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Mathematical Modeling and Theoretical Analysis of Fluid Flow With Heat Transfer over a Stretching/Shrinking Sheet

Thesis Info

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External Link

Author

Tariq Abbas

Program

PhD

Institute

Islamia Collage Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Fluid Dynamics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10914/1/Tariq%20thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726619543

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The study about heat transfer and boundary layer flow over a stretching sheet gotten consideration from numerous analysts due to its significance in many engineering and industrial applications, such as, paper generation, glass-fiber generation, solidification of fluid gems, petroleum generation, extraordinary oils, suspension arrangements, wire drawing, ceaseless cooling and fibers turning, fabricating plastic films and extraction of polymer sheet. In the view of above applications, theocratical analysis is carried out for the flow of Carreau fluid over a stretching/shriking sheet. The problems are formulated under the effects of various parameters with suitable transformations. The obtained boundary layers equations are transformed from PDEs to ODEs with the given boundary conditions. Thesis are divided into 7 chapters. Chapter one deals with fundamental preliminaries that will make this thesis understandable for readers. Literature review is also a part of this chapter. Chapter two deal with the investigation of MHD mixed convection Carreau fluid flow over a nonlinear stretching/ shrinking permeable sheet near a stagnation point. Homotopy Analysis Method (HAM) is utilized to find the solution of the system of nonlinear problem. Qualitative comparison of the HAM and BVP4C numerical routine are presented. The influences of different parameters such as Weissenberg number We2, Magnetic parameter M2, Suction and Injection parameter s, Stretching or Shrinking parameter B, Mixed convection parameter A, Nonlinear parameter m and Lewis number Le on concentration, velocity and temperature distributions are studied graphically and analyzed. Chapter three concerned with the study of magnetohydrodynamic (MHD) boundary layer flow of Carreau fluid with variable thermal conductivity and viscosity over stretching/shrinking sheet. The viscosity and thermal conductivity is considered to vary linearly with temperature. Analysis are made analytically by HAM. Numerical solutions of the problem is also obtained by BVP4C numerical routine, which agrees well with analytical solution. The influence of natural parameters, such as the Prandtl number, Weissenberg number, Lewis number, Magnetic parameter, Suction parameter, Stretching/ Shrinking parameter and the heat flux constants are shown in several plats and in tabulated results. The purpose of chapter four is to examine an unsteady motion of Carreau fluid produced by stretching/ shrinking sheet with a magnetic field applied normal to the sheet. The governing momentum and the energy equation admit a self similarity solution. Results are discussed in terms of Weissenberg number, Unsteadiness parameter, Stretching/ Shrinking parameter, Power law index, Prandtl number, Blowing and Magnetic parameter. The aim of chapter five is to study the MHD Carreau fluid slip flow together with viscous dissipation and heat transfer by taking the impact of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the liquid is expected to differ straightly with temperature. The effects of various parameters such as magnetic parameter M2, Weissenberg number We2, porosity parameter D,power law index n, wall thickness parameter α, power index parameter m, thermal conductivity parameter ε, slip parameter λ ,radiation parameter R and Prandtl number Pr on velocity and temperature profiles are studied graphically and analyzed. The focus of chapter six is to study of Carreau fluid flow over sheet stretching in the xy-plane. For this purpose equations are modeled from the set of Naiver-Stoke equations combine with heat and mass transport taking into account the effects of thermophoresis and Brownian motion. From similarity transformations non-dimensional parameters of our interest such as Weissenberg number We2, Magnetic parameter M2, Suction parameter S, Stretching parameters B,A, power law index n, thermophoresis parameter Nt, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and Biot numbers B1,B2 are introduced. The effects of these parameters are analyzed with the help of graphs.
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دنیا نال نہ جانی

دنیا نال نہ جانی

اُٹھ جاگ مسافر دور دیا ، تینوں قافلہ واجاں ماردا اے
اوہ آخر نوں پچھتاوے گا جو ستیاں رین گزاردا اے

