Oscillatory Blood Flow in Bifurcating Capillaries | Chapter 12 | Theory and Applications of Mathematical Science Vol. 1

Oscillatory blood flow in bifurcating capillaries is examined. The governing nonlinear and coupled equations expressed in the form of the Boussinesq approximations are solved by the method of perturbation series expansions. Solutions for the concentration, temperature and velocity are obtained, and presented quantitatively using Malple 18 computational software. The results show that the rate of chemical reaction, Hartmann number (M2≤I.0), heat exchange parameter and Grashof number (Gr/Gc≤I.0) tend to increase the velocity of the flow. The increase in the velocity structure has some attendant implications. In fact, it tends to increase the rate of transport of oxygen and nutrient-rich blood to the tissues, and this in turn enhances the physiological well-being of man.

Author(s) Details

Dr. W. I. A. Okuyade
Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria.

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Thermally-Driven Blood Flow in a Bifurcating Artery | Chapter 07 | New Insights on Chemical Research Vol. 1

A thermally-driven oscillatory blood flow in bifurcating arteries is studied. Blood is treated as Newtonian, viscous, incompressible, homogeneous, magnetically susceptible, chemically reactive but of order one; the arteries are porous, bifurcate axi-symmetrically, and have negligible distensibility. The governing non-linear and coupled equations modeled on the Boussinesq assumptions are solved using the perturbation series expansion solutions. The solutions obtained for the temperature and velocity are expressed quantitatively and graphically. The results show that the temperature is increased by the increase in chemical reaction rate, heat exchange parameter, Peclet number, Grashof number and Reynolds number, but decreases with increasing magnetic field parameter (in the range of 0.1≤M2≤1.0) and bifurcation angle; the velocity increases as the magnetic field parameter (in the range of 0.1≤M2≤1.0 in the mother channel and 0.1≤M2≤0.5 in the daughter channel), chemical reaction rate (in the range of 0.1≤δ12≤0.5), Grashof number (in the range of 0.1≤Gr≤0.5), Reynolds number and bifurcation angle. The increase and decrease in the flow variables have strong implications on the arterial blood flow.

Author(s) Details

W. I. A. Okuyade
Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria.

Professor T. M. Abbey
Applied Mathematics and Theoretical Physics Group, Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria.

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