اعجاز القرآن کا تحقیقی و تجزیاتی مطالعہ Research and analytical review of I‘jāz-al-Qurān

The Holy Qurān which was revealed to the last Prophet Muhammadﷺ, Just as you are a collection of perfections, so is the word revealed to you a collection of perfections. One of the most important perfections of the Holy Qurān is the miracle of the Holy Qurān. The unique and unique way of reciting the Qurān is called I‘jāz-al-Qurān in Islamic terminology. The Holy Qurān challenged the opponents and deniers of the Holy Qurān to explain its uniqueness.O Beloved! Say: If man and jinn come together and strive to be like the Qurān, they will not be able to make the likeness of it, even if they become helpers of one another. The Qurān is a book of miracles, and miracles are those that are beyond human power and beyond the reach of everyone, power and courage, especially a miracle that lasts for a couple of years or a limited time. Not for the sake of it, but for the challenge of the creation which will come after its coming, and which will make the way of guidance easy for those who ponder within themselves. In this article, I will try to explain the different aspects of I‘jāz-al-Qurān and embellish it with arguments.

Numerical Solutions of Unsteady Models of Non-Newtonian Fluids

The aim of this thesis is to examine the unsteady effects in the two or three dimensional boundary layer flow of non-Newtonian fluids along with the presence of different physical factors. Heat and mass transfer is involved with first order chemical reaction. In some cases, soret and dufour effects are also investigated. The flow models are explained in terms of continuity, momentum, energy, concentration equations which are converted into dimensionless form by using similarity transformation. Solutions are then obtained by an analytic-numeric technique Homotopy analysis method (HAM) and then comparison is shown by using Runge-Kutta-Fehlberg algorithm with shooting method. Convergence of solution and graphs of error analysis are also included to check the authenticity. Study of motion of the fluid’s behavior with heat and diffusion processes are depicted vividly through graphs and tables against different pertinent parameters. It is observed that magnetic force always slows down the velocity rate and presence of Casson and Maxwell parameter enhances the thermal and solute boundary layer as compared to the steady model. In Chapter 2, an endeavor is applied to observe the approximate solutions of unsteady two-dimensional boundary layer flow with heat and mass transfer behavior of Casson fluid past a stretching sheet in presence of wall mass transfer and 1st order chemical reaction. After adopting the similarity transformation; Homotopy analysis method (HAM) is applied to solve these ordinary differential equations. Numerical work is done carefully with a wellknown software MATHEMATICA for the examination of non-dimensional velocity, temperature, and concentration profiles, and then results are presented graphically. It is observed that involvement of time dependent factor reduces the thermal but enhances the solute boundary layer as compared to the steady model. v The Chapter 3 is useful to investigate the analytic-numeric solutions of an unsteady 3-D MHD Casson fluid flow which is embedded in a porous medium past a stretching sheet under the heat transfer influence. The similarity transformation is adopted to convert the partial differential equations of current model into its dimensionless form. Then, it is solved by employing an algorithm of a powerful technique Homotopy analysis method (HAM). After that, solutions are compared by invoking Runge-Kutta based shooting method. The theme of Chapter 4 is to study the first-order chemically reacting Maxwell fluid past a stretching sheet embedded in a porous medium with the discussion of wall mass transfer and Soret, Dufour effects. HAM is invoked on the dimensionless form of flow model for the series solution; where numerical simulation is carried out by a powerful software MATHEMATICA. Furthermore, the impact of disparate physical parameters on the flow, temperature and concentration profiles are shown vividly. Errors graphs are also there to show the authenticity of results. At the end, in Chapter 5, a precise note or conclusion related to whole of my thesis is provided.