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Some Semi Analytical Solutions of Non-Newtonian Nanofluid Flows

Thesis Info

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Author

Zuhra, Samina

Program

PhD

Institute

Abdul Wali Khan University

City

Mardan

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Fluid Mechanics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11775/1/Samina%20Zuhra%20Fluid%20mechanic%202019%20awk%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727206917

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The unsteady flow and heat transfer characteristics of electrically conducting water based thin liquid film non-Newtonian (Casson and Williamson) nanofluids dispensed with graphene nanoparticles past a stretching sheet are considered in the presence of transverse magnetic field and non-uniform heat source/sink. Embedding the graphene nanoparticles effectively amplifies the thermal conductivity of Casson and Williamson nanofluids. Ordinary differential equations together with the boundary conditions are obtained through similarity variables from the governing equations of the prob lem, which are solved by the HAM (Homotopy Analysis Method). The solution is expressed through graphs and illustrated which show the influences of all the param eters. The convergence of the HAM solution for the linear operators is obtained. Favorable comparison with previously published research paper is performed to show the correlation for the present work. Skin friction coefficient and Nusselt number are presented through Tables and graphs which show the validation for the achieved results demonstrating that the thin liquid films results from this study are in close agreement with the results reported in the literature. Results achieved by HAM and residual errors are evaluated numerically, given in Tables and also depicted graphi cally which show the accuracy of the present work. In another study the steady two dimensional magnetohydrodynamic second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. For the biofluid xxii xxiii the thermal boundary layer convective boundary conditions have been handled. The study has been restricted to gyrotactic microorganisms where compensating torques generated by shear and gravity effects manifest in gyrotaxis which controls the ori entation of upswimming microorganisms through rotary motions. By using the ap propriate similarity transformation for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing partial differential conserva tion equations under prescribed boundary conditions are transformed to the ordinary differential equations which are solved analytically by the HAM (Homotopy Anal ysis Method). Graphical solutions are presented to show the influences of all the parameters. Skin friction, wall heat transfer rate, nanoparticle mass transfer rate and microorganism transfer rate are evaluated in Table. Motile microorganism density function enhances with an increase in momentum slip. Applying optimal homotopy asymptotic method (OHAM), a time dependent symmet ric flow with heat transmission of a second-grade fluid containing nanoparticles and gyrotactic microorganisms between two parallel plates in two dimensions is explored. Partial differential equations furnish the nonlinear ordinary differential equations due to the usage of relevant similarity transformations. Motion declines due to second grade fluid, energy elevates due to thermophoresis, concentration enhances due to Brownian motion and gyrotactic microorganisms profile elevates due to Peclet num ber. The unsteadiness parameter has a profound effect on the nanobioconvection flow within the plates. Consistency and smoothness between the first and second orders of the optimal homotopy asymptotic method are revealed through graphs. Also, graphs are provided to manifest the impacts of each parameter. In last problem, the simultaneous flow and heat transfer of two nanoliquids in the environment of gyrotactic microorganisms and cubic autocatalysis chemical reaction through a porous medium is treated under the potentiality of buoyancy. Weissenberg parameter keeps direct relation and the Casson parameter have inverse relationship to xxiv the velocity in the existence of opposing features of dominant agent and space keep ing pores. Energy keeps low position to the peak position of slippery environment. The dual behavior on concentration profile for the ascending range of strength of homogeneous reaction parameter can be observed. Small organisms are treated pos itively through homogeneous reaction while porous medium, magnet existence and heterogeneous reaction keeps opposite behaviors. Required substitutions are adopted to receive different order differential equations from the original equations which are treated via an efficient scheme. The potentialities of all the representatives are put into graphs and are elucidated.
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منقبت درمدح مرشد گرامی خواجہ محمد شریف چشتیؒ

منقبت در مدح
پیرو مرشد خواجہ محمد شریف چشتی ،نظامی ، قادری، قلندری
(دربارِ عالیہ شمس آباد پاک پتن شریف)

جو تمھارے غم کا پیکر ہو گیا
مطمئن واللہ یکسر ہو گیا

آپ کی جس کو غلامی مل گئی
وہ مقدر کا سکندر ہو گیا

وہ بھی میرے سر تا سر ہی ہو گئے
جب سے میں اُن کا سراسر ہو گیا

جب سے اُن کے پائوں پہ رکھا ہے سر
فخر سے اونچا مرا سر ہو گیا

آپ کی ہے دید حجِ اکبری
میرا کعبہ آپ کا در ہو گیا

Kitabiyyah Mother and Ḥaḍanah of the Muslim Child: Religious and Legal Practices in Pakistan

The article attempts to analyze the religious and legal practices inside Pakistan regarding the issue of the kitabiyyah mother and ḥaḍanah of any Muslim child. The discussion primarily addresses the major issues emphasizing kitabiyyah mother and her relatives’ right to retain the custody of the Muslim child, and duration of ḥaḍanah under the supervision of kitabiyyah mother in shari‘ah and Pakistani Family Laws. Furthermore, it argues that kitabiyyah mother is permitted to raise the Muslim child according to her faith under both Islamic and Pakistani Family Laws. The article is delimited to the opinions of four Sunni schools of thoughts, Statute law, and Case laws. Nonetheless, in-depth comparative analysis has been carried out in most persuasive way to examine the rules related to kitabiyyah mother in custody of Muslim child after divorce under both Islamic Law, and Case Laws in Pakistan. Additionally, the existing similarities and differences consequent to religious differences have also been appropriately figured out to point out plausible way forward to address prevailing schism. Contradictions between the legal practices and Islamic law need keen attention Islamic and legal scholars to carefully craft to harmonize both in the best interest of child.

