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Item Design optimization of vehicle suspension with quarter car model(UMT Lahore, 2015) Nagina FatimaOptimization includes the determination of optimum point of an objective function, supply system and test functions. Here we do the comparative study of three optimization methods, hooke-jeeves method, nelder-mead method and multidirectional search method and these methods have been applied to the solution of the fully constrained optimization problem. There are many derivative free methods which could be used for solving different constrained optimization models. These methods will also be implemented to different models, test functions and then compare the results. The focus of this research project is to execute and evaluate these optimization methods and those methods which do not need gradient information. In order to discuss the solution of the completely constrained optimization problems, numerous constraint handling methods are evaluated, including the penalty function level. Here we also discuss a model which is called quarter vehicle model with different types of constrains which involve the comparative study of three optimization method, named as hooke-jeeves, nelder-mead and multidirectional search method for design optimizing vehicle suspensions constructed on quarter vehicle model with different types of constrains. It was resulted from the comparative study that hooke-jeeves search method is more reliable than multidirectional and nelder-mead search methods. The optimum results of quarter car model were obtained by using matlab programming which demonstrated the effectiveness and applicability of the methods.Item General solutions for free convection flow of Casson fluid over an infinite vertical plate(UMT Lahore, 2015) Allia NaseemIn this thesis, we consider the flow behaviour of Casson fluid under different circumstances. Firstly, some basic definitions and concepts regarding the fundamentals of fluid motion and methods to solve the flow problems have been discussed. In chapter 2, the free convection flow of Casson fluid past an upright plate subject to the time dependent velocity f(t) with constant wall temperature has been investigated. The vertical plate is set in motion with a time dependent velocity f(t) at time t = 0+. And so the motion will be produced in the fluid. Exact solutions are obtained through the Laplace transform method. The solutions corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Also, we have discussed some consequences of various parameters like Casson parameter, Grashöf and Prandtl numbers on velocity and temperature and presented them graphically. Chapter 3, particularly deals with the jerky and unformed free convection flow of Casson fluid subject to an upright plate with mass transfer and Newtonian heating. With the help of Laplace transform, the expressions for velocity and temperature will be established. For particular cases when (a) Pr=1, Sc=1, (b) Pr ≠ 1, Sc=1 and (c) Pr = 1, Sc ≠ 1, solutions are investigated. For different physical parameters, graphical representation is displayed and discussed.Item General solutions for free convection flow of Casson fluid over an infinite vertical plate(UMT Lahore, 2015-11) Allia NaseemIn this thesis, we consider the flow behaviour of Casson fluid under different circumstances. Firstly, some basic definitions and concepts regarding the fundamentals of fluid motion and methods to solve the flow problems have been discussed. In chapter 2, the free convection flow of Casson fluid past an upright plate subject to the time dependent velocity f(t) with constant wall temperature has been investigated. The vertical plate is set in motion with a time dependent velocity f(t) at time t = 0+. And so the motion will be produced in the fluid. Exact solutions are obtained through the Laplace transform method. The solutions corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Also we have discussed some consequences of various parameters like Casson parameter, Grashöf and Prandtl numbers on velocity and temperature and presented them graphically. Chapter 3, particularly deals with the jerky and unformed free convection flow of Casson fluid subject to an upright plate with mass transfer and Newtonian heating. With the help of Laplace transform, the expressions for velocity and temperature will be established. For particular cases when (a) Pr=1, Sc=1, (b) Pr ≠ 1, Sc=1 and (c) Pr = 1, Sc ≠ 1, solutions are investigated. For different physical parameters, graphical representation is displayed and discussed.Item General solutions for unsteady free convective flow for Brinkman type fluid(UMT Lahore, 2015-10) Maryam AleemThe main aspire of this desertion is to represent generalized solutions for Brinkman type non-Newtonian fluids in which we will reckon time dependent velocity along the boundary. In chapter 1, a few cardinal concepts concerning the rates of flows, dissimilar types of fluids, a couple of constitutive equations and equations of apparent movement, Navier Stokes equations and integral transform i.e., The Laplace transform are discoursed. In chapter 2, an analysis is followed by the un-firm or jerky free convection stream of a Brinkman type fluid flowing across an upright plate subject to time dependent velocity f(t) which fulfills the condition of f(0)=0. By inserting the suitable variables, the basic governing equations are abbreviated to dimensionless equations sound to all levied initial and boundary conditions. The exact solutions of initial value problem has been attained by using Laplace transform technique. When β∗ = 0, the results will be true for Newtonian fluid for the analogous motion. The impression of assorted values of the tangible parameters specified for temperature, skin friction, velocity and Nusselt number is underscored diagrammatically. In chapter 3, the velocity domain of jerky convection stream of Brinkman type flowing materials passing through an upright plate imbedded in permeable medium with mass diffusion and Newtonian heating condition is dissected. The exact solution is received by means of Laplace transform and deduced to the results for Newtonian fluids. The effects of several parameters upon the velocity dispersion, temperature, mass diffusion and skin friction is tested graphically.Item Existence of n symmetric positive solutions for singular second order two-point and four-point boundary value problems(UMT Lahore, 2015) Marfua AlamIn this dissertation, we find positive symmetric solution of singular second order two-point boundary value problem using fixed point theory, monotone iterative technique and then extend this method to find solution for singular second order four point boundary value problem. By symmetric solution we mean a solution w is positive w(t) > 0 and w(t) = w(1 − t), 0 ≤ t ≤ 1. Here we consider the coefficient h(t) is singular at end points t = 0 and t = 1 and w(t) is symmetric and concave whereas w′(t) is skew-symmetric on interval [0, 1]. We consider ordered Banach space having an appropriate norm and cone k of continuous differentiable functions. Then we construct an integral operator t (w) using Green’s function and take its mapping on cone (on k into itself) and use Arzela-Ascoli theorem to show that this operator is completely continuous. This operator is symmetric and concave whereas its derivative is skew-symmetric in [0, 1]. Then by selecting some suitable constants and imposing conditions on norm we construct the monotone iterative technique to obtain the fixed point of the operator and this fixed point is positive symmetric solution of our considered boundary value problem. First we do it for one symmetric positive solution and then extend this technique to find n symmetric positive solutions of second order two-point and four-point boundary value problems.Item Fifth order numerical methods for heat equation with variable coefficient subject to non homogeneous boundary conditions(UMT Lahore, 2015) Naveed AhmadIn this thesis, two numerical methods, based upon Pade’s approximation to the matrix exponential function, for solving one dimensional heat diffusion equations with variable coefficients, are developed. These methods are L-stable and fifth order accurate in space and time. These methods are tested on heat conduction problems through a thermally insulated thin wire. The solution of these problems gives the temperature at any distance from one end of the wire after any time of the heat conduction. The methods are found to be highly accurate and stable.Item A study of generalized variational-like inequalities in normed spaces for pseudo-monotone type III operators(UMT Lahore, 2015) Muhammad Talha NazirIn this thesis, we shall review some existence results for solutions of generalized variational-like inequalities for Pseudo monotone type III operators. These results will be extensively and thoroughly studied in normed spaces on non-compact sets.