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Solutions of Couple Stress and Non-Newtonian Fluid Flows

Thesis Info

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External Link

Author

Farooq, Muhammad

Program

PhD

Institute

National University of Computer and Emerging Sciences

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13692/1/muhammad.farooq.phd.thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727189486

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The equations governing the flow of couple stress and modified second grade non-Newtonian fluid flows for systems of non-linear ordinary differential equations are formed and thus these systems have no general solutions. The general solutions become more rare if we study these flows together with heat transfer analysis and even more harder if we introduce the variable viscosity instead of constant viscosity. In the first part of the thesis we study the steady incompressible couple stress channel fluid flows together with the energy equations taking variable viscosity into account. The Reynolds and Vogel’s viscosity models have been used for the temperature dependent viscosity. Depending on the relative motion of the plates, four different problems are considered, viz plane Couette flow, plug flow, plane Poiseuille flow and Couette- Poiseuille flow. Approximate analytical and numerical approaches have been used to solve the nonlinear developed equations arising during the mathematical modeling of these problems. Solutions for the velocity profiles, temperature distributions, volumetric flow rates, average velocities Nusselt number and shear stresses are obtained. The influence of different emerging parameters on the flow pattern has been discussed and presented with the help of graphs. A study of thin film flows for the Generalized (modified) second grade fluid together with the energy equation is carried out in the next part of the analytical investigation. Two different problems have been investigated, (i) when a wide belt is moving vertically upward through a container with a constant speed V0 and (ii) when fluid is falling on the stationary infinite vertical belt under the influence of gravity. For the above stated problems the governing equations are converted into ordinary differential equations and then solved exactly for the velocity profile and temperature distribution. Expressions for the volume flux, average velocity and shear stress are obtained in both these problems. Effects of different parameters on velocity and temperature are presented graphically. Furthermore approximate solutions have been developed for the Generalized second grade fluid in cylindrical coordinates.
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استفہام بمعنی امر

استفہام بمعنی امر

بسااوقات استفہام امر کے معنوں میں استعمال ہوتا ہے ۔ ذیل کی آیت:

"إِنَّمَا يُرِيدُ الشَّيْطَانُ أَنْ يُوقِعَ بَيْنَكُمُ الْعَدَاوَةَ وَالْبَغْضَاءَ فِي الْخَمْرِ وَالْمَيْسِرِ وَيَصُدَّكُمْ عَنْ ذِكْرِ اللَّهِ وَعَنِ الصَّلَاةِ فَهَلْ أَنْتُمْ مُنْتَهُونَ"۔ [[1]]

"شیطان تو یہی چاہتا ہے کہ شراب اور جوئے کے ذریعے تمہارے درمیان دشمنی اور بغض کے بیج ڈال دے اور تمہیں اللہ کی یاد اور نماز سے روک دے ، اب بتاؤ کہ کیا تم ان چیزوں سے باز آ جاؤ گے"۔

اس آیت میں ’’فھل انتم منتھون ‘‘ در اصل ’’انتھوا عنھا‘‘ کے معنی میں مستعمل ہے ۔

"فَإِلَّمْ يَسْتَجِيبُوا لَكُمْ فَاعْلَمُوا أَنَّمَا أُنْزِلَ بِعِلْمِ اللَّهِ وَأَنْ لَا إِلَهَ إِلَّا هُوَ فَهَلْ أَنْتُمْ مُسْلِمُونَ"۔[[2]]

"اس کے بعد اگر یہ تمہاری بات قبول نہ کریں تو (اے لوگو) یقین کر لو کہ یہ وحی صرف اللہ کےحکم سے اتری ہےاور یہ کہ اللہ کے سوا کوئی عبادت کے لائق نہیں، تو کیا اب تم فرما بردار بنو گے"۔

جناب فلاحی کی رائے میں آیت مذکور میں ’’فھل انتم مسلمون‘‘ استفہام کے معنی میں نہیں بلکہ امر کے مفہوم میں استعمال ہوا ہے یعنی ’’اسلموا لھذا لاکتاب و آمنو ‘‘ ۔[[3]]

" قُلْ أَرَأَيْتُمْ إِنْ أَهْلَكَنِيَ اللَّهُ وَمَنْ مَعِيَ أَوْ رَحِمَنَا”[[4]]

"اے پیغمبر ان سے کہو کہ ذرا یہ بتلاؤ کہ چاہے اللہ مجھے اور میرے ساتھیوں کو ہلاک کر دے یا ہم پر رحم فرما دے"۔

قاضی ثناء اللہ پانی پتی کے مطابق ’’ارءیتم‘‘ میں ابتدائی ہمزہ استفہام تقریری کے لیے...

