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Home > Numerical Study of a Few Problems for Steady and Incompressible Flows of Micropolar Fluids

Numerical Study of a Few Problems for Steady and Incompressible Flows of Micropolar Fluids

Thesis Info

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Author

Shafique, Muhammad

Program

PhD

Institute

Gomal University

City

Dera Ismail Khan

Province

KPK

Country

Pakistan

Thesis Completing Year

2011

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1795

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726781362

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The present research work is the numerical study of some problems in micropolar fluids flow. The micropolar fluids are viscous fluids having five additional coefficients of viscosity as compared to usual Newtonian fluids. In the micropolar fluid theory, in addition to the usual classical field of velocity, there are two supplementary field variables, the micro-rotation ν (or spin) and the gyration parameter j which have been introduced to elucidate the kinematics of micro-motions. A micropolar fluid contains rotating micro-constituents that cause the fluid to exhibit non-Newtonian behavior. Micropolar fluid model has been found useful in the study of flows of exotic lubricants, colloidal suspensions, polymeric fluids, liquid crystals, additive suspensions, body fluids, turbulent shear flows and flows in capillaries and micro channels. The study investigates the numerical solution of a few problems for steady, laminar and incompressible flow of both the micropolar fluids and Newtonian fluids. The body couples are neglected in case of micropolar fluids flow. The similarity transformations have been used to reduce the governing partial differential equations of motion in to ordinary differential equations. The resulting boundary value problems have been solved by using appropriate numerical techniques. The central differences are applied to these differential equations. The difference equations thus obtained are solved by using Successive Over Relaxation (SOR) method and Simpson’s (1/3) rule. The numerical results have been shown both in tabular as well as in graphical forms. To obtain accuracy of the present numerical results, the computation has been carried out on three different grid sizes. The purpose of this study is to present the numerical solution of different types of flow problems in micropolar fluids as well as in computational fluid dynamics by using appropriate numerical techniques which are straightforward, easy to program and economical. It has been concluded that our numerical scheme works well to solve various flow problems of Newtonian and micropolar fluids. Moreover, the present results of both Newtonian and micropolar fluids are calculated up to six decimal place. The corresponding results of Newtonian fluids for each problem considered have been obtained and presented for comparison purposes.
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مولانا عبدالرشید نعمانی

مولانا محمد عبدالرشید نعمانی
اگست کے آخری عشرہ میں پاکستان سے یہ اندوہ ناک خبر آئی کہ مولانا محمد عبدالرشید نعمانی جے پوری کا کراچی میں انتقال ہوگیا، اناﷲ وانا الیہ راجعون۔
مولانا کی نظر دینی علوم تفسیر، حدیث اور رجال پر اچھی اور گہری تھی۔ ان کی تعلیمی زندگی کا کچھ زمانہ دارالعلوم ندوۃ العلماء لکھنؤ میں بھی بسر ہوا۔ ملک کی تقسیم سے پہلے اور بعد میں بھی ان کا تعلق ندوۃ المصنفین دہلی سے رہا۔ یہیں سے ان کی کتاب لغات القرآن شایع ہوئی جو ایک مفید قرآنی خدمت ہے، یہ حروف معجم پر مرتب کی گئی ہے اور چھ جلدوں میں مکمل ہوئی ہے۔ شروع کی چار جلدیں جو الف سے شروع ہو کر ع پر ختم ہوئی ہیں مولانا نعمانی کے قلم سے ہیں اور آخری دونوں جلدیں مولانا سید عبدالدائم جلالی نے مرتب کی ہیں، پہلی جلد کے شروع مولانا عبدالرشید نعمانی کا بسیط مقدمہ ہے جس میں کتاب کی نوعیت اور اس کی ترتیب میں ملحوظ رکھے جانے والے امور کے علاوہ اپنی محنت و جاں فشانی وغیرہ کا ذکر کیا ہے۔ دہلی میں قیام کے زمانے میں ماہنامہ برہان میں ان کے مضامین بھی شایع ہوئے۔
تقسیم کے چند برس بعد وہ کراچی میں متوطن ہوگئے تھے، یہاں انہوں نے امام ابن ماجہ پر جو عالمانہ و محققانہ کام انجام دیا وہ ان کا بڑا کارنامہ ہے، جس سے حدیث کا کوئی طالب علم مستغنی نہیں رہ سکتا، اردو میں ان کی کتاب ’’امام ابن ماجہ اور علم حدیث‘‘ اور عربی میں ’’ماتمس الیہ الحاجۃ لمن یطالع سنن ابن ماجہ‘‘ نور محمد اصح المطبع و کارخانہ تجارت کتب کراچی نے شایع کی۔ یہ دونوں تصانیف نہ صرف امام ابن ماجہ کے حالات و کمالات اور ان کی سنن کی خصوصیات کا مرقع ہیں بلکہ ان میں فن حدیث...

Status of Abandoned Children: A Comparative Study of Islamic and Pakistani Law

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Synthesis, Characterization and Fabrication of Metal Organic Framework Composites for Adsorption and Electrochemical Applications

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