Modeling of Blood Flow through Stenosed Artery with Heat in the Presence of Magnetic Field
K. W. Bunonyo *
Department of Mathematics and Statistics, Federal University Otuoke, Yenagoa, Nigeria.
C. Israel-Cookey
Department of Physics, Rivers State University, Port Harcourt, Nigeria.
E. Amos
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
An investigation of an oscillatory blood flow in an indented artery with heat source in the presence of magnetic field was carried out. The formulated governing models are solved using Frobenius method where the solutions are transformed into Bessel functions I0(βr) and K0(βr) of order zero of the first and second kind. The computational results are presented graphically for the velocity profile w(r, t) , the temperature profile θ(r) . The study reveals that the blood flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof Gr number. It is observed that the presence of the magnetic field M retards the velocity profile as well as the flow rate; the Grasof number Gr causes an increment in the velocity profile which is consistent with the existing laws of physics. Furthermore, the radiation parameter Rd does affect the velocity profile which means, it is a welcome development in thinning of the blood for effective treatment of cardiovascular disease considering the standard Prandtl number of blood ( Pr = 21 ). In addition, the temperature of the fluid is caused to rise due to an increase in radiation parameter irrespective of the height of the stenosis.
Keywords: Modeling, blood, Stenosis, heat, Darcy number.