جدید اور ہم عصر ریاستوں كے مقابلے میں خلافت راشدہ كی انفرادیت

During the Dark middle ages of Europe, The Holy Prophet Muhammad (PBUH) established the first ever Islamic state, in the Arab soil, at Medinah. The successors of the Prophet, known as Khulfa-i- Rashideen (the Glorious Caliphs) not only maintained it rather they extended with further development. The Caliphate was not only a model statefor the world but also a unique one with respect to its political appratus, principles and the governance. This paper discovers the same uniqueness of the Caliphate in past and modern perspective.

Magnetohydrodynamic Flows in Pipe and Boundary Layer With Heat Transfer

In a viscous flow the viscosity effects are prominent only in a thin region near the solid boundary, namely, the boundary-layer or the thin shear layer. Since the start of the last century the study of boundary layer flows has been identified as a self- standing field of research in the area of fluid dynamics. The theory of boundary-layer has greatly helped the scientists and engineers towards the understanding of flow and heat transfer phenomenon in viscous flows. Despite the continuous research of scholars the understanding of three dimensional boundary-layers is still a demanding area of research. Three dimensional boundary-layer momentum equations are more complicated in comparison to the two dimensional ones but still there is a class of flows which are three dimensional with less complicated equation. Such flows are commonly known as axisymmetric flows. Axisymmetric flows occur inside/outside the pipes, over blunt bodies and in rotating disk systems. In this dissertation, we aim to examine various flow situations of multi- dimensional boundary-layer flows of axisymmetric nature. The impact of surface expansion/contraction and rotation has been investigated on the internal boundary- layer flow inside a pipe of uniform cross-section. The effects of surface stretching, rotation and oscillation on momentum and thermal transport in the external boundary- layer have been considered in the flow near a solid cylinder. The stagnation point flow has also been studied in rotating disk boundary-layer flow. Furthermore the effects of magnetohydrodynamic (MHD), suction/injection and unsteadiness have also been investigated in some cases. The calculation of skin friction coefficient and the coefficient of heat transfer has been the major study. Analytic and (or) numerical solutions have been obtained in all cases, however, the preference has been given to the analytic solution. Homotopy analysis method has been used for analytic solution and for numerical computations the shooting technique or the finite difference schemes have been applied. The accuracy and validity of these solutions have been proved in detail either by calculating the residual errors or through comparison with authentic results or both. The analysis reveals that both the momentum and energy transport strongly depend upon the curvature of cylinder. As compared to the flat plate case the coefficient of skin friction and heat transfer are bigger in magnitude for a cylinder of large curvature. For efficient cooling the dissipation effects are recommended to be minimized. Furthermore, the fluids of high Prandtl number are observed to be serving as good coolant.