سیرت نبوی ﷺ: ایک تحقیقی جائزہ

Prophet Hood consists of guidance from Allah to humankind. It is a Allah given blessing and a favor that is bestowed on an individual chosen be Him to convey His message, which cannot be acquired or earned otherwise. There has never been a human being so well-respected, loved and followed as Muhammad (SAW), the final messenger of Allah. There has never been a person who has changed world history so dramatically as Muhammad (SAW) and his message. The Prophet (SAW) was the single most important person in the history of the world. Knowledge of the Prophetic Biography is necessary for every Muslim and sharing it with everyone is a responsibility. The importance of a complete biography of the Messenger as available to us cannot be under estimated in this troubled time since both Muslims as well as Non-Muslims have serious knowledge gap when it comes to even approaching the nature of the Final Prophet and the Ultimate Messenger of God sent to all of humanity, who came to restore the primordial religion of Man, the submission to Allah and His Commands. Muhammad (SAW) serves as: - Allah’s messenger and prophet to all mankind as an example of human behavior and noble character Therefore, in studying his life-story we should derive lessons and morals that can help us in our lives today.

An Assessment of Major Ozone Depleting Substances Odss and Their Impacts on Climate Change Using Rs/Gis in Lahore, Pakistan

The aim of this thesis is to quantify emissions of selected halogenated refrigerant Ozone Depleting Substances (ODSs) and to make an assessment of some important non-halogenated trace gases, that involve or affect atmospheric O3 chemistry, over megacity Lahore (Pakistan). Ozone Depleting Potential (ODP) and Global Warming Potential (GWP) weighted emissions of halogenated gases such as CFC 11, CFC 12, HCFC 141b and HFC 134a have been quantified in Lahore during 2005-2013. Additionally, anthropogenic emissions, spatial patterns, seasonal variabilities and trends have also been discussed for non-halogenated trace gases such as nitrogen dioxide (NO2), methane (CH4), carbon monoxide (CO), sulphur dioxide (SO2) and carbon dioxide (CO2) and ozone (O3) by using multi satellite and emission inventories data, and air masses trajectories analyses. To estimate ODP and GWP weighted emissions from Lahore, ODSs emissions have been quantified from production, repair/maintenance, and waste/disposal phases. During these phases the cumulative emissions of CFC 11, CFC 12, HCFC 141b and HFC 134a have been estimated to be 1.48 giga-grams which have contributed 293.3 tonnes of ODP (CFC 11-equivalent) and 1.87 mega-tonnes of GWP (CO2-equivalent). Significant declines in ODP (-8.4% yr-1) and GWP (-7.1% yr-1) have been observed during production phase for the period from 2005 to 2013 largely linked to the implementation of Montreal Protocol (1987) phase out programme. Emission Database for Global Atmospheric Research (EDGAR) based anthropogenic emissions of CH4 in Lahore have been recognized as the highest with 27% increase compared to the emissions from neighboring megacities Karachi, Delhi and Faisalabad during 2000-2008. SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) retrieved CH4 total column (TC) is found to be increasing at 4% over Lahore during 2003-2012. SCIAMCHY data also indicate a clear seasonality in CH4 TC with the highest column in August, whereas minimum column is observed in April. OMI observations identify Lahore and its surroundings as a prominent hotspot of tropospheric NO2 (tropo- NO2). A significant increase of 65% has been observed in tropo-NO2 column during 2004-2014. AIRS tropospheric CO (tropo-CO) observations indicate that Lahore has the second highest mean value of tropo-CO column in South Asia after megacity Delhi. An increase of 1.2 % is noted for tropo-CO column over Lahore during 2003-2012. July is found with the highest decadal increase of CO at 10.4% followed by August at 4.9%. It is observed that background CO has greater decrease rate of –0.84% yr–1 than the recent emissions at –0.56% yr–1. OMI Planetary Boundary Layer (PBL) SO2 observations over Lahore reveal 2.4% yr-1 increase in SO2 during 2005-2014 with the highest monthly mean peak in December. EDGAR anthropogenic CO2 emissions and AIRS mid-tropospheric CO2 concentration show increasing trends at 3.1% yr-1 (during 1990-2008) and 1.8 ppm yr-1 (during 2002-2012) respectively. Satellite data suggest that long-range transport of volcanic SO2 from Jabal Al-Tair (Yemen), Dalaffilla (Ethiopia), Nabro (Eritrea) and Mount Etna (Italy) volcanoes has played a significant role in PBL-SO2 enhancements over Lahore. Ozone Monitoring Instrument (OMI) TOC observations over Lahore show a minor increase at 1.1% yr-1 with the highest monthly mean value in April during 2004-2014. This rise is majorly linked to enhancements in ozone precursors and decline in chlorofluorocarbons (CFCs) emissions. This study identifies Lahore as a prominent hotspot of gaseous pollution at regional scale mainly associated with urbanization, industrialization, motorization, large scale crop-residue burning and power generation. The air masses trajectories analyses show that, apart from the transport of gaseous pollution between Lahore and the Indian states of Punjab, it can also be transported from northwestern areas near Pak-Afghan border, Nepal and Arabian Sea.