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.

Inherent fluctuations in the availability of energy from renewables, particularly solar, remain a substantial impediment to their widespread deployment worldwide. Employing phase-change materials (PCMs) as media, saving energy for later consumption, offers a promising solution for overcoming the problem. However, the heat conductivities of most PCMs are limited, which severely limits the energy storage potential of these materials. This study suggests employing circular fins with staggered distribution to achieve improved thermal response rates of PCM in a vertical triple-tube heat exchanger involving two opposite flow streams of the heat-transfer fluid (HTF). Since heat diffusion is not the same at various portions of the PCM unit,

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

The cross section evaluation for (α,n) reaction was calculated according to the available International Atomic Energy Agency (IAEA) and other experimental published data . These cross section are the most recent data , while the well known international libraries like ENDF , JENDL , JEFF , etc. We considered an energy range from threshold to 25 M eV in interval (1 MeV). The average weighted cross sections for all available experimental and theoretical(JENDL) data and for all the considered isotopes was calculated . The cross section of the element is then calculated according to the cross sections of the isotopes of that element taking into account their abundance . A mathematical representative equation for each of the element

The analysis of time series considers one of the mathematical and statistical methods in explanation of the nature phenomena and its manner in a specific time period.

Because the studying of time series can get by building, analysis the models and then forecasting gives the priority for the practicing in different fields, therefore the identification and selection of the model is of great importance in spite of its difficulties.

The selection of a standard methods has the ability for estimation the errors in the estimated the parameters for the model, and there will be a balance between the suitability and the simplicity of the model.

In the analysis of d

In this paper, the effects of subsurface water retention technology (SWRT) on crop coefficient (k_c) and crop evapotranspiration (ET_c) of eggplant were investigated in sandy loam soil. For this purpose, two treatments plot (with SWRT and without using SWRT) were adopted during 93 days of cultivation. The study was conducted in open field within Al-Fahamah Township, Baghdad, Iraq during summer growing season 2017. The accumulated ET_c of eggplant was 403.3 and 515.2 mm for SWRT treatment and control plot, respectively by reduction percentage 21.7 %. The average values of ET_c during the growing season were 4.3 and 5.5 mm/day, respectively. The crop coefficients value during the gro