احصاء - دكتوراة
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Item Geometrical Reformulation of some Equations of Fluid Mechanics(Al-Neelain University, 2015) Mansour Hassan MansourAbstract The aim of this thesis is to explain some of the connections between fluid mechanics and differential geometry and to shed light on formulation of classical fluid mechanics in a differential geometric language. The thesis presents a reformulation of some of the most basic entities and equations of fluid mechanics, the continuity equation and the momentum equation of motion, in a modern differential geometric language using calculus of exterior differential forms on manifold (exterior calculus). Also, the study investigates the integrability of some fluid problems from geometrical perspective, with particular attention to the Euler equations of motion.Item Convective Heat Transfer in Micropolar Fluid in Presence of Radiation(Al-Neelain University, 2009) Mohamed Elhafiz MohamedAbstract In this thesis we study the developing theory of micropolar fluids and compare that with ordinary fluids, and the of heat transfer mechanism in boundary layer micropolar fluids, after reviewing of boundary layer in ordinary fluid as well as magnetohydrodynamics. Mainly the effects of radiation on the flows and heat transfer of an electrically conducting micropolar fluid past semi-infinite vertical plate in presence of uniform magnetic field are considered. The non-linear partial differential equations governing the problem under consideration are converted into a system of non-linear ordinary differential equations by means of similarity transformations, the resulting system of coupled non-linear ordinary differential equations, is solved numerically for a range of values of radiation, magnetic, microrotation and vortex viscosity parameters and also, Grashoff’s number, is obtained by applying an efficient numerical technique based on shooting method, using (mathematica pages). The effects of these parameters are examined on the velocity of the fluid, temperature distribution and angular velocity of microstructure, as well as the coefficient of heat flux and shearing stress at the plate. The velocity of fluid, angular velocity and temperature profiles are shown graphically and the numerical results are obtained. 4 الخلاصة نافشت الرسالة النظرية والتطبيق فى الموائع الميكروبولرية ( دقيقة القطبية ) و مقارنتها بالموائع التعتيادية . وبصسسورة رئيسسسية درست انتقال الحرارة جوار جدار راسسى نصسف لنهسائى وتساثيرات العشعاع فى وجود مجال مغناطيسى تعلى حركسة المسائع, وفسى هسذا حلت معادلت النظام تعدديا بعد تحويلها من معادلت تفاضلية جزئية غير خطية التماثلية الى معادلت تفاضلية تعادية غيسر خطيسة وامكسن رسسم منحنيسات توزيسع سسرتعات النمسوذج للمسائع, السسرتعة الزاويسة للجزئيات و توزيع الحرارة لقيم مختلقسة للعوامسل الستى تتحكسم فسى الحركة. كما امكن ايضا حسساب القيسم العدديسة لمركبسات الحتكساك .تعلى جدارومعامل انتقال الحرارة