The Relationship of Emotional Intelligence With Academic Achievements of the Students

Numerous researches on intelligence like those of E.L. Thorndike (1914), David Wechsler (1940), Gardner (1983) etc. lead to findings that intelligence does not consist of cognitive aspect only. There are many non-cognitive factors that contribute to the intelligence of an individual. These non-cognitive factors like social skills, emotional skills, problem solving techniques etc. contribute to a successful life. There is much evidence present that proves that IQ alone cannot predict success in life. For leading a balance life physically, socially and emotionally, exploration, control and monitoring of emotions are very necessary. Researchers have found out that successful people have following traits in them, which cannot be achieved by having cognitive abilities only, traits like: empathy, self-awareness of one’s own emotions, managing their anger, anxiety and stress, having good interpersonal relationship (Goleman,1998). Emotional Intelligence deals with factors related to how humans use their emotions in their daily lives. Emotionally intelligent individuals experience success in important areas in their lives such as work and their relationships. Overall, emotionally intelligent individuals seem to be healthier, happier, and emotionally more stable than those who have low Emotional Intelligence (Schutte, Malouff, Simunek, Kenley & Hollander, 2002). These evidences motivated the researcher to explore link between emotional intelligence and academic achievement of students. Major objectives of the study were to find out the relationship between emotional intelligence and academic achievement; to compare the emotional intelligence of private and public school students; comparison of emotional intelligence between male and female students’ and its impact on academic achievement. Hypothesis of the study was “there is no relationship between emotional intelligence and academic achievement”. The researcher used Quantitative Research involved quantitative data. The population of the study were male and female students, both from secondary and higher secondary schools of Peshawar, Khyber Pukhtoonkhwa. Ages of the sample range from 13-18 years. According to Bureau of Statistics KP, there were 500900 students enrolled in secondary and higher schools in Peshawar in 2014. Out of which 25852 male students and 242388 female students were enrolled both in public and private sector. Researcher took 384 students as a sample which consist of nearly 10% of the population, according to Krejcie, R.V. & Morgan, D.W. (1970). The researcher did stratify random samplings. The stratification was done on the basis of age, school, gender. The sample consists of male and female students from private and public schools. Age wise sample was distributed in three groups i.e.13-14 yrs., 15-16 yrs. and 17-18 yrs. of age. 12 schools were selected for collection of data out of which 6 were private and 6 were public. Out of 384 students 124 male students and 153 female students were selected. 231 public school students and 153 private school students were selected by the researcher. The researcher used standardized tool, Bar- On EQi-Youth Version, taken from Multi Health Systems. It consists of 60 items lasting for 25 minutes. It is intended for 7-18 years of age. It is a widely used Emotional Intelligence measurement tool which targets primarily the youth. Bar On EQi-Youth Version consists of seven scales. These are: “interpersonal”, “intrapersonal”, “adaptability”, “stress management”, “general mood”, “positive impression” and overall Emotional Quotient.The test also includes an inconsistency index which checks the consistency of answers given by the students for analysis of data. The inventory contains the reliability test for both “interpersonal scale” (0.73) and “general mood skill” (0.90). The researcher used t-test and Pearson Product Correlation Coefficient for data analysis. All variables in this study were tested at the P=0.05 level of significance. Mean and standard deviated of the variable were also sought out. Pearson Product correlation co-efficient was also used to measure the strength and direction of the linear correlation between two variables which can range between + and –1. The Quantitative data from questionnaires were put into the SPSS software and analyzed with the help of version 17 of the package. The data was presented in tables and interpreted through the use of percentage, mean, standard deviation, t-tests and correlations. Regarding emotional intelligence and gender, the present study found no relationship between these two variables. Apart from this, no significant difference in emotional intelligence was found between male and female students with the p-value 0.86. For public and private schools, it was established that there is no major variation among Emotional Intelligence and educational institutions (Public, Private) with the p-value 0.49. The study found significant relationship between Emotional Intelligence and academic success. Significant relationship was found between students who secured 65% - 80% grades in their class performance and their overall Total EQ on Emotional Intelligence scales, with the p-value of 0.011. The mean difference of students with high scores was found greater than the mean of students with low scores. All Emotional Intelligence variables except interpersonal skills and stress management were found helpful in achieving academic success.