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On Mathematical Models Subject to Homogeneous-Heterogeneous Reactions

Thesis Info

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Author

Hussain, Zakir.

Program

PhD

Institute

Quaid-I-Azam University

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/123456789/9301/1/Zakir_Hussain_Maths_HSR_2018_QAU_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726798505

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Nanoliquids strengthen low thermal conductivity of materials. Nanoliquid consists of nano-material (1 − 100 nm) and base-liquid. Nanoliquids are regarded functional in engineering, electronic process and many other fields. Nanoparticles include CNTs (MWCNT, SWCNT), oxides and carbides ceramics and semiconductors. These nanoparticles are submerged in an ordinary fluid to make them nanofluids. Non-Newtonian fluids like Oldroyd-B, Powell Eyring, Williamson are regarded helpful in physiological phenomena, pharmaceutical process, paper production and metallurgy. That is why Oldroyd-B, Powell Eyring and Williamson fluids are adopted in this thesis for modeling and analysis of flows in boundary layer region. The boundary-layer flows due to stretching surface have wide range of applications in industries and engineering. Further it is also taken into account that heterogeneous-homogeneous reactions in liquid flow have vital role following combustion, biochemical processes, catalysis and in many other fields. Keeping all these aspects in mind the prime objective of this thesis is to study nonlinear mathematical models subject to homogeneous-heterogeneous reactions. The structure of this thesis is as follows. Chapter 1 contains literature survey and some basic conservation laws. Mathematical model and boundary-layer expressions for Oldroyd-B, second grade, Powell Eyring and Williamson fluids are incorporated. Five different techniques are used to deal with the flow problems. Thus basic concepts homotopy analysis method (HAM), Bvp4c matlab solver, Optimal homotopy analysis method (OHAM), shooting technique and Keller box method are provided. Chapter 2 addresses the impact of diffusion species in flow of CNTs nanofluid saturating porous medium. Melting heat transfer is present. Auto catalyst and reactant have same diffusion coefficients. Flow induced by stretched cylinder. Homotopy analysis method (HAM) is adopted for solutions procedure. The outcomes for CNTs flow are disclosed. This chapter contents is reported in Journal of Molecular Liquids 221 (2016) 1121 − 1127. Chapter 3 deals diffusion species via CNTs with convective conditions. Flow generated is because of stretching cylinder. OHAM is adopted for outcomes. Graphical outcomes are discussed via variables for flow. The outcomes are reported in Journal of the Taiwan Institute of Chemical Engineers 70 (2017) 119 − 126. Chapter 4 reports computational aspects for Forhheimer flow of CNTs nanofluids with diffusion species. In this chapter thermal conductivity of CNTs nanofluid is compared via renovated Hamilton-Crosser (H-C) and Xue models for flows by stretching cylinder and flat sheet. The results are obtained via Keller box method. The findings of this chapter are submitted in Physica E for possible publication. Chapter 5 examines stagnation flow of carbon water and carbon kerosene oil nanofluids via nonlinear stretched surface. CNTs nanofluids fill the porous medium. Homogeneousheterogeneous reactions and melting effects are considered. Outcomes are obtained via (OHAM). Heat transferred is addressed via different variables involved in solutions expressions. The contents of this chapter are published in Advanced Powder Technology 27 (2017) 1677 − 1688. Chapter 6 presents 3D nanoliquid flow by stretched (nonlinear) sheet with diffusion species. Nanoliquid is saturated via porous space. Convective condition and heat source/sink are used for heat mechanism. The numerical outcomes are analyzed via shooting approach. Graphical illustrations and tabulated values are disclosed. The main findings of this chapter can be seen through Computer Methods in Applied Mechanics and Engineering 329 (2018) 40 – 54. Chapter 7 describes three-dimensional (3D) nanoliquid flow via slendering stretching (nonlinear) sheet with slip effects. bvp4c technique is used for numerical outcomes. Tabulated and graphical findings are explored via sundry variables. These contents are published in Computer Methods in Applied Mechanics and Engineering 319 (2017) 366 − 378. Chapter 8 discloses flow of MHD non-Newtonian liquid via Newtonian heating and diffusion species. Results are developed via HAM. Numerical results of skin friction and Nusselt number are disclosed. The findings of current chapter are published in PloS one 11 (6) e0156955 (2016). Chapter 9 describes flow of MHD viscoelastic fluid with species. Flow is due to stretched cylinder. Viscous dissipation, Newtonian heating and Joule heating are also accounted. The results are constructed via HAM. Characteristics of different variables are elaborated graphically. The outcomes of this chapter are published in Journal of Mechanics 33 (2017) 77 − 86. Chapter 10 includes species influence in flow of second grade material. Melting heat contribution is inspected. Inclined magnetic line is used to electrified the liquid. Numerical results are addressed via heat transfer and skin friction. The contents are addressed in Journal of Molecular Liquids 215 (2016) 749 − 755. Chapter 11 investigates homogeneous-heterogeneous reactions in thermally stratified stagnation flow of viscoelastic liquid with mixed convection. Flow is by a stretched sheet. Influences of various variables on quantities of interest are discussed. The findings of this chapter are published in Results in Physics 6 (2017) 1161 − 1167. Chapter 12 addresses convective flow of Williamson fluid by cylinder and flat sheet. Convective condition is used for heat transfer mechanism. The species of auto-catalyst and reactant are used to regulate the concentration. Convection or evaporation for temperature phase change is analyzed through homogeneous-heterogeneous reactions. The transformed ordinary differential equations are dealt numerically via Keller box method.Impacts of pertinent parameters of interest are graphically discussed. Comparison of results for cylinder and flat sheet is arranged. The contents of this chapter are submitted for possible publication in International Journal of Mechanical Sciences.
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محمد خان وامق

