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The Study of Nanofluid Flows and its Mathematical Analysis With Applications

Thesis Info

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Author

Nasir, Saleem

Program

PhD

Institute

Abdul Wali Khan University

City

Mardan

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11451/1/Saleem%20Nasir%20Maths%202019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727597674

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This thesis is regarding the development of mathematical flow models and analytical techniques for Newtonian and nan-Newtonian nanofluids containing different nanoparticles on stretching sheets and thin film flows on stretching cylinder and starching disc. For stretching sheet, a mathematical model of MHD three-dimension rotating flow of nanofluids is analyzed. SWCNTs are utilized as nano-sized materials while water is used as a based fluid. In this study the heat exchange phenomena deliberated subject to thermal radiation, Brownian motion and thermophoresis. Now for horizontal stretching cylinder, a mathematical formulation of thin film of 2 3 2 Al O H O g − and 2 3 2 6 2 Al O C H O g − nanoliquids is considered. The effect of effective Prandtl number, viscosity and thermal conductivity is discussed. For a starching disc of same problem, an unsteady thin film flow of 2 3 2 Al O H O g − and 2 3 2 6 2 Al O C H O g − nanoliquids is developed. Similarly, another problem of Darcy Forchheimer 2D thin film flow of nanofluids through unsteady stretchable sheets is developed. In this analysis water base SWCNTs are accounted as a nanoparticle. The transformation of nonlinear PDEs arising in these problems into strong ODEs is formed through appropriate variables. HAM techniques have been proposed to solve these problems while the solution of problem three are carried out by using OHAM scheme. In addition, in all these problems the effect of some model flow parameters on velocity and heat are calculated and studied through graphs. The certain physical factors of these problems skin friction coefficient (surface drag force) and Nusselt number (rate of heat transfer) are derived and present through tables.
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صرع کے دوروں کا الزام

صرع کے دوروں کا الزام
مستشرقین اپنے مذموم عزائم کو برواکار لاتے ہوئے آپ ﷺ کو مصروع ثابت کرنے کے لیے چند واقعات کا سہارا لیتے ہیں جو ان کی ذہنی اختراع اور باطل تاویلات کا نتیجہ ہیں جبکہ ایسے واقعات دیگر مقدس ہستیوں کو بھی پیش آئے لیکن مستشرقین و منکرین سب کو چھوڑ کر صرف حضور ﷺ کے سر الزام دھرتے ہیں اور دوسری برگزیدہ شخصیات کا نام تک نہیں لیتے کیونکہ ایسا کرنے سے ان کی اپنی محبوب ہستیاں بھی زد میں آتی ہیں۔ وہ واقعات جن سے یہ مستشرقین آپ کو مصروع ہونے کی ناکام کوشش کرتے ہیں درج ذیل ہیں ۔
۱۔اسپرنگر حضرت آمنہ کے فرشتوں کو دیکھنے کو مرگی سے تعبیر کیا اور یہی مرض حضور کو ورثہ میں ملا‘ کا الزام دھر دیا ۔ علامہ محمد احسان الحق سیلمانی لکھتے ہیں کہ حضرت آمنہ ؓ ، حضور ﷺ کی والدہ ماجدہ نے اپنے رویا میں فرشتوں کو دیکھا جو انہیں احمد ﷺ کی خوشخبری دینے اور آپ کا نام مبارک تجویز کرنے آئے تھے ۔‘‘ سپرنگر نے کہا کہ فرشتوں نے کیا بشارت دینی تھی ، حقیقت میں حضرت آمنہ کو ضعف دماغ اور صرع کی بیماری تھی ۔ حضرت آمنہ ؓ تو فرشتوں کو دیکھے اور یہی کہے کہ یہ فرشتے ہیں لیکن مستشرقین اسے صرع کہتے ہیں ، عجیب منطق ہے۔ جو ساتھی آپ کے ساتھ مدت العمر رہے انہوں نے کسی موقع پر بھی مصروع نہیں کہا ۔ یہ سب کچھ پیغمبر اسلام اور آپ کے گھرانہ کی شان گھٹاناچاہتے ہیں(۲) دوسرا واقعہ یہ ہے کہ آپ ﷺ اپنے بچپن میں اپنے رضاعی بہن بھائیوں کے ساتھ بکریاں چرانے گئے کہ آپ کا رضاعی بھائی اپنے والدین کے پاس دوڑتا ہوا آیا کہ دو سفید پوش مردوں نے میرے قریشی بھائی کا لٹا کر اس کا...

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