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غزل

داغ ایسے کہ جو دھلتے ہی نہیں پانی سے

آج برسی ہے مری آنکھ پریشانی سے

مضطرب رہنا زمانے میں اسے بھاتا ہے

یعنی درویش بہت خوش ہیں نمک دانی سے

کیوں سکردو میں بھی آتا ہے پسینہ اتنا

کیوں علاقے ہمیں لگتے نہیں برفانی سے

اب بھی ہر پیڑ تحیر میں اسے کھوجتا ہے

اس نے اک پھول چھوا تھا کبھی حیرانی سے

حسین بن منصور حلاج اور ان کی صوفیانہ تعلیمات کا علمی وتحقیقی جائزہ

A Sufi poet, teacher and philosopher, Hallaj was executed on the orders of an Abbasside caliph for uttering these words, taken to mean Hallaj as claiming himself to be God. After more than a decade of imprisonment, Hallaj was eventually executed publically in Baghdad in the year 922. He is seen by many as a revolutionary writer and teacher of his time, when practices of mysticism were not meant to be shared publically. Yet he remains a controversial figure, revered by Rumi, hated by many, he was labeled an intoxicated Sufi and is still read today. After his arrest in Sūs and a lengthy period of confinement (c. 911–922) in Baghdad, al-Ḥallāj was eventually crucified and brutally tortured to death. A large crowd witnessed his execution. He is remembered to have endured gruesome torture calmly and courageously and to have uttered words of forgiveness for his accusers. In a sense, the Islāmic community (ummah) had put itself on trial, for al-Ḥallāj left behind revered writings and supporters who courageously affirmed his teachings and his experience. In subsequent Islāmic history, therefore, the life and thought of al-Ḥallāj has been a subject seldom ignored. Here we get a realistic overview about him and his teachings.

Fluid Flow Due to Stretching/Shrinking Surfaces

Considering the vast applications of stretching (shrinking) and porous sheets and tubes, the main objectives of this thesis is to study the fluid flow driven by stretching (shrinking) and porous sheet in case of rectangular and cylindrical coordinate system for two dimensional flows. In fluid mechanics, the no slip conditions (moving sheets, walls, cylinder etc.) will set the fluid into steady motion, qualitatively solid body motion, pressure gradient and buoyancy force and many more may cause such flows. Almost all these problems have been addressed and analyzed for boundary layer approximations and interesting results have been presented. Keeping in view, active role and applications of flow and heat transfer by stretching (shrinking) and porous sheet, a lot of work has been carried out for linear, power law and exponential stretching sheets in Newtonian and non-Newtonian fluids. However, the scope of the study is enlarged by considering the flow and heat transfer over stretching (shrinking) and porous surfaces with three different thermal behavior such as (i) prescribed surface temperature (ii) variable (uniform) convective heat transfer at plat surface and (iii) prescribed variable (uniform) heat flux. Throughout this thesis different and complex scenario have been seen in each stretching (shrinking) problem emulsify the geometry of sheet which allows different similarity transformation, as a result different governing equations in form of ODEs have been met. The problem in hand is solved by appropriate different mathematical techniques of interest and each method is significant for a particular case. Lest the researchers think that the model problems of viscous flow over stretching (shrinking) and porous sheet (cylinder) are so over simplified that it is not worth making a fuss over, we further noticed that these formulations has borne the brunt of almost all the theoretical models of viscous flow over stretching (shrinking) and porous (injection/suction) sheet to this date. This has always been a challenge for the scientists and engineers to introduce new and generalized similarity transformations that have been made to give a unified approach to solve all such stretching (shrinking) and porous problems in one lope. For the first time such a new, unusual and generalized similarity transformations are introduced to reduce the governing boundary value problem into self-similar form for rectangular and cylinder coordinate system. The formulation of such special type models and the methodologies associated with many other problems regarding stretching (shrinking) and porous sheet (cylinder) have been reviewed and since then some issues regarding all these simulations and their solutions have been addressed in this thesis. We are focused on generalized formulation of these problems in view of generalized transformations in terms of boundaries and different solutions (numerical, exact and series solutions). The very illuminating feature of this study is that a number of earlier works is abridged into one generalized problem through the introduction of new similarity transformations and found its solutions (exact, numerical and series solutions) encompassing all the earlier solutions. The analyses prevail over previous models of rectangular and axi-symmetric flows toward stretching (shrinking) cylinder discussed so far and all these simulations can be easily retrieved from the current model.
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Asian Research Index Whatsapp Chanel

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