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العنوان
Solutions of Some Problems of Flow of Different Fluids with Heat and Mass Transfer over Different Surfaces /
المؤلف
Alhanafi, Ahmed Mohammed Sedki Ahmed.
هيئة الاعداد
باحث / Ahmed Mohammed Sedki Ahmed Alhanafi
مشرف / Nabil T. M. El-Dabe
مشرف / Elsayed M. A. Elbashbeshy
مشرف / Ismail Kaoud Abdel-Aziz Yousef
مناقش / Nabil T. M. El-Dabe
مناقش / Emad M. Abo-Eldahab
مناقش / Ismail K. A. Youssef
تاريخ النشر
2016.
عدد الصفحات
246 p. :
اللغة
الإنجليزية
الدرجة
الدكتوراه
التخصص
الرياضيات التطبيقية
تاريخ الإجازة
1/1/2016
مكان الإجازة
جامعة عين شمس - كلية العلوم - Mathematics
الفهرس
Only 14 pages are availabe for public view

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Abstract

The fluid flow with heat and mass transfer along different surfaces has drawn consideration not only due to their extensive relevance in chemical, mechanical, civil, nuclear and biochemical engineering but also because of their relevance to flow of blood through arteries and veins. Similarly, the flow through the porous medium has become increasingly important due to its applications in many engineering and biological phenomena including flow behavior through human organs like lungs, kidneys and lymphatic. Continuously moving surface or stretching permeable surface with high temperature than that of ambient temperature has many engineering applications. Such applications include drawing of wires, laments spinning, extrusion of metal, growth of crystals, continuous casting, fiberglass production, pulsating diaphragms modeling, and separation of isotopes, irrigation and manufacturing of paper.
While working with the fluids, we cannot address the subject of heat and mass transfer, unless we include the mechanisms of fluid flow to our discussion. These mechanisms can be responsible for the movement of the fluid. These mechanisms include the pressure gradient, movement of surface which the fluid is resting upon or the surfaces which the fluid is contained in and buoyancy force resulting due to density gradient. The density gradient can be either due to the temperature difference or due to concentration difference. These important mechanisms are studied in this dissertation. These basic mechanisms are pressure gradient i.e. pressure stress work, surface motion i.e. contracting or expanding walls and buoyancy force i.e. temperature difference or concentration difference. The other important feature in these problems is the different type of conditions imposed on the surfaces under consideration.
The coupling of these phenomena gives rise to very interesting results in term of velocity, temperature and concentration profiles. The source of thermal buoyancy force either due to the heating or cooling of a deforming surface or due to variable concentration surface may alter significantly the flow field and the fields of temperature and concentration. This, as a result, changes the behavior of heat and mass transfer in any process of production and manufacturing. The convective transfer of heat along different surfaces is primary area of interest for researchers and has many applications. With the recent improvements in nanotechnology, the production of particles with sizes on the order of nanometers (nanoparticles) can be achieved with relative ease. As a consequence, the idea of suspending these nanoparticles in a base liquid for improving thermal conductivity has been proposed recently. Such suspension of nanoparticles in a base fluid is called a nanofluid. The boundary layer of Cu-nanofluid flow and heat transfer over an unsteady moving surface with variable thickness has been investigated in this thesis. The effects of magnetic field and heat source or sink are considered.
Research activities aiming to explore fluid physics at nano and micro scales have been increasing over the past 20 years. There are existing literatures that have analyzed fluid mechanics in microchannels and micromachined fluid systems (e.g. pumps and valves) using Navier–Stokes equations. Fluid flows differently in the micro scale than that in the macro scale. There are situations in which the Navier–Stokes equations, derived from classical continuum, become incapable of explaining the micro scale fluid transport phenomena. The reason is that when the channel size is comparable to the molecular size, the spinning of molecules, which have been observed in molecular dynamics simulations, affects significantly the flow field. This effect of molecular spin is not taken into account in the Navier–Stokes equations. In micropolar theory each particle has a finite size and contains a microstructure that can rotate and deform independently, regardless of the motion of the centroid of the particle. The formulation of the micropolar theory has additional degrees of freedom, gyration, to determine the rotation of the microstructure. Hence, the balance law of angular momentum is given for solving gyration. This equation introduces a mechanism to take into account the effect of molecular spin. The micropolar theory thus represents a promising alternative approach to numerically solving micro scale fluid dynamics that can be much more computationally efficient than the macro dynamics simulations. Unsteady boundary layer flow and heat transfer of micropolar fluid flow over nonlinearity stretching surface with variable thickness through non Darcian media in the presence of magnetic field and heat source or sink have been investigated throughout this work.
In this work, we have studied flow of different fluids with heat and mass transfer over different surfaces. Mainly the numerical algorithms are used to obtain the solution of problems but to ensure the validity; comparisons with previous studies are also given. The numerical methods used are namely: method of shooting with fourth Runge-Kutta scheme and finite difference method with Newton’s linearization scheme.
