الفهرس 
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Abstract
Rotating disk flow along with heat transfer is one of the classical problems of uid mechanics, which has both theoretical and practical value. In respect to its practical value, it has dierent applications in many areas, such as rotating machinery, lubrication, oceanography,
computer storage devices, viscometry, gas turbine engines,ywheels,gears, and brakes etc. On the other hand, its theoretical value appears
through the interest of the great researchers of mathematics to this problem. Accordingly, exact solutions for this problem in a variety of situations have been obtained by a number of researchers, such as [54, 57].
Pioneering study of uid ow due to an in nite rotating disk was carried by Von Karman 1921 [70]. Von Karman gave a formulation
of the problem and then introduced his famous transformations which reduced the governing partial dierential equations to ordinary dierential
equations and solved them by approximate integral method. In 1934, Cochran [15] pointed out that Von Karmons momentum integral
solution contained errors. He obtained more accurate results by patching two series expansion. In 1966, Benton [12] improved Cochrans
solutions and solved the unsteady problem.
Heat transfer problem for rotating disk systems under dierent situations was analyzed by many authors [5, 6, 7, 8, 27, 35, 39, 47, 56, 58,
59, 64]. The importance of heat transfer from a rotating body can be ascertained in cases of various types of machinery, for example computer
disk drives and gas turbine rotors. The problem of heat transfer from a rotating disk maintained at a constant temperature was rst considered by Millsaps et. Al. 1952 [43] for the values of Prandtl number (Pr) between 0.5 and 10 in the steady state. Later Sparrow et. Al.1971 [62] extended this work for a range 0.1 < Pr < 100. Recently, Atiii
tia [8] studied the steady ow over a rotating disk in porous medium with heat transfer. Very recently, Shahmohamadi et. Al. [57] have
presented totally analytical solutions for steady
ow over a rotating disk in porous medium with heat transfer using the combination of the
variational iteration method and the Pade approximate (VIM-Pade).
The problem still attracts the attention of researches from various disciplines, since rotary type ow has many applications in dierent
elds. In the above mentioned studies the radiation eect is ignored.
When technological processes take place at high temperatures, thermal radiation heat transfer become very important and its eects cannot
be neglected (Siegel et. Al. [60]; Necati [44]). In the case of high temperature, radiation e
ects are quite signi cant. The thermal radiation
of gray uid which is emitting and absorbing in a non-scattering medium has been examined by [2, 21, 26, 29, 40, 53, 67].
The magnetohydrodynamic (MHD)
uid ow problem of a rotating disk nds special places in several science and engineering applications,for instance, in turbomachinery, in meteorology, in computer disk drives and nuclear reactors . The rst traceable interest in MHD
ow was in 1907, when Northrup [46] built a MHD pump prototype.
The hydromagnetic ow due to a rotating disk was rst investigated by Katukani [31]. Some interesting results on the eects of the magnetic
eld on the steady ow due to the rotation of a disk of in nite or nite extent was pointed out by El-Mistikawy et. Al. [22] and Ariel [4]. Kumar et. Al. [36] and Turkyilmazoglu [69] covered the e
ects of a uniform external magnetic eld on the steady ow over a rotating
disk.
As it shown that the rotating disk ow along with heat transfer is an important topics, so this thesis is devoted to study the dierent eects on steady
ow over a rotating disk in porous medium with heat transfer. This thesis consists of four chapters. The aims of them are mentioned in the following paragraphs and it should be noted that the
solution of the current results is obtained by using Fortran programme and then the present graphics is drawn by using Excel.
The introductory Chapter 1 is considered as a background for the material included in the thesis. The purpose of this chapter is to
present a short introduction on the uid mechanics, a brief survey of uid properties and the basic
ow equations. Moreover, it contains a
short survey of some needed concepts of the material used in this thesis with a great of many enrichment details.
The goal of Chapter 2 is to study the eect of porous medium on the steady ow over a rotating disk with heat transfer. In this study the governing equations are transformed into nonlinear ordinary dierential equations by applying the Von Karman [70] similarity transformation.
Moreover, the resulting equations are then solved numerically by the nite dierence method. Furthermore, numerical and graphical
results for the velocity and temperature pro les are presented and discussed for various parametric conditions. Finally, comparisons with
previously published works are performed and showed that the present results apply with White’s results [71]. Some results of this chapter
are accepted for \Journal of Applied Sciences Research”.
The purpose of Chapter 3 is to study steady
ow over a rotating disk in porous medium with heat transfer and radiation eect. The Von Karman [70] similarity transformation is applied to transform the governing equations into nonlinear ordinary dierential equations. In addition, the resulting equations are then solved numerically by the nite dierence method. Moreover, numerical results are presented the distribution of velocity, and temperature pro les. The eects of varying
the Prandtl number, the radiation parameter and porosity parameter are determined. Furthermore, comparisons the present results with Childs’s results [14], Rahman’s results [51] and Owen and Rogers’s results [49] are showed that the present results have high accuracy and are found to be an excellent agreement. At the end of this chapter the
conclusions are summarized. The work in this chapter is preparing to submission.
The main aim of Chapter 4 is to study the steady
ow over a rotating disk in porous medium with heat transfer and magnetic eect. In addition, the governing equations are transformed into nonlinear ordinary dierential equations by applying the Von Karman [70] similarity
transformation and then solved numerically by applying the nite difference method. Moreover, the solutions are found to be governed by
four parameters, the magnetic parameter M, the porosity parameter M, the Prandtl number Pr and the thermal radiation parameter Rd.
We have compared the present radial, tangential and axial velocities and temperature distribution with the previously published work Anjali
Devi et. Al. [3], at dierent values of the M, M, Rd and Prparameters. Furthermore, numerical and graphical results for the velocity and temperature pro les are presented and discussed for various
parametric conditions. Finally, the conclusion is summarized. The work in this chapter is preparing to submission.