<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA<sup>®</sup> 9.0.</p>
There are still areas around the world suffer from severe shortage of freshwater supplies. Desalination technologies are not widely used due to their high energy usage, cost, and environmental damaging effects. In this study, a mathematical model of single-bed adsorption desalination system using silica gel-water as working pair is developed and validated via earlier experiments. A very good match between the model predictions and the experimental results is recorded. The objective is to reveal the factors affecting the productivity of fresh water and cooling effect in the solar adsorption system. The proposed model is setup for solving within the commercially-available software (Engineering Equation Solver). It is implemented to so
... Show MoreThe laminar fluid flow of water through the annulus duct was investigated numerically by ANSYS fluent version 15.0 with height (2.5, 5, 7.5) cm and constant length (L=60cm). With constant heat flux applied to the outer duct. The heat flux at the range (500,1000,1500,2000) w/m2 and Reynolds number values were ≤ 2300. The problem was 2-D investigated. Results revealed that Nusselt number decrease and the wall temperature increase with the increase of heat flux. Also, the average Nusselt number increase as Re increases. And as the height of the annulus increase, the values of the temperature and the local and average Nusselt number increase.
In this work, a numerical study is performed to predict the solution of two – dimensional, steady and laminar mixed convection flow over a square cylinder placed symmetrically in a vertical parallel plate. A finite difference method is employed to solve the governing differential equations, continuity, momentum, and energy equation balances. The solution is obtained for stream function, vorticity and temperature as dependent variables by iterative technique known as successive over relaxation. The flow and temperature patterns are obtained for Reynolds number and Grashof number at (Re= -50,50,100,-100) (positive or negative value refers to aidding or opposing buoyancy , +1 assisting flow, -1 opposing flow) and (102 to 105) , respective
... Show MoreThis research aims to numerically solve a nonlinear initial value problem presented as a system of ordinary differential equations. Our focus is on epidemiological systems in particular. The accurate numerical method that is the Runge-Kutta method of order four has been used to solve this problem that is represented in the epidemic model. The COVID-19 mathematical epidemic model in Iraq from 2020 to the next years is the application under study. Finally, the results obtained for the COVID-19 model have been discussed tabular and graphically. The spread of the COVID-19 pandemic can be observed via the behavior of the different stages of the model that approximates the behavior of actual the COVID-19 epidemic in Iraq. In our study, the COV
... Show MoreThe galvanic corrosion of the (Cu - Fe), (Cu - Zn) and (Fe - Zn) couples have been investigated in 3.5% NaCl solution, 40ºC, different velocities (Re = 5000, 10000 and 15000) and different area ratio’s of cathode to anode (AR= 0.5,1 and 2), by using commercial metal pipe (cylindrical tube).The Zero Resistance Ammeter has been used to measure the galvanic current (Ig) and galvanic potential (Eg) with time. The galvanic current density increases with increasing velocity (Re) and the area ratio (AR). The galvanic potential (Eg) is shifted to less negative with increasing velocity (Re) and the area ratio (AR). A statistical relations for the galvanic current density and galvanic potential as a function of (Re). and the area ratio had been
... Show MoreIn this study, hexadecyltrimethylammonium bromide (HDMAB) - bentonite was synthesized by placing alkylammonium cation onto bentonite. Adsorption of textile dye such as direct Yellow 50 on natural bentonite and HDMAB -bentonite was investigated. The effects of pH, contact time,dosage clay and temperature were investigated experimentally .The Langmuir and Freundlish isotherms equations were applied to the data and values of parameters of these isotherm equations were evaluated. The study indicated that using 0.2 g of HDMAB (hexadecyltrimethylammonium bromide) lead to increase the percentage removal(R%) from 78% for pure bentonite to 99 %. The optimum pH value for the adsorption experiments was found to be pH=3 and therefore all the experim
... Show MoreThe main parameters and methods influencing the removal of Gentian Violet (GV) dye from aqueous media were investigated using a stachy plant in this study. The surface of the stachy plant was determined using FTIR spectra. Adsorption is influenced by the adsorbent's characteristic groups. The research took into account the usual conditions for GV dye adsorption by the stachy plant, such as the impact of contact time. Mass dosage , after 0.3 g the amount of adsorbed dye declines. Study pH and ionic strength, the results obtained showed that at pH 3 the largest adsorption of (GV) was seen, while at pH 9, the lowest adsorption was observed at 298 K, the adsorption kinetics and equilibrium constants were achieved, and the equ
... Show MoreThe adsorption behavior of congo red dye from its aqueous solutions was investigated onto natural and modified bauxite clays. Both bauxite and modified bauxite are primarily characterized by using, FTIR, SEM, AFM, and XRD. Several variables are studied as a function of adsorption including contact time, adsorbent weight, pH, ionic strength, particle size and temperature under batch adsorption technique. The absorbance of the solution before and after adsorption was measured spectrophotometrically. The equilibrium data fit with Langmuir model of adsorption and the linear regression coefficient R2 is found to be 0.9832 and 0.9630 for natural and modified bauxite respectively at 37.5°C which elucidate the best fitting isotherm model. The gene
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