For developing the simulation techniques applicable to engineering system, the modeling of a vertical inverted U–tube steam generator (UTSG) operating in a Nuclear Power Plant (NPP) has been carried out for finding the temperature distribution, optimum boiling length in the tube and addressing the interaction of technical and environmental factors involved in the system. Modeling of a system consists of three stages: (i) Development of computer code, (ii) Application of the model in the steam generator, (iii) Evaluation of the model in the power plant. Computer model has the ability for optimization of steam generator parameters to be used in simulation. The steam generator modeling for the temperature distributions comprises of development of a specific mathematical model considering the real engineering constraints. The modeling approach used for the simulation of a conventional boiler has to be revised, since the heat transfer regime in each tube can not be fixed by the equipment design. General equations have to be used for each tube of the boiler and the actual heat transfer conditions in the tube has to be identified. The solution of the model has been discussed analytically under steady state conditions. Empirical equations are available to predict the saturation temperature in each region of the steam generator. The computed results show the temperature distribution of the primary fluid along the whole length of the tube and the point of saturation temperature, where steam formation starts. The behaviours of important parameters involved in the process are studied by the comparison of simulated results. The analytical solution is based on certain simplifying assumptions, which to some extent limits the scope of its applicability. A numerical simulation technique has been developed by adopting Euler–Cauchy method to obtain a solution independent of the assumptions made in the analytical solution. This makes the model more realistic and flexible and enables to find the relative temperature distribution behaviours of the primary and secondary fluids in UTSG and an optimum boiling length of the tube (Lb). The main advantage of the proposed method is that it permits a better understanding of the influence of the design parameters on the cycle performance. A boundary condition needs to be prescribed along the tube to start calculations.7 The solution of the model has also been discussed under unsteady (Transient) conditions. To simulate the transients, the mathematical model is discretised in terms of time and space coordinates. The flow model in transient state is used to derive a time dependent finite difference simulation technique which gives the relative temperature distributions of the fluids and an optimum boiling length (Lb) with respect to time from 0.0% Reactor Power (RP) level to 100% RP level. For further analysis, the graphs of the temperature distributions of secondary and primary fluids are drawn at specified intervals of time. These results can be used for a multi–objective optimization of the steam generator in future. The model provides a significant analytical capabilities for the specialists working in the field of NPP safety. The purpose of the work is to predict the behaviour of steam generator working in NPP and to help correctly for defining the operator action validation and verification of Emergency Operating Instruction (EOIs). The model is practically feasible under prevailing constraints. Evaluation of the model in terms of calibration, sensitivity and verification yields a good agreement between observed and computed results (hydrograph) of the steam generator and its components. The work on unsteady (transient) heat flow in a UTSG is very scarce in the literature. Mostly, the steady flow problems have been discussed. Few attempts have been made regarding the transient flows. Keeping the above facts in view, the entire work of the present thesis is organized as follows: Chapter 1 consists of some introductory remarks, complete modeling process, explanation of computer codes, the physical model and general features of Nuclear Power Plant (NPP) and Nuclear Steam Generator (NSG). Objectives, scope of study and previous work are also mentioned in this chapter. Chapter 2 studies the basic preliminaries relevant to the laws for system analysis and energy balance equations. Parallel and counter flow heat exchangers and their temperature distributions with length are explained. Shell and tube and multipass shell and tube heat exchangers are also discussed. Heat exchangers effectiveness against the number of transfer units is described