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A Mathematical Approach for Rheological Fluid Flows With Heat and Mass Transfer

Thesis Info

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Author

Bilal Ahmad

Program

PhD

Institute

HITEC University

City

Taxila

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10276/1/Bilal%20Ahmad_Maths_2019_HITEC_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725399396

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The rheology of non-Newtonian fluids is of an immense importance in wide range of engineering applications involving flows over stretching surfaces along with heat and mass transfer. The present thesis focuses on examining steady two dimensional nonlinear flows in the presence of heat and mass transfer effects. Mathematical formulations for nonlinear flows over vertical and horizontal stretching surfaces in the presence of viscosity variation, magnetic field, magnetic dipole, convective and mass flux boundary conditions are carried out in Cartesian coordinate system. Nanoparticles presence is very beneficial for enhancing thermal properties of base fluids and has importance in engineering processes. The shape and size of the nanoparticles play vital role in improving thermal conductivity and this thesis emphasis on examining these effects. The close form and numerical solutions are presented for emerging nonlinear coupled partial differential equations by using shooting algorithm embedded with Runge- Kutta Fehlberg method. The validity of numerical results is performed through comparison tables in the limiting sense with available literature. The effects of pertinent physical parameters are discussed through graphs and tabulated results are presented for skin friction coefficient, Nusselt and Sherwood numbers
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مولاناعنایت اﷲ دہلوی

مولانا عنایت اﷲ صاحب دہلوی مرحوم
گزشتہ اکتوبر کو علمی جماعت کے پرانے ممتاز رکن مولوی عنایت اﷲ صاحب دہلوی مرحوم سابق ناظم دارالترجمہ حیدرآباد دکن نے انتقال کیا، مرحوم علی گڑھ کالج کے دور اول کے ممتاز تعلیم یافتہ تھے، علم و ادب کا مذاق اپنے نامور باپ مولوی ذکاء اﷲ صاحب دھلوی سے ورثہ میں پایا تھا، طالب علمی ہی کے زمانہ سے ان کے یہ جوہر نمایاں تھے، سرسید کے بہت سے علمی اور ترجمہ وغیرہ کے کام وہی انجام دیتے تھے، اس دور کے ان کے بعض تراجم اب تک یادگار ہیں، ان میں سب سے اہم پروفیسر آرنلڈ کی مشہور کتاب ’’پریچنگ آف اسلام‘‘ کا ترجمہ ’’دعوتِ اسلام‘‘ ہے، تعلیم سے فراغت کے بعد ۱۸۹۳؁ء میں وہ کالج لائبریری کے لائبریرین مقرر ہوئے، کچھ دونوں تک ریاضی کی پروفیسری کی۔ اعزازی خدمت اور تہذیب الاخلاق کی ادارت کے فرائض انجام دیئے، ۱۹۰۰؁ء میں گورنمنٹ کے سلسلۂ ملازمت میں داخل ہوئے اور جونپور کی عدالت ججی میں منصرم مقرر ہوئے، ۱۹۱۵؁ء میں ریاست گوالیار نے گورنمنٹ سے ان کی خدمت مستعار لے کر اپنے شعبہ فنانس کا انڈر سکریٹری بنایا۔ دوران ملازمت میں ترجمہ کا مشعلہ برابر جاری رہا اور اس میں ان کو اتنی شہرت حاصل ہوگئی کہ جامعہ عثمانیہ کے قیام کے سلسلہ میں حیدرآباد میں جب دارالترجمہ کا قیام عمل میں آیا، تو گورنمنٹ نظام نے ان کو حیدرآباد میں منتقل کراکے ۱۹۲۰؁ء میں ان کو دارالترجمہ کا ناظم مقرر کیا، ۱۴ سال تک بڑی قابلیت کے ساتھ اس خدمت کو انجام دیتے رہے، ۱۹۳۴؁ء میں اس سے سبکدوشی حاصل کرکے دہرہ دون کی پر سکون فضا میں قیام اختیار کیا اور یہیں ۲۲؍ اکتوبر ۱۹۴۳؁ء کو وفات پائی۔
مرحوم کا خاص کمال ترجمہ کی مہارت تھی، اس میں ان کو ایسا ملکہ حاصل تھا کہ غیر زبانوں کی کتابوں...

