In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

Original Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio

Extended utilization of adaptive algorithms, Evaluative Algorithms (EAs), to address these issues offers a way to handle massive multi-objective optimization, even if the algorithmic method for handling combinations of objectives (CO) has been accessible for quite some time. Combining the idea of superiority with the Hypervolume (HV) tag approach, the GSA algorithm utilizes various target effects to explain several algorithms depending on the Hypervolume (HV) spacing. The Multi-objective Gravitational Search Algorithm with Hypervolume (MOGSA/HV). Since rapid convergence could result from GSA foundation work, Hypervolume rewrites the multi-objective problem (MOP) as a sequence of Tchebycheff solutions, improving it. Since the one in charge h

The esterification of oleic acid with 2-ethylhexanol in presence of sulfuric acid  as homogeneous catalyst was investigated in this work to produce 2-ethylhexyl oleate (biodiesel) by using semi batch reactive distillation. The effect of reaction temperature (100 to 130°C), 2-ethylhexanol:oleic acid molar ratio (1:1 to 1:3) and catalysts concentration (0.2 to 1wt%) were studied. Higher conversion of 97% was achieved with operating conditions of reaction temperature of 130°C, molar ratio of free fatty acid to alcohol of 1:2 and catalyst concentration of 1wt%. A simulation was adopted from basic principles of the reactive distillation using MATLAB to describe the process. Good agreement was achieved.

In this research we prepared nanofibers by electrospinning from
poly (Vinyl Alcohol) /TiO2. The spectrum of the solution (Emission)
was studied and found to be at 772 nm, several process parameters
were such as concentration of TiO2 , and the effect of distance from
nozzle tip to the grounded collector (gap distance). The result of the
lower concentration of, the smaller the diameter of nanofiber is.
Increasing the gap distance will affect nanofibers diameter