ایتھے چار دناں دا واسا اے
اے دنیا کوڑ دلاسا اے
نہ اس گل دا بھرواسا اے
کدوں وجناں سد سرکار دا اے

تیرے محل تے ماڑیاں سجدے نیں
جدوں موت نگارے وجدے نیں
پھر محل ناں چنگے لگدے نیں
ایہہ سب کجھ ہن کس کار دا اے

دھن دولت مال کمایا توں
سوہنے رب نوں دلوں بھلایا توں
ناں درشن یار دا پایا توں
تینوں فکر رہیا گھر بار دا اے

ایس دنیا نال نہ جانا اے
اوتھے کسے نہ دکھ ونڈانا اے
چنگے عملاں ہی کم آنا اے
کر ذکر توں رب غفار دا اے

ایہہ دنیا رنگ برنگی اے
ایہدی ہر دم چال بے ڈھنگی اے
ایتھے رزق دی قادریؔ تنگی اے
کوئی پچھے نہ حال بیمار دا اے

Desain didaktis berbasis Permainan Tradisional Engklek di Sekolah Dasar

Abstract This research motivated by the findings of learning obstacles experienced students in material around square. This is known based on the results of  test questions conducted during preliminary study to fourth grade elementary school students. To overcome  learning obstacles experienced by students, researchers will design a didactic design. The purpose of this study is to describe the didactic design on the material around square and describe the students' responses the implementation of didactic design. The didactic design can be interpreted  learning design that emphasizes the didactic aspect, namely the teacher's teaching method. This study uses method with a Didactical Design Research (DDR) research design consisting of three research stages, namely a prospective analysis of the didactic situation before learning (prospective analysis) in the form of a Hypothetical Didactic Design including ADP (Pedagogical Didactic Analysis), metapedadidactive analysis, and retrospective analysis (retrospective analysis), with data collection techniques used in the form of interviews, observations, and attitude scales. The research subjects were 26 students in grades IV and VI and 1 teacher for grade IV at SDN 1 Sindangrasa. Based on results of study, through application of the didactic design carried out in stages I and II,   can help overcome learning obstacles experienced by students in the material around a square. This is shown from the students' responses on the attitude scale, results of the LAS (Student Activity Sheet) work and interviews with teachers. In addition,   didactic design is able to create a fun and meaningful learning atmosphere for students. Keywords: learning obstacle, didactical design research, square, meaningful learning, LAS Abstrak Penelitian ini dilatarbelakangi oleh adanya temuan learning obstacle  yang dialami siswa pada materi keliling persegi. Hal ini diketahui berdasarkan hasil soal tes yang dilakukan pada saat studi pendahuluan kepada siswa kelas IV Sekolah Dasar. Untuk mengatasi learning obstacle yang dialami siswa, peneliti akan merancang sebuah desain didaktis. Tujuan dari penelitian ini adalah untuk mendeskripsikan desain didaktis pada materi keliling persegi serta memaparkan respon siswa dan guru terhadap implementasi desain didaktis tersebut. Desain didaktis dapat diartikan sebagai desain pembelajaran yang lebih menekankan pada aspek didaktik yakni cara pengajaran guru. Penelitian ini menggunakan metode Didactical Design Research (DDR) yang terdiri dari tiga tahap penelitian, yakni analisis situasi didaktis sebelum pembelajaran (prospective analysis) berupa Desain Didaktis Hipotesis termasuk ADP (Analisis Didaktis Pedagogis), analisis metapedadidaktif, dan analisis retrospektif (retrospective analysis), dengan teknik pengumpulan data yang digunakan berupa wawancara, observasi, dan skala sikap. Subjek penelitian yaitu 26 siswa kelas IV dan VI serta 1 guru kelas IV SDN 1 Sindangrasa. Berdasarkan hasil penelitian, melalui penerapan desain didaktis yang dilakukan pada tahap I dan II dapat membantu mengatasi learning obstacle yang dialami siswa pada materi keliling persegi. Hal ini ditunjukkan dari respon siswa pada skala sikap, hasil pengerjaan LAS (Lembar Aktivitas Siswa) serta wawancara terhadap guru. Selain itu, desain didaktis mampu menciptakan suasana pembelajaran yang menyenangkan dan bermakna bagi siswa.  Kata kunci : hambatan belajar, desain didaktis, persegi, pembelajaran bermakna, LAS

