قرون اولی میں مناہج اصول فقہ اور اس کا نشو و ارتقاء

It is a matter of fact that development of principles and the legal maxims of Islamic jurisprudence is a gradual process; it took more than a century. These principles and maxims are extracted from the Holy Quran, Hadith and the judgments or sayings of companions of Holy Prophet. This article presented the various examples of principles which were produced by companions of the Holy Prophet (peace be upon him), so that people know the origin of this filed of knowledge.

Mathematical Study for Stagnation Point Flows of Newtonian and Non-Newtonian Fluids

Non-Newtonian °uids feature in an extensive range of industrial and technological applica- tions including polymer processing, biotechnology, lubrication of aerospace and automotive vehicles and Nuclear thermo-hydraulics. Moreover, oblique stagnation point °ows have at- tracted some attention in recent years as they generalize the models used by engineers to include all possible angle of impingement of industrial °ows on solid surfaces. Motivated by simulating non-Newtonian multi-physical transport phenomena, the present thesis is devoted to the mathematical modeling, computation and subsequent physical analysis for non-orthogonal stagnation °ow of various type of °uid models namely Casson °uid model, Je®rey °uid model and Oldroyd-B °uid model which is a generalization of the upper con- vected Maxwell model. The governing equations for mass, linear momentum, heat (en- ergy) and concentration are modeled and then transformed by using applicable similarity conversions. The emerging strongly coupled nonlinear non-dimensional boundary value problems are solved with robust well-tested Runge-Kutta Fehlberg numerical quadrature and a shooting technique with tolerance level of 10¡5 and Keller box method, validation with Adomian decomposition method is also included. Comparison with the previous ex- isting published literature is also made and a very good agreement between the results is observed for limiting case. An extensive parametric study has been conducted to evaluate heat, momentum and concentration characteristics for the aforementioned °uid models. Mathematical modeling of these non-Newtonian models is presented with various physical e®ects such as mixed convection, thermal radiation, MHD, homogeneous-heterogeneous reactions and incorporation of nano°uids and micro-organisms. Results for physical quan- tities such as local skin friction, local Nusselt number and Sherwood number are depicted through graphs and tabular form. The obtained graphical results are discussed physically in a lucid manner. The result provides interesting insights into certain nuclear reactor x transport phenomena and furthermore a benchmark for more general CFD simulations. The present work retain signi¯cant validity in actual coating °ows and generalizes the conventional orthogonal case to the industrially relevant scenario of oblique °ow.