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Purely Analytic Solutions to Some Multidimensional Viscous Flows With Heat Transfer

Thesis Info

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Author

Mehmood, Ahmer

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2010

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1157

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727045975

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Exact solution of Navier-Stokes equations is possible only for very simple flow situations such as unidirectional flows. Due to the nonlinear nature of these equations their analytic solutions are rare and the situation gets worse in the case of unsteady and multidimensional flow problems. In this thesis we report highly accurate and purely analytic solutions to some steady/unsteady multidimensional viscous flows over flat surface. Heat transfer analysis has also been carried out where the flat surface is considered as a stretching sheet. In each case the skin friction and the rate of heat transfer has been reported. The issue of cooling of stretching sheet in the presence of viscous dissipation has been discussed in detail. We have considered multidimensional flows of viscous fluid over a flat plate in different flow situations such as flow over an impulsively started moving plate; flow over a stretching sheet, viscous flow in a channel of lower stretching wall, and the channel flow with lower wall as a stretching sheet in a rotating frame. In all the above mentioned flow situations similarity transformations have been used in order to normalize the problem. The reduced governing equations are then solved analytically. We have used homotopy analysis method to solve the governing nonlinear differential equa- tions. The results are purely analytic and highly accurate. The accuracy of results has been proved by calculating the residual errors and (or) giving the comparison with the existing re- sults. For unsteady flows it is worthy to mention here that our analytic solutions are uniformly valid for all time in the whole spatial domain.
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وہ غیر سمجھے مجھے غیر ہی شمار کرے

وہ غیر سمجھے مجھے غیر ہی شمار کرے
میں اس کو چاہوں وہ میرا نہ اعتبار کرے

اگر یہ طے ہے اسے لوٹ کر نہیں آنا
تو اُس کی یاد بھی مجھ کو نہ بے قرار کرے

تباہ کر دیا چاہت کو رازداروں نے
تو کیا کسی کو یہاں کوئی رازدار کرے

اگر وہ کہتا ہے مجھ سے کہ لاتعلق ہے
تو پھر وہ ذکر بھی میرا نہ بار بار کرے

کوئی تو ہو جو یہ تائبؔ کو بات سمجھا دے
ہمیں بھلا دے ہمارا نہ انتظار کرے

فلسفۂ اخلاق کی تشکیل نو اور سیرت طیبہ میں اس کی نظریاتی بنیادیں

Reformation of Moral Philosophy and its Foundation in Seerah of the Prophet Muhammad (ﷺ) Though, the twenty first century is passing through a great development in the field of science, intellect, education and technology, human beings seem spiritually and ethically in a more miserable condition day by day. We observe inflation in the problems and complications regarding their solutions in human societies with every passing day. Today’s man is highly engaged in universe and its enquiry, we are developing knowledge and physical efforts for taking control over all phenomena of universe, but in this effort, we lost our capability of good values and ethics mostly. In such conditions, the one and only personality, the Ambassador of peace, beloved Muhammad ﷺ is the source of guidance, by whom the spirit of a man could meet with peace and stability. But the solution of this major problem never can be just adopting his ethical teachings and the rejection of bad actions. If so, then the thousands of past writings about the issue have brought the revolution already on the face of the earth. Modern philosophy of ethics and Morality is based upon the concept of relativity as “Good” or “bad” is not universal truth at all. For this reason, it is less effective in terms of practicality. The roots of philosophical concepts we find in the teachings of Prophet’s Muhammad (ﷺ). Have no enigmas and ambiguity Morality. Promoting the prophetic philosophy of Ethics and Morality can change the behavior of man automatically rather than forcefully. In this article, effort has been made to critically analyze the modern Moral philosophy in the light of Sῑrah of the Holy Prophetﷺ. Analytical and critical research methodology is adopted in this study.

Potential of Sirna and Artificial Mirnas Against Cotton Leaf Curl Burewala Virus V2 Gene Yielding Resistance to Begomoviruses

Diseases of crop plants caused by begomoviruses (whitefly-transmitted viruses of the family Geminiviridae) are a major constraint to productivity across the warmer parts of the world. Cotton leaf curl disease (CLCuD) across Pakistan and northwestern India has caused severe losses to cotton cultivation since the early 1990s. In Pakistan the disease at this time is caused by a single begomovirus, Cotton leaf curl Burewala virus (CLCuBuV), and a betasatellite, Cotton leaf curl Multan betasatellite (CLCuMuB). Efforts to prevent losses due to CLCuD rely on the use of insecticides to control the vector whitefly and the use of tolerant cotton varieties; no immune varieties so far having been identified. RNAi technology offers a possible mechanism of rapidly developing resistant crop varieties to counter diseases caused by plant-infecting viruses. Here antisense RNA and artificial micro (ami)RNA have been investigated for their potential to yield resistance to CLCuBuV. A major challenge to use of RNAi is the need to identify the best target sequence. Here three fragments of the virion-sense gene V2 of CLCuBuV have been transformed into Nicotiana benthamiana in antisense orientation and assessed for their ability to yield resistance against CLCuBuV and three heterologous begomoviruses. The results are consistent with the idea that RNAi is a homology-based response with transgenic plants showing levels of resistance that correlate with the levels of sequence identity between the transgene and the inoculated virus. However, only for CLCuBuV was resistance at near immunity levels with the V2 sequence closest to the promoter providing the best resistance. Nevertheless, with all three constructs, transgenic plants inoculated with CLCuBuV showed no symptoms, or recovered from initial mild symptoms, and viral DNA levels were low. Additionally, inoculation of CLCuBuV with the CLCuD-associated betasatellite CLCuMuB to transgenic plants did not significantly affect the outcome although it increased the numbers of plants in which viral DNA could be detected, suggesting that the betasatellite may impair RNAi resistance. This effect is likely due to the betasatellite encoding a strong suppressor that inhibits RNAi at both the transcriptional and post - transcriptional levels. xiv Earlier studies have shown that the sequences of naturally occurring miRNA genes can be changed to alter the messenger RNAs that they bind to. Here a cotton microRNA gene (miR169a) was altered to replace the sequence of the mature miRNA with 21 nucleotides of sequence from the V2 gene of CLCuBuV and transformed into N. benthamiana. Two constructs were produced. In one construct (P1CN) the sequence of the miRNA backbone, with the exception of the 21 nucleotides, was left unchanged. In the other (P1DM) the sequence of the backbone was changed to, at least in part, restore the secondary structure of the immature miRNA (referred to as a precursor - miRNA). Inoculation of plants with a range of begomoviruses showed P1CN to give efficient resistance against the homologous virus (CLCuBuV) but not against heterologous viruses. Overall the levels of resistance exhibited depended upon the levels of sequence identity to the target (21nt) sequence, although other factors also likely play a part. For a small number of P1CN plants inoculated with CLCuBuV symptoms were initially evident but the plants recovered and contained low levels of viral DNA. In contrast, transgenic plants inoculated with heterologous viruses showed a greater number of plants symptomatically infected, that did not recover and showed high levels of viral DNA although lower than in infected non-transgenic plants. Transgenic plants harbouring P1DM showed poor resistance to CLCuBuV and little resistance to the heterologous viruses, indicating that the backbone sequence of the premiRNA is important for the biogenesis of mature miRNA. The results indicate that both antisense-RNA and amiRNA have the potential to deliver resistance against begomoviruses. The significance of the results are discussed.