In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

The aim of this paper is to present a method for solving third order ordinary differential equations with two point boundary condition , we propose two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by compared with conventional method .

Various industrial applications include the dyeing of textiles, paper, leather, and food products, as well as the cosmetics industry. Physic-chemical methods are required to breakdown dyes because they are known to be harmful and persistent in the environment. Many companies' treated effluents contain small amounts of dyes. When it comes to removing dye from wastewater, adsorption has verified to be aneconomical alternative to more traditional treatment procedures. It's important to degrade color impurities in industrial effluents since they constitute a serious health and environmental concern. One way that's been tried is using clay minerals as an adsorbent. Using adsorption for removing

A mixture of algae biomass (Chrysophyta, Cyanophyta, and Chlorophyte) has been investigated for its possible adsorption removal of cationic dyes (methylene blue, MB). Effect of pH (1-8), biosorbent dosage (0.2-2 g/100ml), agitated speed (100-300), particle size (1304-89μm), temperature (20-40˚C), initial dye concentration (20-300 mg/L), and sorption–desorption were investigated to assess the algal-dye sorption mechanism. Different pre-treatments, alkali, protonation, and CaCl2 have been experienced in order to enhance the adsorption capacity as well as the stability of the algal biomass. Equilibrium isotherm data were analyzed using Langmuir, Freundlich, and Temkin models. The maximum dye-sorption capacity was 26.65 mg/g at pH= 5, 25

In the current study, haemoglobin analytes dissolved in a special buffer (KH₂PO₄(1M), K₂HPO₄(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10^-8 to 10^-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity  ≥99%  dielectric mirrors (dia

The effect of applied current on protection of carbon steel in 0.1N NaCl solution (pH=7) was investigated under flow conditions (0-0.262 m/s) for a range of temperatures (35-55°C) using rotating cylinder electrode. Various values of currents were applied to protect steel from corrosion, these were Iapp.=Icorr., Iapp.=2Icorr. and Iapp.=2.4Icorr. under stationary and flow conditions. Corrosion current was measured by weight loss method. The variation of protection potential with time and rotation velocity at various applied currents was assessed. It is found that the corrosion rate of carbon steel increases with rotation velocity and
has unstable trend with temperature. The protection current required varies with temperature and it inc

The 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

This research presents a new study in kinetics under reactive distillation by using consecutive two – step reaction : the saponification reaction of diethyl adipate with sodium hydroxide solution . The distillation process takes the role of withdrawing the intermediate product (sodium monoethyladipate SMA) which otherwise converts to the final product of low purity.The effect of three parameters were studied through a design of experiments applying 2³ factorial design. These parameters were : the mole ratio of DA to NaOH solution (0.1 and 1) , NaOH solution concentration (3 N and 8 N) , and batch time (1.5 hr. and 3.5 hr.) . The conversion of DA to sodium monoethyladipate(SMA)(intermediate product) was the effect of these pa