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Home > Some New Results in the Theory of Fractional Second Grade and Ordinary Oldroyd-B Fluids

Some New Results in the Theory of Fractional Second Grade and Ordinary Oldroyd-B Fluids

Thesis Info

Access Option

External Link

Author

Imran, Muhammad

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2007

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1727

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727204082

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In this thesis some results regarding the flow behavior of second grade fluid with fractional derivatives and ordinary Oldroyd-B fluid under different circumstances have been studied. Firstly, some basic concepts regarding fluid motion and integral trans- forms have been discussed. Then the fluid motion of fractional second grade and ordinary Oldroyd-B fluids through a cylinder and annulus is studied. In chapter 2, the motion of fractional second grade fluid through an infinite cir- cular cylinder has been studied. After time t = 0+ the fluid motion is produced by rotating the circular cylinder about its axis. Laplace and finite Hankel transforms are used to find exact solutions. The similar solutions for Newtonian and ordinary second grade fluids are obtained as limiting cases of general solutions by making κ → 1 and α1 → 0, respectively κ → 1 . Chapter 3 intends to establish exact solutions for the unsteady flow of a fractional second grade fluid between two infinite coaxial circular cylinders. The general expres- sions for velocity and shear stress are obtained by using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder which is ro- tating around its axis due to a time-dependent torque per unit length 2πR1 at2 . The solutions that have been obtained satisfy all imposed initial and boundary conditions. For κ → 1, respectively κ → 1 and α1 → 0, the corresponding solutions for ordinary second grade and Newtonian fluids, performing the same motion, are obtained as limiting cases. In chapter 4 the unsteady helical flow of an Oldroyd-B fluid through an infinite circular cylinder is studied. The motion of the fluid is produced by cylinder that, after time t = 0+ , is subject to both torsional and longitudinal time dependent shear stresses. The general solutions are presented in series form in terms of Bessel functions J0 (•), J1 (•) and J2 (•), and satisfy all imposed initial and boundary conditions. The corresponding solutions for Newtonian, second grade and Maxwell fluids are obtained as limiting cases of general solutions. Finally, the obtained solutions are compared by graphical illustrations and the influence of material parameters on the fluid motion is also underlined. Chapter 5 concerns with the unsteady Taylor-Couette flow of an Oldroyd-B fluid in an annulus due to a time-dependent torque applied to the inner cylinder. Motion is studied by means of finite Hankel transforms. The exact solutions are presented in series form in terms of usual Bessel functions, satisfy both the governing equations, and all imposed initial and boundary conditions. Similar solutions for Newtonian, second grade and Maxwell fluids performing the same motion are obtained as limit- ing cases of general solution. Finally, some characteristics of the fluid motion, as well as the influence of pertinent parameters on the behavior of the fluid motion, analyzed by graphs.
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سیدسجاد حیدر یلدرم

سید سجاد حیدریلدرم مرحوم
۱۲؍ اپریل ۱۹۴۳؁ء کی رات کو سید سجاد حیدر مرحوم نے جو ادب کی دنیا میں یلدرم کے نام سے مشہور تھے، قلب کے عارضہ سے دفعتہ وفات پائی، یہ علی گڑھ کالج کے پرانے تعلیم یافتوں میں اور اسی تعلق سے کالج کے ان چند طالب علموں میں تھے جنہوں نے مولانا شبلی مرحوم کے درس اور صحبت سے شعر و ادب کا ذوق حاصل کیا تھا، مرحوم مولانا کے درس کے اس قسم کے واقعات کو مزے لے لے کر بیان کیا کرتے تھے، ان کا اصل وطن نہٹور (یوپی) میں تھا، ۱۹۰۱؁ء میں بی، اے کی سند پاکر تعلیم سے فراغت پائی۔
ہماری زبان میں اس وقت ادب لطیف کا جو رواج ہے، اس کے پرانے لکھنے والوں میں سب سے پہلا نام سید حیدر مرحوم کا ہے اور چونکہ قادر مطلق کو ان سے یہ کام لینا تھا، اس لئے ان کی زندگی میں اس کا مناسب سامان بھی پیدا کردیا یعنی یہ کہ کالج کے زمانہ ہی میں ان کو ترکی پڑھنے کا خیال ہوا، علی گڑھ میں نواب محمد اسمٰعیل خان صاحب رئیس علی گڑھ کے والد بزرگوار ہجرت کرکے مکہ معظمہ چلے گئے تھے، وہیں نواب محمد اسمٰعیل خاں صاحب کی تعلیم و تربیت ہوئی، اس زمانہ میں ترکی وہاں کی سرکاری زبان تھی، اس لئے ان کو ترکی بھی پڑھائی گئی اور جب وہ ہندوستان آئے تو وہ ترکی ادب کے گویا نمائندہ ہوکر آئے، چنانچہ سرسید کے ’’تماشائے عبرت‘‘ میں وہ اسی ہیئت سے اسٹیج پر آئے ہیں اور معارف علی گڑھ میں جس کے وہ شریک ایڈیٹر تھے، وہی ترکی ادب کی اشاعت کا ذریعہ بنے۔
بہرحال سجاد حیدر مرحوم نے انہی سے ترکی زبان سیکھی اور اس کا یہ فائدہ ان کو پہنچا کہ سرکار انگریزی نے ان کو علی گڑھ...

