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Steady Flow of Fluids With Variable Viscosity

Thesis Info

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Author

Tabassum, Rabil

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/123456789/12531/1/Rabil%20Tabassum%20Maths%202019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727239157

Similar


Nanofluids have wide range applications in processes involving heat transfer due to their proficient thermal conductivity. Such fluids exhibit substantial viscosity variation with temperature. This dissertation presents oblique stagnation point flow of variable viscosity nanofluid over a stretching surface. Porous medium, magnetic field, heat generation, thermal radiation and homogeneous-heterogeneous effects along with partial slip, thermal slip and convective surface are considered. Micro-rotation phenomenon is also fused with nanofluid flow comprising micropolar nanofluid. Nanofluid thermal conductivity is estimated by Maxwell-Garnett model, Hamilton Crosser thermal conductivity model is also employed when shape effects of nanoparticles are considered. Flow problems are first modeled and afterwards converted to non-linear system of ODEs via appropriate similarity transformations. Numerical solutions are obtained via stable and efficient Runge-Kutta-Fehlberg scheme with shooting quadrature and Keller-Box scheme. The impact of key emerging dimensionless parameters on non-dimensional normal, tangential velocity constituents, temperature, shear stress (at wall), heat flux along with streamlines distribution is visualized by graphs.
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ممتا

ممتا

شاکر انور

سمندرنیلا اور پر سکون تھا اور دمام کا آسمان بادلوں سے پُر۔ میں بیقراری سے دھوپ کے ایک ٹکڑے کی تلاش میں ہاف مون بیچ کے خوبصورت سبز گھانس کے روش پر اِدھراُدھر گھوم رہاتھا۔کاش! کوئی ایسی پر سکون جگہ مل جائے جہاں پر میں اپنے ناول کے خاتمے پر کام کرسکوں۔

دور مغربی ساحل کے ایک گوشے میں کھجور کے درختوں سے چھن چھن کر آتی سورج کی ریشمی چادر سی تنی نظرآئی۔ میں تیزی سے اس جگہ گیا مگر وہاں پر سیاہ عبایا پہنے ایک نوجوان عورت بے بی اسٹرولر پر جھکی ہوئی لیٹے ہوئے بچے کو دھوپ سنکاتی، مسکراتی ہوئی باتیں کررہی تھی۔کبھی کبھی وہ بے ساختہ ہنس دیتی۔ جیسے اس کے بچے نے کوئی معصوم سی شرارت کی ہو، وہ شاید مصری یا لبنانی ہوگی۔ نہایت گوری، گلابی کالی آنکھوں والی۲۳، ۵۳ سالہ دوشیزہ جوسرخ پھولدار رومال سے سر ڈھانپے ہوئی تھی۔ وہ جس جگہ کھڑی تھی وہ میری اوّلین پسند تھی۔ ہاف مون بیچ سے کچھ دوری پر واقع نہایت ہی پراسرار خاموشی سے گھرا کنارا جہاں خوبصورت سناٹا میرے خیالوں کو مہمیز کرتا۔

 اس نے اچانک پلٹ کر میری طرف دیکھا۔ ایک ادھوری سی مسکراہٹ اس کے ہونٹوں پر تھی……مگر شاید وہ مکمل تھی۔ یہ میرا گمان تھا اور پھر اسٹرولر کو دھکے دیتی آگے بڑھ گئی۔ جیسے کہہ رہی ہو۔ آجاؤ، اپنی مخصوص جگہ مسٹر ادیب۔میں نے اکثر شام کے وقت اسٹرولر پر بچے کو گھماتے ہوئے دیکھاتھا۔ وہ ہمیشہ اکیلی ہوتی اور ساحلِ سمندر کے کنارے پر بنے ہوئے ٹریک پر اِدھر اُدھر گھومتی رہتی۔ بے بی اسٹرولر کے دائیں جانب پانی کی چھوٹی سی رنگین بوتل ہوتی اور دوسری جانب چند کھلونے‘ اوپر کا گلابی حصہ نیچے کی طرف جھکا ہوتا۔اسے...