Contact Tracing: A Forgotten Tool?

Contact tracing is done to interrupt the spread or transmission of the causative agent to others who are in close contact with the index case and are vulnerable by not being immune. Public health experts have relied on contact tracing to reduce the spread of infections throughout history. Now the same method is being used for COVID 19. The healthcare systems in developing countries are ill-equipped to respond to pandemics of this kind. Our healthcare facility effectively employed the traditional contact tracing tool that formed the basis of a strong support system for all those employees who contracted Corona virus infection.

Impact of Science, Technology & Innovation Sti on Economic Growth and Development in Selected East- South Asian Countries

This theses attempts to investigate whether Science, Technology and Innovation (STI) progress impacts on economic growth exogenously or endogenously. The study prefers two models (Solow exogenous growth model and Romer endogenous growth model). Both models (Solow and Romer) comprise of four variables: output (Y), capital (K), labour (L), and technology (A) (here we say STI progress). The data of output, capital and labour is available but the data of fourth variable technology (here we say STI progress) is not available yet. Therefore, study attempts to develop STI index in numeric form to measure STI progress of the country. Although, STI indicators are used to evaluate impact of research and development on economic growth to some extent by researchers and economists but use of STI indicators in the form index in production function as an input variables is reported first time. Science, Technology and Innovation Index (STII) is developed for 100 top economies (on the basis of average GDP of 21 years) to evaluate, determine and measure the overall technological readiness and preparedness of a country to participate in knowledge base economy. The STI index is the average of aggregate of four dimensions (Support for STI Activities, Research and Development, Knowledge, and Innovation). The STII relies on four dimensions, each built around two or three pillars, each of which is composed of individual indicators, for a total of 44 indicators. Ranking of countries on the basis of STI value is also presented and the countries have been classified into six groups, based on their STII values as: i) Leaders (STII ≥ 0.350), ii) Potential Leaders (0.300 ≤ STII ≤ 0.349), iii) Dynamic Adapters (0.250 ≤ STII ≤ 0.299), iv) Slow Adopters (0.200 ≤ STII ≤ 0.249), v) Marginalized Countries(0.150 ≤ STII ≤ 0.199) and v) Laggard (STII < 0.150). The study introduces STII as a policy variable (by replacing ‘A’ with STII) in both Solow and Romer models to assess the impact of science, technology and innovation (STI) on economic growth exogenously and endogenously. This variable (STII) pertinent to science, technology and innovation polices for developing countries in Solow and Romer model. This variable would be very helpful for policy makers and planners to formulate Science, Technology and Innovation (STI) policies for developing countries. To estimate short and long run relationship between STI progress and economic growth, panel data analysis has been carried out. The results of the long-run coefficient in Solow and Romer xxi | P a g e model in all groups of countries are highly significant at 5% level. On the basis of empirical results, we may state that science technology and innovation (STI) is directly, positively and significantly associated with economic growth in the long-run while in the short-run impact of STI on economic growth is insignificant. In Solow the ‘A’=‘STII’ represents the level of science, technology and innovation progress is taken as exogenous because it is determined outside the model, not as a consequence of agents’ actions. Romer introduced an explicit research and development (R&D) sector and production of new technologies in model. It is conceivable, devoting more resource to research yield more discoveries. The only determinant of income in models, other than capital is the enigmatic variable the ‘effectiveness of labor’ represents STI progress whose behaviour taken as endogenous in Romer model. A (STII) L in model is considered to as effective labour and progress in science, technology and innovation that is plausible, more output can be produced at the same quantity of labour and capital that could produce a century ago. It has been observed that value of the coefficient of interest (STI)in Romer model is higher than Solow model in all groups of countries (developing and developed economies). It can be conceived that the impact of science, technology and innovation (refer as STII in model) on economic growth is greater in Romer Model than Solow model. The results indicate that accumulation of STI knowledge is central to worldwide economic growth. Our results confirmed that output / economic growth of the country depends upon the endogenous factors more than exogenous. It has also been found that the impact of STI on economic growth in developing economies is higher as compared to developed economies in both