Steady natural convection in a square enclosure with wall length (L= 20 cm) partially filled by saturated porous medium with same fluid (lower layer) and air (upper layer) is investigated. The conceptual study of the achievements of the heat transfer is performed under effects of bottom heating by constant heat flux (q=150,300,450,600W/m2 ) for three heaters size (0.2,0.14,0.07)m with symmetrically cooling with constant temperature on two vertical walls and adiabatic top wall. The relevant filled studied parameters are four different porous medium heights (Hp=0.25L,0.5L, 0.75L, L), Darcey number (Da1) 3.025×10-8 and (Da2) 8.852×10-4 ) and Rayleigh number range (60.354 - 241.41), (1.304×106 – 5.2166×106 ) for Da1 and Da2 cases respectively. Numerically, COMSOL Multiphysics 5.5a® based on the Galerkin finite element method is used for solving the governing equations with depending Brinkman- Darcy extended mode for porous media region. The results show that, effects of increasing the Rayleigh number on the temperature profile besides the progressively increasing the average Nusselt number. Moreover, symmetrical distribution of local Nu along the bottom heated wall and it is be minimum at midpoint of bottom. Also, the heat transfer and fluid flow are affected by thickness of porous layer and are maximum at porous layer thickness (0.25L) which clearly observed with large heater size to be approximately (93%) for the average Nu. Generally, the heat transfer is enhanced for large Darcy number (8.852×10-4 ) and influenced by the convection regime improvement while it is mainly conduction mode for (Da1) for all Raleigh number with a little effect of convection when increase (Ra).
In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
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We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.
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Problem of water scarcity is becoming common in many parts of the world. Thus to overcome this problem proper management of water and an efficient irrigation systems are needed. Irrigation with buried vertical ceramic pipe is known as a very effective in management of irrigation water. The two- dimensional transient flow of water from a buried vertical ceramic pipe through homogenous porous media is simulated numerically using the software HYDRUS/2D to predict empirical formulas that describe the predicted results accurately. Different values of pipe lengths and hydraulic conductivity were selected. In addition, different values of initial volumetric soil water content were assumed in this simulation a
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Recently emerging pandemic SARS CoV-2 conquered our world since December 2019. Continuous efforts have been done to find out effective immunization and precise treatment stetratigies A way from therapeutic options that were tried in SARS CoV-2, an increased attention is directed to predict natural products and mainly phytochemicals as collaborative measures for this crisis. In this review, most of the mentioned compounds specially flavonoids (biacalin, hesperidin, quercetin, luteolin,, and phenolic (resveratrol, curcumin, and theaflavin) exert their effect through interfering with the action of one or more of this proteins (spike protein, papain like protease, 3 chymotrypsin like cysteine protease, and RNA dependent RNA
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In this paper, we describe the cases of marriage and divorce in the city of Baghdad on both sides of Rusafa and Karkh, we collected the data in this research from the Supreme Judicial Council and used the cubic spline interpolation method to estimate the function that passing through given points as well as the extrapolation method which was applied for estimating the cases of marriage and divorce for the next year and comparison between Rusafa and Karkh by using the MATLAB program.
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A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.
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In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.
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Friction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim
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