Jihad Against Terrorism: A Response to Robert Spencer’s Views on Jihad

The word Jihād has been awfully misinterpreted in the post 9/11 literature. Quite a few critics of Islam have deliberately used Jihād as synonymous with terrorism. Robert Spencer, a prominent critic of Islamic Jihād, also maintains that Islam teaches violence, intolerance and extremism. The following research article is a critique of Spencer’s views on Islamic concept of jihad. It aims to prove that Islam is a tolerant creed and has nothing to do with violence and terrorism. The Holy Qur’an substantiates this claim and shows that the persecuted Muslim community was allowed to take up arms against the terrorists who not only tormented the innocent people but also expelled them from their native homes.

Human Capital and Economic Growth: A Macroeconomic Model for Pakistan

This dissertation work enlightens the contribution of human capital in the economic growth of Pakistan through time series analysis and macroeconomic modelling framework. The first objective of this thesis is to find out the most relevant level of education in Pakistan in terms of its contribution to the economic growth. Second objective is to use that level of education as proxy for human capital and to find out its contribution in the sector wise productionn. Third is to develop a desegregated macroeconomic model for Pakistan illuminating the linkages between human capital and economic growth which enable us to analyze the effects of education spending by government on key macroeconomic variables at desegregated level through policy based simulations. To achieve the first objective, a time series study is conducted. The study employed annual dataset for the period 1981-2014 to find the most relevant level of education in terms of its contribution to the economic growth of Pakistan.The study used three models assuming gross enrolment rates at primary, secondary and tertiary level as human capital and found secondary education as the most relevant level of education for economic growth.The long run coefficients obtained through fully modified ordinary least square (FMOLS) are used to reconfirm the findings of dynamic ordinary least square (DOLS). CUSUM test found that the parameters of equation with secondary education as human capital are stable. It is recommended therefore that secondary education should be given preference in resource allocation to ensure long run economic growth of Pakistan. To address the second objective, another time series study is conducted.This study illuminates the impact of human capital on the production of agriculture, industrial and services sector and compares the strength of this relationship with the coefficients obtained through aggregate data.The study uses an annual data set from 1981-2014 from Pakistan Bureau of Statistics and uses aggregate and sector wise production models.Augmented Dickey Fuller (ADF) is used test the order of integration and J-J co-integration is employed to check the long run relationship. Dynamic Ordinary Least Square (DOLS) and fully modified Ordinary least square (FMOLS) are used to check the consistency of initial findings and sensitivity analysis is performed in order to check the robustness of results. The study found evidences of positive human capital contribution in aggregate and sectoral production however its magnitude is found to be similar in the agricultural and industrial sector which was higher than the magnitude associated with services sector. The results show that human capital contribute directly in the aggregate and sector wise production of Pakistan and its contribution can be enhanced in aggregate or in any specific sector of economy by policies through affecting price level and interest rate. The third objective is achieved through a study based on macroeconomic modelling. The study develops a medium sized macroeconomic model for Pakistan focusing the role of human capital in economic growth. The model divides supply side of economy into agriculture, industrial and services sector which is modelled as per neo-classical theory of production whereas the demand side is modelled as per Keynesian lines. The model is consisted of 43 equations including 23 behavioral equations estimated through fully modified ordinary least square (FMOLS). The forecasting horizon of this model is set to six years from 2015 to 2020 and the time paths of aggregate and sector wise variables are analyzed under 03 scenarios associated with government spending on education including the one stated in VISION 2025 of planning commission. The study found strong linkage between government spending on education and the production of agricultural and industrial sector. The production and employment of services sector is found to be least affected by government spending on education which reflects lack of synchronizing between the types of skills demanded by and supplied to the services sector. It is recommended therefore to increase the government spending on education along with aligning the skills produced in accordance to the demand of services sector.