ادریس طوطی
پیپلز پارٹی کا یہ بہادر نوجوان 1963ء کو دھرم پورہ لاہور میں پیدا ہوا ۔سولہ سال کی عمر میں 1979ء کو پی ایس ایف میں شامل ہوا ۔ضیاء آمریت کے دور میں گھر پر مسلسل چھاپوں اور اہل خانہ کو ہراساں کر نے پر کابل چلا گیا ۔واپسی پر گرفتار ہوا ۔1983ء میں پھانسی دی گئی ۔پھانسی کے وقت آپ کی عمر 21سال تھی ۔
Almighty Allah created the man, endowed him with intellect and raised prophets among humanity for guidance. The scriptures were revealed by him which contained Divine commandments. Allah granted the prophets the power to show miracles to prove the truth of His message. Every prophet was endowed with miracles according to the need of hour and divine wisdom. The prophethood continued generation after generation and the prophet Muhammad (upon whom be peace and greeting) is the last in the chain of prophets. He was stengthened with countless miracles by Allah. Among these miracles, the Holy Qur`an is the greatest which is a universal and eternal miracle of the last prophet (peace be upon him).
The main theme of this thesis is to establish exact solutions for certain flows of non- Newtonian fluids of rate type including Maxwell fluids, generalized Maxwell fluids and Oldroyd-B fluids. The rotational flow of a generalized Maxwell fluid in a circu- lar cylinder, oscillating flows between two coaxial infinite cylinders for Maxwell and Oldroyd-B fluids, as well as the flow induced in Maxwell fluids by a constantly accel- erating plate between two side walls perpendicular to the plate have been discussed here. The mathematical formulation of these problems leads to partial differential equations which are solved by different mathematical techniques like Laplace trans- form, Fourier sine transform and Hankel transform. The associated tangential stresses are also determined. By means of graphical illustrations, the required time to reach the steady-state for oscillating flows of Maxwell and Oldroyd-B fluids are also ob- tained. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions, the differentiating term by term into infinite sums being clearly permissible. Finally, the corresponding solutions for Newtonian fluids are also obtained as limiting cases.