This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this paper, a new form of 2D-plane curves is produced and graphically studied. The name of my daughter "Noor" has been given to this curve; therefore, Noor term describes this curve whenever it is used in this paper. This curve is a form of these opened curves as it extends in the infinity along both sides from the origin point. The curve is designed by a circle/ ellipse which are drawing curvatures that tangent at the origin point, where its circumference is passed through the (0,2a). By sharing two vertical lined points of both the circle diameter and the major axis of the ellipse, the parametric equation is derived. In this paper, a set of various cases of Noor curve are graphically studied by two curvature cases;

Abstract  

Magnetic abrasive finishing (MAF) process is one of non-traditional or advanced finishing methods which is suitable for different materials and produces high quality level of surface finish where it uses magnetic force as a machining pressure. A set of experimental tests was planned according to Taguchi orthogonal array (OA) L27 (3⁶) with three levels and six input parameters. Experimental estimation and optimization of input parameters for MAF process for stainless steel type 316 plate work piece, six input parameters including amplitude of tooth pole, and number of cycle between teeth, current, cutting speed, working gap, and finishing time, were performed by design of experiment

Electrochemical machining is one of the widely used non-conventional machining processes to machine complex and difficult shapes for electrically conducting materials, such as super alloys, Ti-alloys, alloy steel, tool steel and stainless steel.  Use of optimal ECM process conditions can significantly reduce the ECM operating, tooling, and maintenance cost and can produce components with higher accuracy. This paper studies the effect of process parameters on surface roughness (Ra) and material removal rate (MRR), and the optimization of process conditions in ECM. Experiments were conducted based on Taguchi’s L9 orthogonal array (OA) with three process parameters viz. current, electrolyte concentration, and inter-electrode gap. Sig

Recently, the internet has made the users able to transmit the digital media in the easiest manner. In spite of this facility of the internet, this may lead to several threats that are concerned with confidentiality of transferred media contents such as media authentication and integrity verification. For these reasons, data hiding methods and cryptography are used to protect the contents of digital media. In this paper, an enhanced method of image steganography combined with visual cryptography has been proposed. A secret logo (binary image) of size (128x128) is encrypted by applying (2 out 2 share) visual cryptography on it to generate two secret share. During the embedding process, a cover red, green, and blue (RGB) image of size (512

Abstract  

The aim of this paper is to investigate and discuss the mechanisms of corrosion of epoxy coatings used for potable water tanks. Two distinct types of Jotun epoxy coatings: Tankguard 412 contained polyamine cured epoxy and Penguard HB contained polyamide cured epoxy, were tested and studied using the electrochemical impedance spectroscopic (EIS) method. The porosity of epoxy coatings was determined using EIS method. The obtained results showed that the two epoxy coatings have excellent behavior when applied and tested in potable water of Basrah city. Polyamine is more resistance to water corrosion compared to polyamide curing epoxy and has high impedance values. Microscopic inspection after te

To limit or reduce common microbial contamination occurrence in dairy products in general and in soft cheese in particular, produced in locally plants, this study was performed to demonstrate the possibility of implementing HACCP in one of dairy plants in Baghdad city

            HACCP plan was proposed in soft cheese production line. A pre-evaluation was performed in soft cheese line production, HACCP Pre-requisites programs was evaluated from its presence and effectiveness. The evaluation was demonstrated risk in each of: Good Manufacturing Practice (GMP) program, evaluated as microbial and physical risk and considered as critical r

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).