The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

Influence of combined square nozzle with helical tape inserted in a constant heat flux tube on heat transfer enhancement for turbulent airflow for Reynolds number ranging from 7000 to 14500 were investigated experimentally. Three different pitch ratios for square nozzle (PR = 5.8, 7.7 and 11.6) according to three different numbers of square nozzle (N = 3, 4 and 5) and constant pitch ratios for helical tape were used. The results observed that the Nusselt number and friction factor for combination with winglets were found to be up to 33.8 % and 21.4 %, respectively higher than nozzle alone for pitch ratio PR=5.8. The maximum value of thermal performance for using combination with winglets was about 1.351 for pitch ratio= 5.8. Nusselt numb

A finite element is a study that is capable of predicting crack initiation and simulating crack propagation of human bone. The material model is implemented in MATLAB finite element package, which allows extension to any geometry and any load configuration. The fracture mechanics parameters for transverse and longitudinal crack propagation in human bone are analyzed. A fracture toughness as well as stress and strain contour are generated and thoroughly evaluated. Discussion is given on how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid the design of protective systems.

‎ This research aims to estimate stock returns, according to the ‎Rough Set Theory ‎approach, ‎test ‎its effectiveness and accuracy in predicting stock returns and their potential in the ‎field of ‎financial ‎markets, and rationalize investor decisions. The research sample is totaling (10) ‎companies traded at Iraq Stock Exchange. The results showed a remarkable ‎ ‎Rough Set Theory application in data reduction, contributing to the rationalization of ‎investment ‎decisions. The most prominent conclusions are the capability of rough set theory ‎in ‎dealing with financial data and applying it for forecasting stock ‎returns.‎The ‎research provides those interested in investing stocks in financial

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.

  Weibull distribution is considered as one of the most widely  distribution applied in real life, Its similar to normal distribution in the way of applications, it's also considered as one of the distributions that can applied in many fields such as industrial engineering to represent replaced and manufacturing time ,weather forecasting, and other scientific uses in reliability studies and survival function in medical and communication engineering fields.

   In this paper, The scale parameter has been estimated for weibull distribution using Bayesian method based on Jeffery prior information as a first method , then enhanced by improving Jeffery prior information and then used as a se

The present paper addresses cultivation of Chlorella vulgaris microalgae using airlift photobioreactor that sparged with 5% CO 2 /air. The experimental data were compared with that obtained from bioreactor aerated with air and unsparged bioreactor. The results showed that the concentration of biomass is 0.36 g l -1  in sparged bioreactor with CO2/air, while, the concentration of biomass reached to 0.069 g l -1  in the unsparged bioreactor. They showed also that aerated  ioreactor.with CO2/air gives more biomass production even the bioreactor was aerated with air. This study proved that application of sparging system for  ultivation of Chlorella vulgaris microalgae using either CO2/air mixture or air has a significant