Search or add a thesis

Advanced Search (Beta)
Home > Analytical Solutions for Different Motions of Differential and Rate Type Fluids With Fractional Derivatives.

Analytical Solutions for Different Motions of Differential and Rate Type Fluids With Fractional Derivatives.

Thesis Info

Access Option

External Link

Author

Riaz, Muhammad Bilal

Program

PhD

Institute

Lahore University of Management Sciences

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10300/1/Muhammad%20Bilal%20Riaz_Maths_2018_UMT_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725499501

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


In this dissertation, we present the analytical studies of some uid ow models. We analyze the fractional models for the ow of non-Newtonian uids via classical computational techniques to obtain analytical solutions. This study includes the investigation of the unsteady natural convection ow of Maxwell uid with fractional derivative over an exponentially accelerated in nite vertical plate. Slip condition, chemical reaction, transverse magneticeld and Newtonian heating e ects are also considered using a modern de nition of fractional derivative. Moreover, the unsteady ow of Maxwell uid with noninteger order derivatives through a circular cylinder of in nite length in a rotating frame is studied. The motion of Maxwell uid is generated by a time dependent torsion applied to the surface of the cylinder. As novelty, the dimensionless governing equation related to the non-trivial shear stress is used and therst exact solution analogous to a ramped shear stress on the surface is obtained. The rotational ow of an Oldroyd-B uid with fractional derivative induced by an in nite circular cylinder that applies a constant couple stress to the uid is investigated. It is worth mentioning that the considered problem of Oldroyd-B uid in the settings of fractional derivatives has not been found in the literature. Some unsteady Couette ows of an Oldroyd-B uid with non-integer derivative in an annular region of two in nite co-axial circular cylinders are investigated. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time dependent velocity while the inner cylinder is heldxed. Finally, the analysis of the second grade uid with fractional derivative is made. The uidlls the annulus region between two coaxial cylinders in which one cylinder is at rest while the other experiences time dependent shear stress. In all the ow models, we obtained the exact or semi analytical solutions for the motions with technical relevance. These solutions correspond to some ows in which either velocity or the shear stress is given on the boundary are established for di erent kinds of rate and di erential type uids. The obtained solutions presented in all the uid ow models satisfy the imposed initial and boundary conditions. Further, the ow properties and comparison of models with respect to derivative (fractional or ordinary) are highlighted by graphical illustrations.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

دیکھنے تجھ کو اگر چاند ادھر آئے گا

دیکھنے تجھ کو اگر چاند ادھر آئے گا
اذن پائے گا نہ جب، تھامے جگر آئے گا

ہجر لمحے مری غزلوں میں ہیں ایسے ٹھہرے
مجھ کو اب کیسے کوئی اور ہنر آئے گا

منتظر دل ہی نہیں ساتھ میں ہیں آنکھیں بھی
مجھ میں اک بار نہیں بارِ دگر آئے گا

دید کی آخری حد تک جو اسے دیکھا ہے
ہر طرف اب مجھے وہ چہرہ نظر آئے گا

حسن اس کا ہے فضاؔ سارے زمانے کے لیے
چاند ہے وہ بھلا کب تیرے ہی گھر آئے گا

لأزمة الأخلاقية في المجتمع الباكستاني المظاهر- العوامل- المعالجة

Moral values are seen as the basis of human civilization. Absence of moral values and responsibilities results in the justification of every evil in the society, as it is the case being observed in the present-day societies in many parts of the world. A nation, whose collective morals are high, is capable to lead other nations, irrespective of caste, creed and religious affiliations. If a nation, Muslim or non-Muslim, ignores the high moral values, it cannot avoid its decadence and destruction. Due to this utmost importance of morality for humanity, Islām regards morality as one of the integral parts of the Divine Revelation. Islām aims to create a sense of moral responsibility in its adherents, so that, they may show a complete picture of an ideal society, and enjoy their freedom to carry out the best possible moral deeds. The author of this paper, chose to study the present moral crisis in the Pakistani society and tried to determine the causes, which has brought about this moral crisis and also presents its cure in the light of the Qur’ān and Sunnah. The study focuses on the following aspects: Definitions of moral values & society, Prevalent social evils in our society, Causes of crimes and social evils, Remedies to root out unethical practices and evils from the society, Conclusion and recommendations.

