الفهرس 
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Abstract
In this thesis, we studied and solved analytically some problems of electrohydrodynamic peristaltic
ow with heat transfer in the presence of ac electric eld. The stream function, temperature distribution and electric potential function are obtained up to second order in terms of electrical Rayleigh number, temperature parameter, Reynolds number,amplitude ratio, wave number and channel width. In our analysis,we assumed that the velocity components, the pressure gradient, the temperature and the electric potential could be expanded in a regular perturbation series of the amplitude ratio.
The present thesis consists of three chapters in addition to two ap-pendices and references section and arabic and english summaries.
These chapters are outlined as follows:
Chapter 1
Chapter 1 is an introduction. We give in it some information about the following items:
Fluid mechanics.
Stress and Strain.
Newtonian’s law of viscosity.
On non-Newtonian
uids.
Biomechanics.
On perturbation theory.
Heat transfer.
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SUMMARY
Boussinesq approximation (buoyancy).
Fundamental equations of a Newtonian and non-Newtonian u-ids.
Dimensional analysis.
Non-dimensional numbers.
peristalsis.
peristaltic pump.
Electrostatics and Electrohydrodynamics.
Conductors and insulators.
permittivity.
Maxewell’s equations.
Volume forces in the electrostatic eld.
Equation of temperature (heat equation).
Chapter 2
In this chapter, we study the eects of a vertical ac-electric eld and heat transfer on peristaltic
ow of an incompressible Newtonian di-electric
uid in a symmetric exible channel by considering small wave number. The mathematical modeling includes the interactions among electric eld,
ow eld and temperature is presented. The stream
function, the heat distribution and the mean electric potential func-tion have been computed analytically up to second order in terms of
the electrical Rayleigh number L, the temperature parameter L2, the Reynolds number Re, the amplitude ratio a0 and the wave number
0. In our analysis, we assumed that the velocity components, the pressure gradient, the temperature and the electric potential could be
expanded in a regular perturbation series of the amplitude ratio. The non-linearity of the equations of motion is taken into account. The nu-
merical results show that the possibility of ow reversal increases near
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SUMMARY
the lower bound of the channel and decreases near the upper bound of the channel by the increasing of the electrical Rayleigh number and by the decreasing of the temperature parameter. It is also found that the heat transfer increases by increasing the electrical Rayleigh number.
Also, the mean electric potential increases near the lower bound of the channel and decreases in the remaining wide part of the channel by the
increasing of the temperature parameter. Streamlines have been also discussed. It is observed that the size of the trapped bolus decreases at the upper bound of the channel and increases at the lower bound of the channel by the increasing of the electrical Rayleigh number and
by the decreasing of the temperature parameter. Also, as the electri-cal Rayleigh number and the temperature parameter tend to zero, the
results of the problem reduce to the same as that found by Fung and Yih [18].
Chapter 3
In this chapter, we study the eects of a vertical ac-electric eld and heat transfer on peristaltic
ow of an incompressible dielectric vis-coelastic (Oldroyd) uid in a symmetric
exible channel. The math-ematical modeling includes the interactions among electric eld,
ow eld and temperature is presented. The stream function, temperature distribution and electric potential function are obtained up to second
order in terms of electrical Rayleigh number, temperature parameter,Reynolds number, amplitude ratio, wave number and channel width.
The perturbation solution of the modeled problem is derived by con-sidering a small wave number. The in uence of pertinent parameters
is shown and discussed with the help of graphs. Streamlines have been also discussed. The non-linearity of the equations of motion is taken
into account. The numerical results show that the possibility of ow reversal increases near the lower bound of the channel and decreases near the upper bound of the channel by the increasing of (L, Re and W2) and by the decreasing of (L2 and W1). It is also found that near the lower bound of the channel the possibility of ow reversal increases
by the increasing of 0, while in the remaining wide part of the chan-nel, the possibility of
ow reversal decreases by the increasing of
0. It is observed that the trapped bolus decreases in size at the upper bound of the channel and increases in size at the lower bound of the channel
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SUMMARY
by the increasing of L and by the decreasing of L2. Also, the trapped bolus does not exist for
0 =0, but the trapping exists when 06=0 and
the bolus volume decreases with increasing the wave number 0. It is also found that the trapped bolus increases in size by the increasing
of (W2, Re and a0) and by the decreasing of W1. Also, the results in-dicate that the ow reversal in the case of a Newtonian uids are less
than these for Oldroyd uids. Also, as the electrical Rayleigh number,the temperature parameter, the relaxation time and the retardation time tend to zero, the analytical results reduce to the well-known case of a Newtonian uid in agreement with Fung and Yih [18]. The con-tents of this chapter have been accepted for publication to ”Delta
Journal of Science”, Tanta university (2012). Also, it have been presented as a poster in the 8th International Scienti c Conference, Al-
Azhar university, faculty of science, ”Environment, Development And
Bio-Informatics”, 26-28 March (2012), Cairo, Egypt.