فتح مکہ میں آنحضرت ﷺکا سیاسی کردار

The conquest of Makkah is an extraordinary and unprecedented event of the Muslim history in which the Holy Prophet (PBUH) demonstrated his political discernment and strategy that Islam is an unassailable entity that can never be eradicated. Your democratic engagement in the conquest of Makkah facilitated the establishment of a government of peace and reconciliation in Arabia, which led the Arabs to grow submissive to the Sharia. They all became Muslims as a consequence of your political participation; hence, Makkah's government was then altered and structured accordingly with Islamic principles. The political role of the Holy Prophet (PBUH) in the conquest of Makkah has been addressed in this article. The methodology chosen to go ahead with this piece was astounding. However, the challenge faced during the research was: Muslims in the modern age encounter a slew of political issues. And as a result, Politicians, if they try, can overcome their challenges by remembering the Holy Prophet's (PBUH) political involvement in the Conquest of Makkah. Keywords: The Holy Prophet (PBUH), political problems, The Conquest of Makkah, Modern era.

Plasma Proteomics Analysis of Hydroxyurea Treated Patients Suffering from Thalassemia

β thalassemia is the most prevalent autosomal recessive disorder characterized by absence or reduced production of hemoglobin (Hb) levels, primarily caused by mutations on β globin locus. β thalassemia is heterogeneous at the molecular level, presenting variable phenotypes accompanied with severe medical complications. Current standard of care for clinical management of β thalassemia includes regular, long-life safe blood transfusion along with appropriate iron chelation therapy. At present, the only permanent cure is bone marrow transplantation. An emerging and exciting therapeutic approach to handle β thalassaemia is production of fetal hemoglobin (HbF) which is major Hb of fetal life. In recent years, Hydroxyurea (HU) has proven to be a promising HbF augmenting agent but response to HU therapy varies from transfusion elimination to insignificant clinical response. Various approaches are being made to understand the mechanism HbF augmentation with differential responses. Advancement in proteomics offers an efficient tool to study differential proteome in response to treatment leading towards precision and personalized medicine. This study is designed to improve mechanistic understanding of proteomic changes that HU therapy exerted on β thalassemia patients, in consort with deciphering differential protein expression in HU responder and non-responder. Firstly, samples were subjected to twodimensional gel electrophoresis to assess differentially expressed proteins. Later, differential proteins were identified by label free quantitative proteomics approach. Two hundred and eighty seven proteins were identified with two or more unique peptides in samples studied. Among these, twenty eight proteins were found to be significantly different in pre versus post HU treated β thalassemia patients at probability of < 0.05. Eighteen proteins were down-regulated while ten were found to be up-regulated after HU treatment. Clinically important proteins include Hemopexin (HPX), Haptoglobin (HP), Haptoglobin-related protein (HPR), Hemoglobin subunit beta (HBB), Hemoglobin subunit delta (HBD), Hemoglobin subunit alpha (HBA1), Protein S100-A8 (S100A8), Apolipoprotein L1 (APOL1), Apolipoprotein C-I (APOC1), Transferrin receptor protein (TFRC), Complement C4-A (C4A), Apolipoprotein A (LPA), Ceruloplasmin (CP) and Ficolin-3 (FCN3). HU therapy in β thalassemia patients started reverting protein profile towards healthy pattern, in addition with decrease in transfusion requirements. A follow up study on plasma of HU treated β thalassemia patients was performed to compare proteomic profile of HU responder and non-responder. Twenty six proteins were found to be differentially expressed in HU responder versus non-responder at p < 0.05. Among these, fifteen proteins showed a significantly increased level while eleven proteins revealed a decreased in expression. Clinically relevant altered proteins in HU responder are Peroxiredoxin-2 (PRDX2), Carbonic anhydrase 1(CA1), Hemoglobin subunit gamma-1 (HBG1),Hemoglobin subunit beta (HBB), Hemoglobin subunit delta (HBD), Hemoglobin subunit alpha (HBA1), Properdin (CFP), Cholinesterase (BCHE), Phospholipid transfer protein (PLTP) and Plasma protease C1 inhibitor (SERPING1). We suggest that further research would be required for validation of identified proteins in large cohort to endorse as potential predictive biomarker for HU therapy. Considering the association of oxidative stress with β thalassemia, we also studied markers of oxidative stress in response to HU therapy in β thalassemia covering Paraoxonase1 (PON1), Reactive oxygen species (ROS), and Malondialdehyde (MDA). Although PON1 serve as an antioxidant to reduce the adverse effects of the oxidative stress in β thalassemia, our results indicate that mode of action of HU may not directly be through oxidative imbalance