at the end of this chapter. Chapter 3 describes modeling and simulation of the steam generator in steady state – a case study. The formulation of the mathematical model and its analytical solution are given. Equation which governs the primary side incompressible fluid flow in8 a UTSG is also modeled here. Model layout and solution procedure is also discussed in this chapter. One fortunate outcome of the graphical approach works best to find percentage changes in the outlet temperature of the primary fluid corresponding to any desired changes in the mass flow rate (m) and the factor Rh. The results of this chapter are published in “Pakistan Journal of Scientific Research, Vol. 60, pp. 40–43, (2008)”. Chapter 4 is concerned with the formulation of numerical models for primary and secondary of fluids. The numerical scheme evaluates the temperature distribution of the primary fluid relative to the temperature distribution of the secondary fluid and vice– versa for the user specified input data. An iterative procedure is followed until the program converges for an optimum boiling length of the tube using relative error criteria. A reasonable agreement between experimental observations and numerical solutions is presented through graphs. These results are published in “Pakistan Journal of Engineering and Applied Sciences, Vol. 4, pp. 74–79, (2009)”. Chapter 5 deals with the solution of the model of UTSG in transient condition. The flow model in transient state is used to derive a time dependent finite difference simulation technique which gives the relative temperature distributions of the fluids and an optimum boiling length (Lb) with respect to time from 0.0% Reactor Power (RP) level to 100% RP level. The results obtained from the suggested models have been found to be in good agreement with the experimental data. The contents of this chapter are published in “Pakistan Journal of Engineering and Applied Sciences, Vol. 5, pp. 10–15, (2009)”. Some observations from chapter 5 have also been accepted for publication in “International Journal of Mathematical Modeling, Simulation and Applications, (2009)”. To upgrade the existing control system, an improved control strategy can be developed. The numerical simulation techniques show that the procedures are effective and can be used for a multi–objective optimization of the steam generator in future.
The Immensely Merciful to all, The Infinitely Compassionate to everyone.
33:01 a. O The Prophet! b. Remain conscious of Allah - The One and Only God of everyone and everything, and c. do not yield to pressures brought about by the disbelievers and the hypocrites. d. Surely Allah is All-Knowing of what they say and what their motives are and All-Wise.
33:02 a. Instead, follow what is being revealed on to you from your Rabb - The Lord. b. Surely Allah is All-Aware of whatever you do: your deeds, dealings, and motives.
33:03 a. And trust Allah. b. And Allah is Sufficient for you as a Guardian - to look after your affairs.
33:04 a. Allah has not placed two hearts in any person’s body. b. And just as HE has never made your wives - whom you declare to be as your mothers’ backs - your biological mothers, c. And, so too, HE has never made your adopted sons to be your biological sons. d. These are merely phrases you utter from your mouths, e. whereas Allah Speaks the truth in this and all matters. f. And thus HE Guides you along the way of truth.
33:05 a. As for your adopted children, address them by the names of their biological fathers. b. That is more just in the Sight of Allah. c. But if you do not know the names of their biological fathers, then they are your brethren in faith and your protégés - so observe the due relationship within that social framework. d. However, you will not be blamed for...
This paper focuses the issue of shrinking civic space in Pakistan. The study presents civil society activists’ responses on this issue, highlights their perception, present and future strategies to address this issue, and their effectiveness, as such, as well. Pakistan presents a unique case due to its involvement in the ‘war on terror’ and the consequences being faced by both the state and society at large. Present shrinking of civil society action is directly linked with it. In an attempt to grapple with the problems emerging from ‘war on terror’, the overgrown state is encroaching upon citizens’ space, thus denying the civil society to play its due role which can provide safety for the state as well. The preferred strategies of the NGOs include lobbying with parliamentarians and mobilizing the citizenry about the situation.
