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Mathematics: Unsteady Flow of Non-Newtonian Fluid in a Curved Pipe With Rectangular Cross-Section

 

Unsteady Flow of Non-Newtonian Fluid in a Curved Pipe With Rectangular Cross-Section

Morad M.A. and Abdul-Hadi A.M.

Department of Mathematics, College of Science, University of Baghdad. Baghdad-Iraq.

    Abstract

This study is concerned with the unsteady flow of non-Newtonian, viscous, incompressible fluid in a curved pipe with rectangular cross-section, under the action of pressure gradient. An orthogonal coordinate system has been used to describe the fluid motion and it is found that the motion equations are controlled by three parameters namely; Dean number, non-Newtonian parameter and frequency parameter. Solution for the secondary flow and the axial velocity are droved as perturbation over straight pipe. Firstly the expansion was in terms of Dean number and secondly in terms of frequency parameter. Perturbation equations are solved by using variation method namely, Galerkin's method, after eliminating the dependency on time. The solutions have been developed in Cartesian coordinate for harmonic and biharmonic equations. The effect of the non-dimensional parameters mentioned above on the secondary flow, the axial velocity and the flow in the centre plane is considered. In this study we covered the steady state under consideration.

الخلاصة

     في هذا البحث نتناول تحليل الجريان اللامستقر لمائع لا نيوتيني في أنبوب منحنى ذو مقطع مستطيل الشكل.لقد بينا أن ثلاثة أعداد لابعدية تتحكم بمعادلات الحركة وهي ,عدد دين,العدد اللا نيوتيني ومتغير التكرار.أستخدمت طريقة تكرارية لحل معادلات الحركة(كالريكن).قدمنا دراسة تحليلية لتأثير الاعداد الانفة الذكر على كل من الحركة الثانوية والسرعة المحورية.




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