الفهرس 
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Abstract
Summary
We studied and solved analytically some problems of the peristaltic transport of nanofluids under the influence of Cattaneo-Christov theories. Some non-Newtonian models are considered. The impacts of Hall current, Soret & Dufour, non – Darcian porous medium, joule heating, viscous dissipation, electric field, micropolar, couple stress, thermal radiation, chemical reaction, and heat generation are considered in some studies. As well, the slip conditions for both velocity and temperature are imposed in some studies. The convective conditions for nanofluid concentration and fluid concentration are also applied in some studies. The semi – analytical solutions of the equations that govern the fluid motion are relied mainly on the classical perturbation technique together with the Homotopy perturbation method (HPM). Thus, the distributions of the axial velocity, temperature, spin velocity, concentration, and nanofluid concentration are obtained. The influences of several physical parameters on the preceding distributions are displayed and drawn graphically through a set of graphs.
The current thesis consists of six chapters with their illustrated figures in addition to five appendices and a list of references besides Arabic and English summaries. These chapters are outlined as follows:
Chapter 1
This chapter is a general introduction to the subject of the study. The basic concepts of fluid mechanics under the influence of various external forces were explained in it. It contains the following points:
• Peristaltic transport
• Newtonian and non-Newtonian fluids
• Heat and Mass transfer
• Cattaneo – christov theory of heat and mass fluxes
• Porous media
• Magnetohydrodynamics
• Micropolar fluids
• Nanofluids
• Governing equations of fluid motion
• Homotopy perturbation method (HPM)
Chapter 2
Entitled:
“Cattaneo – christov heat and mass fluxes effect on MHD peristaltic transport of Bingham nanofluid through a non – Darcy porous medium”
We investigated the influence of Cattaneo–Christov heat and mass fluxes on peristaltic transport of an incompressible flow. The fluid is obeying Bingham alumina nanofluid. The fluid flows between two co-axial vertical tubes. The system is expressed by a varying radially magnetic field with respect to the space. Soret effect and the permeability of the non-Darcy porous medium are considered. The governing system of equations is solved by utilizing the approximations of long wavelength with low Reynold’s number with the help of the traditional perturbation technique together with the homotopy perturbation method (HPM). It is noticed that the axial velocity magnifies with an increase in the value of the Bingham parameter. Meanwhile, the value of the axial velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of the thermal relaxation time leads to a reduction in the value of fluid temperature. Furthermore, an increase in the value of the mass relaxation time parameter makes an enhancement in the value of nanoparticles concentration. It is noticed also that the size of the trapped bolus enhances with the increment in the value of the Bingham parameter. The current study has many accomplishments in several scientific areas like the medical industry, medicine, and others. Therefore, it represents the depiction of the gastric juice motion in the small intestine when an endoscope is inserted through it.
The contents of this chapter are Published in: International Journal of Applied Electromagnetics and Mechanics, 68 (1), 59-84, (2022).
Chapter 3
Entitled:
“Chemical reaction and thermal radiation via Cattaneo-Christov double diffusion (CCDD) effects on squeezing non-Newtonian nanofluid flow between two - parallel vertical plates “
We examined the influences of Cattaneo-Christov double diffusion (CCDD) on an incompressible nanofluid flow. The fluid is obeying Eyring – Powell model. The fluid flows between two - parallel vertical plates. The impacts of Soret number, porous medium, heat generation, and thermal radiation are taken into consideration. A suitable similarity transformation is utilized to convert the governing system of non-linear partial differential equations to ordinary differential equations. Moreover, the semi-analytical solutions of these equations are obtained by the means of the homotopy perturbation method (HPM) up to the second order. The influences of the distinct several physical embedded parameters on the distributions of velocity, stream function, temperature, and nanofluid concentration are pointed out via a set of graphs. Furthermore, the values of physical quantities of our interest “skin friction coefficient and nano Sherwood number” are computed and presented graphically through some draws. It’s detected that the velocity has a dual performance under the impacts of the different physical parameters. Hence, it enhances with a development in the value of the Darcy parameter along the interval . However, at the remaining interval, the vice versa occurred. In contrast, the magnetic field parameter has inverse conduct on the velocity when compared with the Darcy number. In addition, the velocity enriches with an increment in the value of the squeezing parameter. On the other hand, the value of the temperature declines with the enhancement in the value of thermal relaxation time. Moreover, the elevate in thermophoresis parameter leads to an enlargement in the value of nanofluid concentration. In the end, the nano Sherwood number has a dual behavior under the impact of the Brownian motion parameter. from the physical illustration, the current investigation of squeezing flow has great relevance in view of various applications. Such as injection shaping, squeezing film pressure sensors, flow rheostats, bearings, polymer industries, liquid-metal lubrication, compression and injection shaping, and food processing, etc.
