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Applied mathematics to biological systems gives the ability to construct mathematical models.
Such models are mathematical systems that attempt to represent the complex interactions of
biological systems in a way simple enough for their consequences to be understood and
explored. Traditionally models that allowed biologists to see a problem in a simplified way have
been complicated structure, while mathematical models that constructed to exhibit simple
biological properties that could be analyzed. This kind of model, however, is restricted by
technology as well as technological ingenuity. Mathematical models have no such restriction and
can be used to construct any sort of biological system; respiratory flows, pulsating blood flow,
micro-and macro-circulation systems bio heat and mass transfer models are some examples of
these mathematical models these flows may be studied under a well-known branch of science it
is named by bio fluid mechanics. By bio fluid mechanics we can understand the physiological
processes that occur in the human circulation and analyze the physical mechanisms that under
line them. Understanding the basic processes occurring in the human body will facilitate the
engineering design and construction of new medical devices and machinery. Our thesis concerns
with A computational Study of the external forces effects on the motion of fluids through
biological tissues such as blood flow through tissues.
The present thesis consists of four chapters with two summaries one of them with Arabic
language and the other with English language and list of references for books and papers related
to the subjects of the thesis.
This chapter includes the introduction which is closely related to the subjected of the thesis.
Such asMechanics, Newtonian fluid and Non-Newtonian fluid, magneto-hydrodynamics,
and basic equations, porous medium, porosity, Darcy law and non- Darcian equations.
We summarized the basic equations of Newtonian and non- Newtonian fluids(continuity
equation, momentum equation, Energy equation, and Concentration equation), models of
heat transfer (radiation, convection, conduction, evaporation), bio heat and mass transfer.
The second chapter investigatesthe influence of the electric field with heat and mass
transfer on the pulsatile flow of viscoelastic fluid in a channel bounded by a porous layer of
smart material. The problem is modulated mathematically by a set of partial differential
equations, which represent the continuity, momentum, energy and concentration equations,
besides the Maxwell equations with appropriate boundary conditions. The system of equations
which describes the motion of fluid phase and layer porous phase are solved analytically by
using perturbation technique for steady and unsteady cases. The effects of various emerging
parameters on the flow characteristics, heat and mass processes are shown and discussed with the
help of graphs.
In this chapter, The flow due to the pulsatile pressure gradient of non-Newtonian fluid
with heat and mass transfer along a porous oscillating channel is considered. The system is
stressed by transvers magnetic field. The non-Newtonian fluid under consideration is obeying the
viscoelastic model. The governed system of partial differential equations which describe the
motion of this fluid is written, in non-dimensional form. This system of equations with an
appropriate boundary conditions is solved analytically by using perturbation technique for small
material parameter α . The velocity, temperature and concentration distributions of the fluid are
obtained as functions of the physical parameters of the problem. The effects of these physical
parameters of the problem on these solutions are discussed and illustrated graphically through a
set of figures.
In this chapter, We have analyzed the MHD flow of a conducting couple stress fluid in
oscillating channel with heat and mass transfer. The non-Newtonian fluid under consideration is
obeying the Bi-viscosity model. In this analysis we are taking into account the induced magnetic
fieldand porous medium . The analytic solution for the problem has been obtained by using
homotopy perturbation method for steady and unsteady cases.The distributions
ofthevelocity,temperature and concentration functionsare discussed and illustrated graphically
for different values of the physical parameters of the problem for various parameters such
assuch as the couple stress parameter, the Hartmann number , the Reynolds