عہد اورنگ زیب کے محمد خان وامق سیالکوٹ کے پہلے اردو شاعر ہیں۔ وہ اپنے وقت کے اہم شاعر تھے۔ وامق وڈہرہ قوم کے کھتری تھے اور ان کو مسلمان کرنے کا فخر اس وقت کے جید عالم مولانا عبد اﷲچلپئی کو تھا جنہوں نے ان کا نام محمد خان رکھا۔ اشفاق نیاز تاریخِ سیالکوٹ میں آپ کے بارے رقمطراز ہیں:

آپ نہ صرف اعلی درجے کے شاعر تھے بلکہ ایک انشا پرداز بھی تھے اور یہی شہرت اور قابلیت انہیں دربارِ عالمگیر تک لے گئی۔ بادشاہ ان کا بہت قائل تھا بعد میں بادشاہ نے ان کے فن و ادب کی قدر کرتے ہوئے انہیں اخلاص خاں کے اعلیٰ خطاب سے سرفراز بھی فرمایا۔ آپ صاحبِ دیوان بھی تھے۔ اردو اور فارسی میں شاعری کرتے تھے مگر افسوس کہ باوجود سعی بسیار کے کلام مفقود ہے۔ (۱)

راقم الحروف بھی کوشش کے باوجود ان کا اردو کلام دریافت نہیں کر سکا۔تاریخِ سیالکوٹ کے مطابق آپ نے محمد شاہ کے عہد ۱۷۶۶ء میں سیالکوٹ میں وفات پائی۔(۲)

 

۱۔اشفاق نیاز‘ ’’تاریخِ سیالکوٹ‘‘ ‘ سیالکوٹ‘ سیالکوٹ ایڈورٹائزرز ‘ ۲۰۰۹ء، ص : ۲۹۳

۲۔           ایضاً‘ ص: ۲۹۴

أمير الشعراء أحمد شوقي: نثره الفني ومنهجه

It is very clear that Ahmad shoqi was titled as king of modern Arabic poetry due to his unforgettable literary deeds towards it. Apart it all, his good struggle toward Arabic prose were ignored in his life, because of the prose was not his field to be tried in and it has its own experts. Some of these experts collected his prose and compiled it in a huge encyclopedia of his literary works named “al mosoa al shoqia” (الشوقية الموسوعة). This article also discussed his literary prosaic struggles, his methodology which he acquired and the deficiencies which were pointed out by critics. Adding more, the feature of the prose are also drawn in.

Recent Advances in Detecting Outliers in Moment Distributions

The study of outliers is one of the challenges existed for at least several hundred years. Outliers are the observations which are stranger from the bulk of data. Sometimes outliers may not be noticed but most of the times they can change the entire statistical data analysis. At the earlier stage of the data analysis, summary statistics such as the sample mean and variance, outliers can cause totally different conclusion, e.g. a hypothesis may or may not be rejected due to outliers. In fitting regression line outliers can significantly change the slope and 2R . If the detection of outliers is not done properly before data analysis then it may lead to model misspecification, biased parameter estimation and incorrect results. It is therefore pertinent to identify the outliers prior to proceed further for analysis and modeling. Much work has been done in Univariate probability distributions. The objective of this study is to develop the methods which are used to detect the outliers in Univarite Moment Distributions. Two discordancy tests are developed to detect the single and two outliers from data characterized by Moment distributions. The exact distribution of developed tests does not exist, therefore for finding the Tables of critical values simulation study was used. The Tables of critical values are developed at 5% and 1% level of significance by means of a simulation study.Applications of two other methods which are based on sample skewness and Kurtoses have been extended to detect the outliers in Moment distributions. The Tables of critical values are also generated for these two methods at 5% and 1% level of significance on the basis of a simulation study. The performance rates of four methods are found at various sample sizes by means of a simulation study. It is worth mentioning that methods ?1 and ?2 only indicates the presence of outliers in the data, while methods ?1 and ?2 not only identify the presence of outliers but also specify the particular outliers.