Clinical Assessment of Pediatric Pharmacotherapy and its Predictors at Tertiary Care Hospitals of Peshawar, Pakistan

Pediatric pharmacotherapy aims to ensure safe and effective use of drugs in various population of children. However, due to varied pediatric pharmacokinetic drug profile and lack of pediatric drug data as compared to adults, it is difficult to achieve the optimal drug therapy in pediatrics. Studies regarding dosage errors, drug interactions, unlicensed and off label drug use in pediatric population will help the health care professionals in identification and management of drug interactions as well as unlicensed and off label drug use. Patient drug profiles of 4240 patients were evaluated using Micromedex Drug-Dex and Drug-Reax at pediatric department in four tertiary care hospitals of Pakistan (3 public and 1 private). The association between studied risk factors was analyzed using logistic regression to calculate the odds ratio (OR) and 95% confidence interval (CI). In pediatric surgical units, total of 895 patients drug profiles were analyzed which described mean number of drug was 3.51 ± 1.50. Of all the patients, 351 (39.21%) had sub-therapeutic doses and 67 (7.48%) had overdoses, while 148 (16.54%) patients were exposed to DDIs. A total of 11 drug combinations were observed that led to 160 DDIs. Overall, 3168 drugs were prescribed of which 1931 (64.89%) were unlicensed and 1542 (48.67%) were off labeled. Indication (38.71%) and dose (34.82%) were the most frequent off label categories in all the therapeutics classes. Chi square value revealed that unlicensed drug use was significantly associated with the type of hospital (p<0.0001). A significant association was also found between unlicensed (p<0.0001) and off label (p<0.031) drug prescribing with age groups. Multivariate binary logistic regression analysis revealed that infants (OR 4.092, 95%CI 2.272-7.370) and children (OR 2.691, 95%CL 1.581-4.581) age groups were 4 times and 2.6 times respectively more likely to receive unlicensed medicines, while they were significantly less likely, Abstract v (OR 0.270, 95%CI 0.109-0.667) and (OR 0.320, 95%CL 0.133-0.769), to receive off label medicines than adolescent group. Pediatric patients receiving less than 5 medications were significantly less likely to receive unlicensed drug (OR 0.105, 95%CL 0.051-0.213) and off-label drugs (OR 0.117, 95%CL 0.42-0.323) as compared to pediatric patients that received 5 or more medications. Male patients were 2.1 times more likely to receive unlicensed medicines (OR 2.103, 95%CL 1.507-2.937), while they received substantially less amount of off-label medicines (OR 0.685, 95%CL 0.458-1.024) as compared to females. Hospital stay of less than 5 days (OR 0.397, 95%CL 0.228-0.629) carried significantly less risk of off label prescription as compared to patients staying at hospital for more than 5 days. In the pediatric medical wards of all the hospitals 1375 patients were analyzed. The mean number of prescribed drugs per patient was 3.93 ± 1.85. Analysis of 1375 cases revealed sub-therapeutic doses in 571 (41.2%) cases while overdoses was observed in 136 (9.89%) cases. In 1375 medical ward patients, 239 (17.38%) had at least one DDI regardless of type of severity. A total of 101 interacting drug pairs were identified causing 417 drug-drug interactions, while 100 drugs were prescribed 5708 times, of which 65.66% prescriptions were unlicensed by FDA. The percentage of off label prescriptions were 52.99%. Evaluating off label drug categories showed that dose (35.7%) and age (19.4%) were the highest reason observed for off label prescriptions. Significant association was found between unlicensed drug use with type of hospitals (p<0.001). A significant association was also found between unlicensed (p<0.002) and off label (p<0.0001) use of drugs with age groups. Multivariate binary logistic regression revealed that