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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Biomechanics of a Bifurcating Green Plant: The Roles of Bifurcation Angle and Soil Nature on Crops Growth and Productivity | Chapter 01 | Theory and Applications of Chemistry Vol. 3

Analytic study of the xylem flow in a bifurcating green plant is presented. The model involves a set of non-linear differential equations, which are tackled using the perturbation method of solutions. Solutions of the velocity, temperature, concentration, Nusselt and Sherwood numbers are obtained and presented graphically. It is observed that increase in the bifurcation angle increases the flow velocity and concentration, Nusselt and Sherwood numbers, whereas the soil parameter (magnetic field force) decreases the velocity and Nusselt number but increases the concentration and Sherwood number. These results have tremendous effect on the growth and yield of the plant. In particular, the increase in the transport velocity and concentration tend to increase the rate at which water and nutrients are made available to the plant, thus enhancing the growth and yield of the plant (crops); the variation in the electrolytic strength of the soil mineral salt water leading to a lower or higher Lorentz force tends to accounts for why some plants do well in some regions than in the others. Furthermore, it is seen that when the angle of bifurcation is zero (i.e.  α =0) and the magnetic field and thermal diffusion parameter are neglected the flow structures.

Author(s) Details

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

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

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Fluid Flow in Bifurcating Rectangular Porous Systems under Magnetic Field Influence | Chapter 08 | Current Research in Science and Technology Vol. 2

Steady MHD fluid flow in a bifurcating rectangular porous channel is presented. The governing nonlinear equations are solved analytically by the methods of similarity transformation and regular perturbation series expansions. Expressions for the temperature, concentration and velocity are obtained and analyzed graphically. The results show that increase in bifurcation angle and Grashof numbers increase the transport velocity, whereas the increase in the magnetic field parameter decreases it. Furthermore, it is seen that an increase in bifurcation angle increases the temperature of the flow.

Author(s) Details

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

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

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View Volume: https://doi.org/10.9734/bpi/crst/v2