Romer and Solow models. It can be conceived that chance of economic growth in developing economies is higher as compared to the developed economies. The developing economies may get more output by investing and focusing on the R&D and STI development. The results of the study do support the concept that the growth rate of STI knowledge grows at constant rate. It has been found that positive and significant relationship exists between accumulations of STI knowledge and capital & exiting stock of knowledge in all groups of countries but the accumulation of STI knowledge is higher xxii | P a g e in developed countries as compared to the developing countries. It means that production of STI knowledge is not related to growth rate of population. The value of STI knowledge coefficient in highly populated East South Asian countries like China, Japan India, and Pakistan is low as compared to the highly developed (low populated) European countries. This indicates that production of knowledge depends upon the level of STI of the country rather than the population. These results reveal that growth rates of STI knowledge are increasing and resultantly the increase in the growth rate of output per worker continually. Indeed as per Solow model, growth rate of output per worker on the balance growth path is affected by changes in rate of STI progress have growth effects; all other changes have only level effects. The study intends to develop a separate trivariate model for estimating the impact of STI on economic development. HDI is used as dependent variable while capital (K) and STI index are used as independent variable. Data of capital and STII (calculated by author) is available while the data of HDI is not available in required form.Although, the HDI is calculated and published in the form of a Human Development Report (HDR) every year by the UNDP since 1990 but there are, however, variations in its methodology and in the indicators used. Therefore, it is decided to re-calculate the HDI for the current study for 21 years (from 1995-2015) with same three dimensions and indicators by using the same formula as given in the Human Development Report (HDR) 2015 for smoothness and countries are ranked by the 2015 HDI value. The countries are classified into four groups on the basis of their HDI value: i) Very High Human Development (HDI value ≥ 0.800), ii) High Human Development (0.700 ≤ HDI value ≤ 0.790), iii) Medium Human Development (0.500 ≤ HDI value ≤ 0.690), iv) Low Human Development (HDI value <0.500). Econometric techniques have been applied to estimate the influence of STI on economic development. The results of study endorse all economic and others theories speak that impact of STI on economic development in developed countries is higher than the developing countries, conceivably, the developed countries have better infrastructure, human resource, universities, R&D organizations to utilize the scientific development. The developing countries have to improve their infrastructure, environment for STI / R&D to take the miracle advantages of STI and R&D investment. xxiii | P a g e It has also been shown through empirical testing that there is a bi-directional causal relationship between economic growth and STI. It indicates that economic growth cannot be accelerated without STI and STI cannot be enhanced or rose without economic growth. The results of the Pairwise Granger Causality test indicate that STI granger causes economic development (refer as HDI in model) as well as economic development granger cause STI (refer as STII in model). It indicates that bi-directional causality between economic development and science technology and innovation is present. The study also presents a case study regarding the impact of science, technology and innovation on economic growth and development in Pakistan, to seek the information from Pakistani scientists, engineers, technologists and researchers about the impact of STI on economic growth and development. What they think and have opinion about impact of STI on economic growth and development. 305 scientists responded the questionnaire, out of 305, 94% (288) confirm that STI has impact on economic growth and economic development. Out of 288 who responded positively, 74 % scientists think that STI has high impact on economic growth while 71% researchers supported that STI has high impact on economic development, while rest of them considered that STI impact is low or very low on economic growth and development. The survey results support the empirical results of the study that science technology and innovation (STI) is direct, positive and significant association with economic growth and development. At the last, thought provoking policy recommendations and implications for developing countries have been presented. The policy recommendations would be very useful for policy makers and planners. Especially, these are very helpful to upgrade their scientific and technological capabilities in order to remain competent in today’s world economy for developing countries. It is very essential for developing countries, to develop knowledge base economy." xml:lang="en_US