The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
In the present work, the surface properties of mixed binary surfactants containing sodium dodecylbenzene sulfate (SDBS) and Tween 80 (TW80) surfactants in aqueous solutions were studied at temperature 293 K using surface tension measurements. The critical micelle concentration (cmc) magnitude for both individual surfactants and their mixtures were established the obtained results revealed that the magnitude of cmc of the mixtures are less than the magnitude of individual surfactants and decrease with the increase in Tween 80 percent in solution which indicate the nonideal mixing of the two surfactants. The values of molecular interaction parameters and the mole fraction of surfactants in the micelle (X1) were calculated
... Show MoreIn this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio
... Show MoreIn this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio
... Show MoreIn this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].
Dyes are extensively water-soluble and toxic chemicals. The disposing of wastewater rich with such chemicals has severely impacted surface water quality (rivers and lakes). In the current study, an anionic dye, methyl orange, were extracted from wastewater fluids using bulk liquid membranes supplemented with an anionic carrier (Aliquat 336 (QCI)). Parameters including solvent type (carbon tetrachloride and chloroform), membrane stirring speed (100-250 rpm), mixing speed of both phases (50-100 rpm), The feed pH (2-12) and implemented temperature (35-60 °C) were thoroughly analyzed to determine the effect of such variables on extraction effectiveness. Furthermore, the effect of methyl orange (10-50 ppm) in the feed stage and NaOH (0
... Show MoreCoagulation - flocculation are basic chemical engineering method in the treatment of metal-bearing industrial wastewater because it removes colloidal particles, some soluble compounds and very fine solid suspensions initially present in the wastewater by destabilization and formation of flocs. This research was conducted to study the feasibility of using natural coagulant such as okra and mallow and chemical coagulant such as alum for removing Cu and increase the removal efficiency and reduce the turbidity of treated water. Fourier transform Infrared (FTIR) was carried out for okra and mallow before and after coagulant to determine their type of functional groups. Carbonyl and hydroxyl functional groups on the surface of
... Show MoreFor this research, the utilisation of electrocoagulation (EC) toremove theciprofloxacin (CIP) and levofloxacin (LVX) from aqueous solutions was examined. The effective removal efficiencies are 93.47% for CIP and 88.00% for LVX, under optimum conditions. The adsorption isotherm models with suitable mechanisms were applied to determine the elimination of CIP and LVX utilizingtheEC method. Thefindingsshowed the adsorption of CIP and LVX on iron hydroxide flocs followed the Sips isotherm, with correlation coefficient values (R2) of 0.939 and 0.937. Threekinetic models were reviewed to determine the accurate CIP and LVX elimination methods using the EC method. The results showed that itfittedfor the second-order model, which indicated that the c
... Show MoreTitanium oxide nanoparticles-modified smectite (SMC-nTiO2) as a low-cost adsorbent was investigated for the removal of Rhodamine B (RhB) from aqueous solutions. The adsorbents (SMC and SMC-nTiO2) were characterized by scanning electron microscopy, Fourier transforms infrared spectroscopy, and energy-dispersive X-ray spectroscopy. The effects of various parameters like contact time, adsorbent weight, pH, and temperatures were examined. Three kinetic equations (pseudo-first-order (PFO), pseudo-second-order (PSO), and intra-particle diffusion) were used to evaluate the experimental kinetic of the data and the results showed that the adsorption process is in line with the PSO kinetic model. Adsorption equilibrium isotherms were modeled using La
... Show MoreAcademic achievement is a professional standard for measuring student levels in the first stages. Therefore, any indication of the level of achievement makes us in an attempt to employ students in evening schools. The researcher has developed a closed questionnaire of (36) paragraphs. A total of (164) male and (24) female students were chosen from evening schools. The result of this research revealed that the number of students was a reason for the low level of their achievement, the lack of laboratories, educational methods, and techniques of the most prominent problems confirmed by students in these schools. In addition, to support educational institutions with their necessary needs. The most important conclusion in this research is th
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