This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the curr

Twisted tape insertion in smooth plain tube is one of types of passive methods that is used to enhance heat transfer. Swirl fluid flow inside tube and related heat transfer characteristics are very complex. ANSYS FLUENT (V 16.1) and ASPEN industrial program are used in analyzing this technique for enhancement heat transfer. A circular plain tube has length L=8534mm and 17 mm inner diameter with twisted tape has twist ratio of y = (H/D) = (150/17) =8.8 along with a plain tube were considered for this study. Eight Reynolds numbers (Re) of 784, 1000, 2000, 3000, 4000, 5000, 6000 and 7000 are used to analyze the response of thermal performance. Crude oil API 28 exit temperature, film heat transfer coefficient, Nusselt number

This work introduces a new electrode geometry for making holes with high aspect ratios on AISI 304 using an electrical discharge drilling (EDD) process. In addition to commercially available cylindrical hollow electrodes, an elliptical electrode geometry has been designed, manufactured, and implemented. The principal aim was to improve the removal of debris formed during the erosion process that adversely affects the aspect ratio, dimensional accuracy, and surface integrity. The results were compared and discussed to evaluate the effectiveness of electrode geometry on the machining performance of EDD process with respect to the material removal rate (MRR,) the electrode wear rate (EWR), and the tool wear ratio (TWR). Dimensional features an

Twisted tape insertion in the smooth plain tube is one of the types of passive methods that are used to enhance heat transfer. Swirl fluid flow inside the tube and related heat transfer characteristics are very complex. ANSYS FLUENT (V 16.1) and ASPEN industrial program are used in analyzing this technique for enhancement heat transfer. A circular plain tube has length L=8534mm and 17 mm inner diameter with a twisted tape of twist ratio of y = (H/D) = (150/17) =8.8 along the plain tube were considered for this study. Eight Reynolds numbers (Re) of 784, 1000, 2000, 3000, 4000, 5000, 6000 and 7000 are used to analyze the response of thermal performance. Crude oil API 28 exit temperature, film heat transfer coefficient, Nus

Numerical study of separation control on symmetrical airfoil, four digits (NACA

0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range

The purpose of this paper is to gain a good understanding about wake region behind the car body due to the aerodynamic effect when the air flows over the road vehicle during its movement. The main goal of this study is to discuss the effect of the geometry on the wake region and the aerodynamic drag coefficient. Results will be achieved by using two different shapes, which are the fastback and the notchback. The study will be implemented by the Computational Fluid Dynamic (CFD) by using STAR-CCM+^® software for the simulation. This study investigates the steady turbulent flow using k-epsilon turbulence model. The results obtained from the simulation show that the region of the air separation behind the vehicle

Sheet piles are necessary with hydraulic structures as seepage cut-off to reduce the seepage. In this research, the computational work methodology was followed by building a numerical model using Geo-Studio program to check the efficiency of using concrete sheet piles as a cut-off or reducer for seepage with time if the sheet piles facing the drawdown technique. Al-Kifil regulator was chosen as a case study, an accurate model was built with a help of observed reading of the measuring devices, which was satisfactory and helped in checking the sheet piles efficiency. Through the study, three scenarios were adopted (with and without) drawdown technique, it was found that at the short time there's no effect of the drawdown technique on

In this paper, isobutane (R-600a) is used as a suitable substitute for (R-134a) when changing the length of capillary tube. And the experimental data on capillary tube are obtained under different conditions such as (subcooling and ambient temperatures) on domestic refrigerator (9ft3 size), this data shows that (R-600a) a suitable substitute for (R134a) .The test presented a model for a steady state, two-phase flow in capillary tube for vapour compression system .The numerical model depends on conservation equations (mass, energy and momentum) as wall as the equation of state for refrigerant. The solution methodology was implemented by using finite difference techniques. The system results indicate that it is possible to change the refri

    Soft clays are generally characterized by low shear strength, low permeability and high compressibility. An effective method to accelerate consolidation of such soils is to use vertical drains along with vacuum preloading to encourage radial flow of water.  In this research numerical modeling of prefabricated vertical drains with vacuum pressure was done to investigate the effect of using vertical drains together with vacuum pressure on the degree of saturation of fully and saturated-unsaturated soft soils.  Laboratory experiments were conducted by using a specially-designed large consolidometer cell where a central drain was installed and vacuum pressure was applied. All tests were conducted