The contents of this chapter have been accepted for publication in: Egyptian Journal of Chemistry (2022), doi: 10.21608/EJCHEM.2022.145286.6332.
Chapter 4
Entitled:
“Peristaltic transport of Carreau coupled stress nanofluid with Cattaneo -Christov heat flux model inside a symmetric channel”
We discussed the effect of Cattaneo – christov heat flux on an incompressible flow which is represented by Carreau nanofluid inside a symmetric channel under the porous medium. The impacts of couple stress, heat generation absorption, joule heating, couple stress viscous dissipation, and Soret as well as Dufour numbers are all born in mind. Long wavelength and low Reynold’s number approximations are used in solving the governing system of equations. Furthermore, applying the traditional perturbation method together with the homotopy perturbation technique (HPM) yields the resultant solutions to these equations. A set of graphs illustrates the influences of the different physical parameters on velocity, temperature, and nanoparticles concentration distributions. It is revealed that the increase in the value of the slip velocity parameter reduces velocity. Meanwhile, the higher the value of thermal relaxation time, the less the fluid temperature. Furthermore, when the value of the nano Biot number is enhanced, the value of nanoparticles concentration improves correspondingly.
The contents of this chapter have been accepted for publication in “Journal of Advanced Research in Fluid Mechanics and Thermal Sciences” (2022).
Chapter 5
Entitled:
“Thermal diffusion and diffusion thermo impacts with Cattaneo – christov theories on the peristaltic motion of a non – Newtonian micropolar nanofluid inside a tapered stenosis artery”
We described the influences of Cattaneo – christov heat flux, Soret & Dufour, and Hall current with a vertical alternating current produces an electric field on the peristaltic flow of non - Newtonian micropolar nanofluid inside a tapered stenosed artery. The non – Newtonian fluid obeys the tangent hyperbolic model. The effects of heat generation absorption, joule heating, thermal radiation, chemical reaction, and the permeability of the porous medium are imposed. The slip velocity and thermal slip conditions are assumed. The convective conditions for nanoparticles concentration as well as concentration are selected. The coupled differential systems of equations yield Soret and Dufour features. The assumption of the long wavelength with a low Reynold’s number is employed to transform the governing equations of fluid motion from partial differential equations into an ordinary one. Furthermore, the obtained analytical solutions of these equations are based mainly on applying the regular perturbation method together with the homotopy perturbation method (HPM). The impacts of the various physical parameters on the axial velocity, spin velocity, temperature, nanoparticles concentration, and concentration are illustrated and drawn graphically via a set of graphs. It is noticed that the velocity dwindled with an enrichment in the magnitudes of both Hartman number and electromagnetic parameter. Whereas, the axial velocity elevates with an enlargement in Darcy number, tapering angle, and Hall parameter. The spin velocity declines with the increment in the microrotation parameter. The escalating in thermal relaxation time causes a decaying impact on the temperature. Furthermore, enhancement in the nano Biot number leads to a declination in the magnitude of nanoparticles concentration.
The contents of this chapter have been submitted for publication.
Chapter 6
Entitled:
“Impacts of Hall and ion slip Currents with Cattaneo – christov Features on the Peristaltic Blood Flow of Sisko Micropolar Nanofluid inside an Annulus through a Porous Medium”
We exposed the impact of Cattaneo – christov heat and mass fluxes on the peristaltic blood influx. The impacts of Hall and ion slip currents are imposed. The Sisko micropolar nanofluid through a porous medium is also presumed. The influences of heat generation absorption, heat radiation, and chemical reaction are presumed. The slip conditions for both velocity and temperature are postulated. The convective conditions for nanofluid volume fraction and concentration are examined. The coupled differential systems of equations yield Soret and Dufour features. The supposition of the long wavelength with a low Reynold’s number is applied to convert the system of partial differential equations that govern the fluid motion to an unpretentious formula (ordinary differential equations). Over and above, the resultant analytical solutions of these equations are tackled essentially by employing both procedures of the conventional perturbation and the homotopy perturbation method (HPM). impacts of the diverse physical parameters on the resultant distributions are elucidated and exposed graphically through a group of graphs. It is recorded that the axial velocity dwindles with an escalation in the magnitudes of the Hartman number. Meanwhile, it elevates with rising in the Sisko parameter. The spin velocity dwindles with the elevating in the microrotation parameter. The enriching in thermal relaxation time leads to a dwindling influence on the fluid temperature. Moreover, escalating in the mass Biot number causes a declination in nanoparticles volume fraction. This study is very significant in diverse medical implementations, as gold nanoparticles are utilized in the remedy of cancer tumors.
The contents of this chapter have been submitted for publication.