pediatric patients receiving drugs 5 or less drugs were significantly less likely to receive unlicensed prescriptions (OR 0.112, CL95% 0.027- Abstract vi 0.461) and off label drugs (OR 0.180, CL95% 0.073-447) as compared to patients who received 5 or more drugs. Analysis of 250 patients in the cardiology ward of HMC revealed the mean number of prescribed drugs to be 4.67±2.07. Of all the patients, 59.69% had sub-therapeutic doses and 5.52% had overdoses while132 (52.8%) had at least one DDI regardless of type of severity. Out of total drug prescriptions (1231), 43.05% were unlicensed and 44.59% were off labeled. In multivariate analysis, occurrence of unlicensed prescriptions were significantly more likely associated with infants (OR 10.288, CL 1.839-57.547) and children (OR 12.822, CL 2.004-62.025) age group as compared to adolescent group, while infant (OR 5.850, CL 1.131-30.246) age group was significantly 5.8 times more likely to receive off label prescription as compared to adolescent group. Among 1300 neonatal patients, 192 (14.76%) were premature in all nurseries of four tertiary care hospitals. Mean number of prescribed drugs were 2.85±1.35, while 358 (27.5%) had sub-therapeutic doses and 50 (3.8%) had overdoses. At least one DDI was present in 7.38% patients and a total of 21 drug combinations attributed to 112 DDIs. A total of 52 drugs were prescribed 3448 times, of which 1150 (33.35%) were unlicensed and 1798 (52.14%) were off labeled. Dose (61.29%) and indication (13.68%) were the most frequent off label categories in all the therapeutics classes. Chi square value determine that unlicensed drug use was significantly associated with the type of hospital (p<0.0001) and age groups (p<0.0001). Off label drug prescribing was also significantly associated with age groups (p<0.001). Multivariate binary logistic regression analysis showed that neonatal patients of age 0 to 7 days (OR 1.355, 95% 1.021-1.799), were significantly less likely to receive off unlicensed prescriptions as compare to reference age group. Male patients (OR 1.355, 95%CL 1.021-1.799) were significantly 1.3 times more exposed to receive unlicensed medicines compared to Abstract vii females. Neonatal patients of age 0 to 7 days (OR 1.631 (1.048-2.536) were also significantly 1.6 times more likely to receive off label medication as compared to patients of age 22 and above days. Of 420 patients admitted in pediatric intensive care units, the mean number of prescription per child was 4.13 ± 2.19, while 175 (41.66%) had sub-therapeutic doses and 54 (12.85%) had overdoses. Moreover, 74 (17.61%) patients had at least one DDI regardless of type of severity which were due to 41 interacting drug combinations leading to 156 DDIs. A total of 96 different drugs were prescribed 2453 times. Of these, 29.8% prescriptions were unlicensed from FDA and 42.27% were off label prescriptions. Dose (340, 32.79%) and indication (26.13%) was the highest reason for off label prescriptions. Multivariate regression analysis showed that patients receiving medications less than 5 (OR 0.280, 95%CL 0.137-0.570) were significantly less likely to receive off label prescriptions as compared to patients received 6 or more medications. In conclusion, prevalence of dosage errors and drug interactions was found to be higher in pediatric cardiology unit. A high prevalence of unlicensed and off label prescriptions was also observed in the present study which showed poor pediatric pharmacotherapy of our region. Increased number of prescribed drugs and infant age group were found to be significant predictors for unlicensed as well as for off label drug use. Unlicensed and off label drug use can also lead to adverse drug events. Therefore, to avoid exposing pediatrics to unnecessary risks, activities of health regularity agencies and perhaps, extra incentives are required to encourage the proper evidence based pediatric prescribing.