Population, Distribution and Food Habits of Indian Pangolin Manis Crassicaudata in Potohar Plateau

Indian pangolin (Manis crassicaudata), the only pangolin species that occurs in Pakistan, is categorized more recently as “ Endangered” under IUCN Red List criterion and it faces a high risk of extinction in the wild. Ecological data on this species is very scanty in the country, where illegal hunting and killing for obtaining its body scales for trade purpose is the biggest threat to its population. The current study, therefore, investigated the distribution, vegetation analysis of the habitat, current population status, and the diet of Indian pangolin in the Potohar Plateau. Distribution of Indian pangolin was studied by conducting extensive surveys in the study area, in addition to carrying out questionnaire surveys (Interviews by local people). Results showed that Indian pangolin was distributed in all transects taken in district Chakwal and Jhelum while it was found present in some transects but absent in others, in the rest of the two districts (Attock and Rawalpindi) of the Potohar Plateau. Vegetation analysis of the habitat of Indian pangolin was carried out by quantifying trees (by Point-Centered-Quarter method), shrubs and herbs species (by Quadrat method) of the study area. For shrub species, quadrats of 4m x 4m, while for herb species quadrats of 1m x 1m were established at selected sampling sites for data collection. Dominant tree species included Acacia nilotica (IVI=74.9) Zizyphus mauritiana (IVI=61.75), and Acacia modesta (IVI=58.6), dominant shrub species were Zizyphus nummularia ( IVI=199.16), followed by Calotropis procera (IVI= 65.08), Prosopis juliflora (IVI= 35.40), and Lantana camara (IVI= 30.13) xx while the major herb species recorded were Cynodon dactylon (IVI = 40), followed by Cenchrus ciliaris (IVI= 37.56) and Cyprus rotundus (IVI= 31.06). Population density of Indian pangolin in the study area was estimated by using indirect method of its active permanent burrow counts at thirty different selected sampling sites including all four districts of the Plateau. Population estimates of the species showed overall a declining trend in the Potohar plateau; an average population density of 1.08 /km² was recorded during the year 2010 and 0.36 /km² in 2011 and 0.23/km² in 2012, with an overall decline by 79%, with an average decline of 52 % per annum. The population density of the species was found significantly different (p < 0.05) within the study years (2010 - 2013). A total of N=10 specimens of Indian pangolin were recovered from the field from different sampling sites, in addition to two skeletons, for their morphometrical analysis. Average body weight and body length of the specimens were 9 ± 2.2 kg and 99.25 ± 10.5 cm, respectively. Relative tongue weight (RTW) and relative tongue length (RTL) constituted 0.2 % and 37 %, of the body, respectively. Average numbers of scales on the body of juvenile, sub-adult, and adult specimens were 286, 276, and 424, respectively. Food habits of Indian pangolin were investigated by fecal analysis, a total of N = 44 fecal pellet samples were collected from different sampling sites of the study area. Fecal analysis revealed main food components recovered from samples as ants body parts (including heads, and abdominal parts) approximately 41.5%, and soil particles or clay approximately 58%, with minor percentages of bugs, termites body parts, grass and wood. The soil particles or clay contributed the highest % weight (57.95%) of the fecal pellet followed by ants (37%), wood xxi (2.3%), grass (0.89%), termites (0.95%) and least for bugs (0.375%). The main prey species of Indian pangolin identified from the faecal analysis and from the field collections included two species of black ants (Camponotus confuci and Camponotus compressus) and one species of termite (Odontotermes obesus). The biggest threat to the population of Indian pangolin in the study area is its illegal capturing and killing for obtaining its body scales for trade purpose, which are used in making Traditional Chinese Medicines (TCM). A sharp decline of approximately 79% in the population of Indian pangolin during three years of the study period demands urgent conservation measures to be launched to save its little remaining population.