اسم محمد ﷺ اور رسول اللہ کی جلالت قدر کا تحقیقی اور تجزیاتی مطالعہ

Regarding Nabuwat, our Holy Prophet (S.A.W.W) has attained excellence/perfection. His name is foremost (S.A.W.W) among all prophet hood is towards both the worlds. He will be brought before all prophets most respectfully on the Day of Judgment. His teachings are not cancelled as compared to the prophets before him (S.A.W.W). His (S.A.W.W) virtues and excellences are uncountable and unlimited. Below is described his (S.A.W.W) magnificence and dignity in respect of his name; Muhammad (S.A.W.W).

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.