Biology,7, pp. 337–353.

Misra, J. C., Sinha, A. & Shit, G. C. (2010). Flow of a biomagnetic viscoelastic fluid: application to estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment. Applied Mathematics and Mechanics, 31, pp. 405–1420.

Nishimoto, C., Ishiura, Y., Kuniasu, K. & Koga, T. (2006). Effects of ultrasonic radiation on cutaneous blood flow in the paw of decerebrated rats. Kawasaki Journal of Medical Welfare,12, pp. 13-18.

Ogulu,, A. & Bestman, A. R. (1994). Blood flow in a curved pipe with radiative heat transfer. Acta Physica Hungarica 74, pp. 189-201.

Prakash, J. & Makinde, O. D. (2011). Radiative heat transfer to blood flow through a stenotic artery in the presence of magnetic field. Latin America Applied Research, 41, pp. 273–277

Schmidt, R. F., Lang, F., & Heckmann, M. (Eds.). (2017). Physiologie des Menschen: Mit Pathophysiologie. Springer Berlin.

Shah, J., dos Santos, I., Hammerich, D. & Valvano, J. W. (2005). Instrument to measure the heat convection coefficient on the endothelial surface of arteries and veins. Medical and Biological Engineering Computing, 43, pp. 522-527.

Shrivastava, D. & Roemer, R. B. (2005). An analytical study of ‘poisson conduction shape factors’ for two thermally significant vessels in a fine, heated tissue. Physics in Medicine and Biology, 50, pp. 3627-3641.

Szasz, A. (2007) Hyperthermia, a modality in the wings. Journal of Cancer Rerdearch and Therapeutics, 3, pp. 56-66

Downloads

Published

2020-11-28