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Exact Solutions of Different Motions of Non-Newtonian Fluids With/Without Fractional Derivatives

Thesis Info

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Author

Zafar, Azhar Ali

Supervisor

Constantin Fetecau

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2525/1/2578S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726150015

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In the present thesis, we will present the analytical studies of some fluid flow models. We wish to analyze two main scenarios, one of which deals with non-fractional (or- dinary) models and the other with fractional models for the flow of non-Newtonian fluids. We use classical computational techniques capable of accurately operating in order to obtain exact analytical solutions. Our studies include Couette flows of a Maxwell fluid under slip conditions between the fluid and walls. The motion of the bottom plate is assumed to be a rectilinear translation in its plane while, the upper plate is at rest. Two particular cases, namely translation with constant velocity and sinusoidal oscillations of the bottom plate are considered. Next, unsteady motions of Oldroyd–B fluids over an infinite plate between two side walls will be investigated. The motion of the fluid is due to the bottom plate that applies two types of shears to fluid. Extending our studies, we look at the unsteady magnetohydrodynamic (MHD) flow of fractional Oldroyd–B fluid between two side walls perpendicular to a plate. Expressions of the obtained solutions are presented in a series form in terms of the generalized G functions. Finally, the unsteady flow of an Oldroyd–B fluid with frac- tional derivative model between two infinite coaxial circular cylinders is studied. The motion of the fluid is produced by the inner cylinder that, at time t = 0+ , applies a time dependent longitudinal shear stress to the fluid. Expressions of the obtained results are presented in a series form in terms of the generalized G and R functions. In all the flow models, we obtained the exact analytical solutions for motions with technical relevance, both for the velocity field and the shear stress(es). These solu- tions corresponding to some flows in which either velocity or the shear stress is given on the boundary are established for different kinds of non-Newtonian fluids as well as for fractional models. The exact analytical solutions that have been presented in all the fluid flow models satisfy all imposed initial and boundary conditions. Further on, the flow properties of models and the comparison to other models are highlighted with graphical illustrations.
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بھانویں خواب اندر اوہ آگئے

بھانویں خواب اندر اوہ آگئے
ہک وار تاں من پرچا گئے
پا سرمہ نین نشیلیاں وچ
نیناں دے تیر چلا گئے
توں لبھناں ایں پھل بہاراں دے
ساڈے اگلے وی کُرما گئے
اساں رو رو حال سناندے رہے
اوہ چپ دے جندرے لا گئے
ساڈے کولوں آ کے ٹر گئے
تارے چٹے دینہہ وکھا گئے
سُن ناں کرونا وائرس دا
لوکی حجریاں وچ سما گئے

سائنس اور روحانیت کی تمثیل: ایک تحقیقی جائزہ

Spirituality is usually understood as a way of being that flows from a certain profound experience of reality, which is known as ‘mystical’, ‘religious’, or ‘spiritual’ experience. There are numerous descriptions of this experience in the literature of the world’s religions, which tend to agree that it is a direct, non-intellectual experience of reality with some fundamental characteristics that are independent of cultural and historical contexts. Spiritual and scientific quests are two complementary inquiries into reality. Any feeling of antagonism between them is a product of a narrow vision. Science deals with what is measurable; religion is the quest for discovering and understanding the immeasurable. A scientist is not intelligent if he denies the existence of the immeasurable. There is nothing that is anti-science but there is a lot that is beyond science. The two quests have to go hand in hand. We not only need to have an understanding of the laws that govern the phenomena occurring in the external world around us but also we need to discover order and harmony in our consciousness. Human understanding is incomplete unless it covers both aspects of reality: matter as well as consciousness. Indeed the division between the scientific and spiritual quests is itself the creation of the human mind. Reality is one undivided whole which includes both matter and consciousness. Our thoughts, being limited by our experience, divide the external world from the inner world of our consciousness, in much the same way as our mind divides time from space though they are both two aspects of a single continuum۔

Political Leadership: A Case Study of Benazir Bhutto

For the advancement of the cause of democracy, Benazir Bhutto faced a variety of challenges, trails, contests and resistances prior to her becoming the first woman prime minister of Pakistan. The watershed of this first struggle was bound by an era covered by supposedly a dictatorial regime from 1977 to 1988. In terms of realpolitic, this move was a complex and significant ideological struggle based on social justice against conservative forces and status-quo, braced by some international influential clusters. As a resilient woman political leader, she managed to cope with all the crises. The study in hand is the in-depth analysis of the struggle of Benazir Bhutto for upholding the democratic forces. Data sources included Focus Group Discussions with party workers and political leaders, in-depth interviews with historians and civil society members, and content analysis of documents like letters (written by Benazir Bhutto to various party workers and by the author to Benazir Bhutto), reports, Peoples Party’s constitution, press releases by Benazir Bhutto, media documentaries and other published material relevant to the topic. Analysis of the data revealed that Benazir Bhutto confronted significant hardships and challenges to restore democracy in Pakistan. Despite ruthlessness of the ruling regime, betrayals of her party men and unfavorable circumstances she managed to cope with all the difficulties with her charisma and leadership qualities. She successfully exhibited her visionary skills, persistence, determination, influential personality, and immense courage. As part of her reconciliation and resilience, she joined hands with opponents; she was able to bring all conservative clusters on board on its voyage to democracy. The resilience demonstrated by Benazir Bhutto in her political struggle could be a model for political practitioners and political leadership xviii in Pakistan. This research concludes by suggesting for doing scientific studies about the Bhutto legacy of later time periods and making a comparative analysis for drawing lessons for the political landscape of Pakistan. Similarly, in the struggle for democracy in Pakistan, there are many other leaders. In-depth analysis of their terrain is in order to develop strategies for political struggle.