The main purpose of this thesis is to discuss the fluid flow driven by stretching of the sheet. In fluid dynamics, there are many mechanisms to drive the fluid flow: like the motion of the boundaries, the pressure gradient and the buoyancy force. Of these mechanisms, the motion of the boundaries remains the most important. And among many fluid flows driven by the motion of the boundaries, the flow induced by stretching of the surface has been of greatest value and importance. In fact its importance lies in the application of stretching sheets in industry and engineering. Such flows are generally generated in extrusion of polymers, fibers spinning, hot rolling, manufacturing of plastic and rubber sheet, continuous casting and glass blowing. The stretching of the sheets have been initially undertaken in Newtonian fluid and later on extended to non-Newtonian fluids-- because of their application in polymer industry. The heat transfer through a fluid in the presence of fluid flow is also a subject of immense importance both for understanding of fluid flow and its applications in vast areas of industrial problems. Keeping in view the importance of the flow and heat transfer by stretching sheet a huge amount of work has been published for linear, power law and exponential stretching of the sheets in Newtonian and non-Newtonian fluids. However, the bulk of this work describes the flow and heat transfer past a continuous stretching surface taking linear, polynomial, power law and exponential stretching velocities and temperature distributions. However, this has always been a challenge for the scientists and engineers to introduce new stretching velocities for the solutions of non-linear equations on the one hand and its industrial applications on the other hand. The present thesis extends the class of stretching problems by introducing a hyperbolic stretching velocity and temperature distribution on the sheet, for the first time. The appropriate similarity transformations are introduced to reduce PDEs into ODEs. Arbitrary stretching and non- Newtonian fluids are also taken into consideration. These investigations will go a step forward in understanding the fluid flow and heat transfer for so far unaccounted stretching of the sheet and its possible industrial applications both in Newtonian and non- Newtonian fluids. The first chapter of this thesis contains the history and literature related to stretching sheet problems and states the basic definitions and equations to be used in later chapters. In second chapter we introduce the concept of hyperbolic stretching of the sheet for the first time in this thesis. The boundary layer flow and heat transfer analysis of an incompressible viscous ixfluid for a hyperbolically stretching sheet is investigated. The analytical and numerical results are obtained using series expansion method and Local Non-Similarity (LNS) methods respectively. Analytical and numerical results for skin friction and Nusselt number are calculated and compared with each other. The significant observation is that the momentum and thermal boundary layer thicknesses decrease as the distance from the leading edge increases. The well- known solution of linear stretching is found as the leading order solution for the hyperbolic stretching. The contents of this chapter have been published in Applied Mathematics and Mechanics (English Edition), 33(4), 445–454 (2012). Flow and heat transfer of an electrically conducting viscous fluid over a hyperbolic stretching sheet with viscous dissipation and internal heat generation is investigated in third chapter. The suitable transformations reduce the governing equations in a tractable form for the analytical and numerical solutions. The same analytical and numerical methods, as in chapter two, are used to obtain the results. The essence of this paper is to examine the effects of viscous dissipation, magnetic field and heat generation in a recent paper of hyperbolic stretching sheet presented in last chapter. This work has been submitted in International Journal of Numerical Methods for Heat and Fluid Flow for publication. Fourth chapter deals with the study of mixed convection flow and heat transfer of a viscous fluid along a vertical hyperbolic stretching wall. The results have been obtained considering the effect of heat generation/absorption. The solutions for forced convection flow over a linear stretching surface with linear temperature distribution in the presence of heat source/sink are found to be the leading order solutions of mixed convection past a hyperbolic stretching wall. In next chapter, the boundary layer flow and heat transfer analysis of an incompressible nanofluid for a hyperbolically stretching sheet is presented. The model used considers the effects of Brownian diffusion and the thermophoresis. Analytical and numerical results for skin friction, Nusselt number and Sharwood number are calculated and compared with each other. The effects of different physical parameter on velocity, temperature and concentration of nanoparticles are also analyzed. The leading order solution of this problem represents the flow, heat and mass transfer of an incompressible viscous fluid over a linearly stretching surface. The boundary layer flow of second grade fluid over a permeable stretching surface with arbitrary velocity and appropriate wall transpiration is investigated in fifth chapter. The fluid is electrically conducting in the presence of constant applied magnetic field. Exact solution to the nonlinear xflow problem is presented. The contents of this chapter are published in Applied Mathematical Letters, 24 (2011), 1905–1909. The last chapter presents an exact analytical solution of magneto hydrodynamic (MHD) viscous flow over a permeable sheet with partial slip boundary conditions. The flow is induced by an arbitrary stretching of the surface. The exact analytical solution of the problem becomes possible by taking an appropriate wall transpiration velocity. An existing solution for flow generated by arbitrary stretching surface with no slip condition class of the exact solutions of the Navier Stokes equations for stretching surface.