This thesis consists of eight chapters, references, and Arabic and English summaries
Chapter 1:- A general introduction to fluid mechanics and numerical methods are considered. This introduction consists of general definition of fluid mechanics and basic concepts and governing equations of the fluid. Also, the heat and mass transfer and the motion through porous media are introduced. The basic equations of different fluids flow i.e. magneto- hydrodynamic flow, nanofluid flow and micropolar fluid flow are discussed. Also a special introduction of some numerical methods is given. In this thesis, we used two methods, shooting method with Runge-Kutta scheme and an implicit finite difference technique with Newton s linearization method.
Chapter 2:- An analysis is made to investigate the mass transfer over a stretching surface embedded in a porous medium in the presence of first order chemical reaction. Using similarity transformation, the governing partial differential equations are transformed into a set of ordinary differential equations which solved by shooting method. Comparisons with previously published work on special cases of the problem are performed and the results are found to be in excellent agreement. It is observed that the local mass transfer and concentration profile are very sensitive to change in the values of reaction rate parameter, permeability parameter, Schmidt number and concentration parameter. The contents of this study have been published in (International Journal of Computational Engineering Research 2014, 4(2):20-28).
Chapter 3:- An analysis is made to study the mass transfer in boundary layer flow past a moving permeable flat plate embedded in porous medium with variable wall concentration in presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a set of ordinary differential equations by using similarity transformations which are solved numerically by two different methods. The first method is the Keller-Box technique which is an implicit finite difference method with Newtonian linearization scheme and the second method is based on fourth order Runge-Kutta iteration scheme with shooting method. It is found that the existence of dual solutions exists when the surface and the fluid move in opposite directions. The results indicate that the increase of porous parameter decreases the variation of a velocity profiles and the variation of a skin friction coefficient while it increases both concentration profiles and concentration gradient at the surface. It is due to the presence of a porous medium which increases the resistance to flow resulting in decrease in the flow velocity and increase in the solute concentration. This study has been published in (American Journal of Computational and Applied Mathematics 2014, 4(4): 141-153).
Chapter 4:-Temperature dependent viscosity and Viscous Dissipation effects are considered on hydromagnetic (MHD) natural convection flow from horizontal circular cylinder immersed in an electrically conducting fluid with viscosity proportional linearly with the temperature in the presence of pressure stress work and heat generation. The partial differential governing equations are transformed to dimensionless forms and solved numerically by an implicit finite difference technique with Newton’s linearization method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. To support the accuracy of the numerical results, a comparison is made with known results from the open literature for some particular cases of the present study and the results are found to be in good agreement. This study have been published in (Journal European Scientific Journal 2014, 10(36), 81-102).
Chapter 5:- Effects of pressure stress work and temperature dependent viscosity in natural convection flow around a sphere with viscous dissipation and Newtonian heating in the presence of a magnetic field and heat generation have been investigated. The governing boundary layer equations are transformed into non-dimensional forms and solved numerically. We have focused our attention on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number. Comparison of some special cases of this study is made with previously published results and found to be in a good agreement. The results of this study have been submitted for publication in “Heat Transfer Research” journal.
Chapter 6:- chapter 6 is divided into two parts. In part 1, the effects of thermal radiation and pressure stress work on natural convection flow around a sphere embedded in a porous medium are considered. The nonlinear partial differential equations governing the problem is solved numerically using Matlab code based on Keller box method. The results focused on the effects of the radiation parameter, the Darcy number, the surface temperature parameter, Prandtl number and stress work parameter on the skin friction coefficient, the local Nusselt number, and velocity and temperature distributions. This study is submitted for publication in “Heat and mass transfer” journal.
In part 2, Newtonian heating and thermal radiation on natural convection flow around a sphere embedded in a porous medium with pressure stress work is considered. The governing boundary layer equations are solved numerically. Numerical results have been shown through some tabular data and graphically through some figures for some selected values of parameters set consisting of radiation parameter, pressure stress work parameter, Newtonian heating coefficient and Prandtl number. The contents of this study have been submitted for publication in “Thermal Science” journal.
Chapter 7:- The boundary layer of Cu-nanofluid flow and heat transfer over an unsteady stretching surface with variable thickness has been investigated. The effects of magnetic field and heat source or sink are considered. The governing boundary layer equations are transformed into non-dimensional forms of nonlinear differential equations and solved numerically. Comparisons with previously published work are performed. The numerical results for the skin friction and the rate of heat transfer are shown through tabular forms while the velocity and temperature profiles are plotted and discussed for different values of the parameters such as the unsteadiness parameter, a magnetic field parameter, heat generation parameter, surface thickness parameter, nonlinearity surface parameter and nanoparticle volume fraction. This study have been submitted for publication in “Meccanica” journal.
Chapter 8:- Unsteady boundary layer flow and heat transfer of micropolar fluid flow over nonlinearly stretching surface with variable thickness through non Darcian media have been investigated. The effects of magnetic field and heat source or sink are taken in considerate. The governing boundary layer equations are transformed into non-dimensional forms of nonlinear differential equations and solved numerically using Keller box method. Comparisons with previously published work are performed and excellent agreement is obtained. The numerical results for the skin friction and the rate of heat transfer are shown through tabular forms while the velocity and temperature profiles are shown graphically through some figures and discussed for different values of the physical parameters of the problem. The contents for this study have been submitted for publication in “International Journal of Heat and Fluid Flow”.