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Analytical Analysis of Squeezing Flows

Thesis Info

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Author

Khan, Hamid

Program

PhD

Institute

Islamia Collage Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2013

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/934

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725495853

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This thesis covers the investigation of axisymmetric squeezing flows under slip and no slip boundary conditions. In the process, the flow of a fluid in a porous medium between two parallel plates approaching each other symmetrically has also been studied. The stream functions u r ( r , z , t ) = 1 ¶ y 1 ¶ y and u z ( r , z , t ) = - r ¶ z r ¶ r and the transformation function y ( r , z ) = r 2 F ( z ) were used to transfer the Navier-Stockes equations into an ordinary nonlinear differential equation along with the boundary conditions. To solve these nonlinear problems, different analytical methods that are; the Adomian decomposition method (ADM), the new iterative method (NIM), the homotopy perturbation method (HPM), the optimal homotopy asymptotic method (OHAM) and the differential transform method (DTM) are applied and velocity profiles for various parameters of Newtonian fluids are obtained. The velocity of plates and its effects on fluid velocity are established. The above mentioned methods are based on Taylor’s series but their line of action is different and one may face serious problems of convergence in their application. In this case, the convergence of the approximating series solution is discussed and the mathematica built-in code NDSolve is used to validate the results of analytical solutions. The results show that OHAM gives a better approximation under the conditions on which the research is premised.
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جہلم دا سفر

جہلم دا سفر
دل آکھے میں جہلم جانا
’’ڈھوک رجو‘‘ جا درشن پانا
بس ٹر گئی یار قبولے
پئی دیندی پیار دے جھولے
میں جانا عشق سکولے
میں تے ربا کرم کمانا
بس آ گئی عارف والے
سانوں مل گئے دیس نکالے
جنھاں عشق دے دیوے بالے
اگے جا کے موج منانا
بس آ گئی ساہیوال
میرا پیر بڑا لجپال
دیندا دل دے دیوے بال
میرے دل نوں نور بنانا
بس آ گئی شہر اوکاڑے
کیویں پائے عشق پواڑے
گھر کتنے ایس اُجاڑے
سانوں خیر دیدار دا پانا
بس آ گئی شہر لاہور
چلے دل تے نہ کوئی زور
اوہدی دید نوں پاوے شور
دل دے کے یار منانا

بس آ گئی گجرانوالہ
نہیں عشق دا پندھ سوکھالا
ساڈا اللہ اے رکھوالا
پردیس چ نہ گھبرانا

بس آ گئی وچ گجرات
ساڈے نال ہووے گل وات
سانوں دے سجناں اک جھات
ساڈے دل دا شوق ودھانا

بس آ گئی اے وچ کھاریاں
اساں بڑیاں واجاں ماریاں
سن سجناں ساڈیاں زاریاں
سانوں در تے آپ بلانا
بس ’’عالم گیر سرائے‘‘
اساں یار دے نیڑے آئے
ساڈے نین بڑے ترہائے
سانوں سوہنا مکھ وکھانا

بس اپڑی جہلم اڈے
اسیں بھیڑے کم سب چھڈے
ساڈے لیکھ ہوئے اج وڈے
اساں جہلم وقت لنگھانا

پھڑ ویگن گئے سنگوئی
اسیں کلے، نال نہ کوئی
لاہ مکھ توں سجناں لوئی
اساں ول ول درشن پانا

اسیں ’’ڈھوک رجو‘‘ وچ آئے
ساتھے رب نے کرم کمائے
اسیں قادریؔ! درشن پائے
دل آکھے ، مڑ نہیں جانا

Awareness and Accessibility of Right to Information Act: A Comparative Study of Minorities within Pakistan and India

Right to Information (RTI) has become one of the major laws to strengthen the democracy of a country. Therefore, this study aims to analyze the awareness and accessibility of RTI for minorities in Pakistan and India. In this regard, a survey questionnaire was distributed to the total of 50 Pakistani Hindus and 50 Indian Muslims under snowball sampling method. The findings were analyzed with the help of independent-samples t-test on SPSS. Findings indicate Pakistani Hindus have only 12% awareness and right to access information as compare to Indian Muslims. For the future studies, there is a need to develop awareness of Right to Information specially in Pakistan in order to improve accountability and transparency in the structure of government.

Study of Divalent and Trivalent Cations Substitution on X-Type Hexagonal Ferrites

In the present research work four X-type hexagonal ferrites series with compositions Ba2-xMgxCo2-ySryFe28O46, Sr2-xCaxNi2-yBayFe28O46, SrBaCu2-xCoxCryFe28-yO46 and SrBaZn2-xNixAlyFe28-yO46 where x=0.0, 0.1, 0.2, 0.3, 0.4, 0.5 and y= 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 have been synthesized by sol gel auto-combustion method. The characterization of the entire compositions has been done by thermo-gravimetric analysis (TGA), x-ray diffraction (XRD), fourier transform infrared spectroscopy (FTIR), dielectric measurements, vibrating sample magnetometer (VSM) and scanning electron microscopy (SEM). Thermo-gravimetric investigation reveals that hexagonal phase begins to form at a temperature ~1050 ºC and is completed at 1250 ºC for X-type hexagonal phase formation, which is also complimented by the XRD studies. The average crystalline sizes of four compositions were found within the range of 19-40nm. The variations in the lattice constants were in accordance with the dissimilarity in ionic radii of the host and substituted ions. FTIR analysis of entire synthesized compositions was observed in the range of 400-800cm-1 which indicated the existence of two vibrational bands appeared due to the octahedral and tetrahedral stretching vibrations. SEM images showed the hexagonal platelets structure which is best for microwave applications. The dielectric measurements of all synthesized composition were evaluated as the function of frequency and their behavior was described on the basis of Maxwell-Wagner and Koop’s theories. The obtained results revealed that dielectric constants, tan loss and the conductivities were found to be increased with the increased ratio of Mg-Sr, Ca-Ba and Co-Cr substituted synthesized samples. While the decreased trend in the dielectric constant for Ni-Al substituted samples are observed. Electric modulus studies were done to examine the relaxation behavior for all samples. To ensure the influence on magnetic characteristics of different divalent and trivalent cations substitution in synthesized compositions, vibrating sample magnetometer (VSM) was used. The variation in saturation magnetization, coercivity and remanence was observed on the basis of allocated cations in the different hexagonal lattice sites. The linear increase in saturation magnetization, remanence and coercivity in Co-Cr and Ni-Al substituted hexaferrite made them useful as permanent magnets while the decrease in saturation magnetization and coercivity in Mg-Sr and Ca-Ba substituted samples proposed these materials best for magnetic recording media as well as for microwave devices.