This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

Abstract

 In this work, pure Polypyrrole (PPy) and Polypyrrole (PPy)/Graphene (GN) was synthesized by in-situ polymerization in different weight percentages (0.1, 0.3, 0.5, 1, 3 and 5 wt.% (g)) of GN nano particles using chemical oxidation method at room temperature. The FTIR, SEM and electrical properties were studies for the nano composites. The result show that when concentration of GN Nano particle increase, the electrical conductivity increased and the graphene sheets were merging to form a continuous area of the GN through the polypyrrole base material. The FTIR spectra shows that the characteristics absorption peaks of polypyrrole that is, 1546.80, 1463.87 and 3400.27 cm^-1(stretching vibration in the pyrrol

Microbial Desalination Cell (MDC) is capable of desalinating seawater, producing electrical power and treating wastewater. Previously, chemical cathodes were used, which were application restrictions due to operational expenses are quite high, low levels of long-term viability and high toxicity. A pure oxygen cathode was using, external resistance 50 and 150 k Ω were studied with two concentrations of NaCl in the desalination chamber 15-25 g/L which represents the concentration of brackish water and sea water. The highest energy productivity was obtained, which amounted to 44 and 46 mW/m³, and the maximum limit for desalination of saline water was (31% and 26%) for each of 25 g / L and 15 g / L, respectively, when using an ex

Objective. This study aimed to evaluate and compare the force degradation of two types of elastomeric chains following different periods of immersion in zinc-containing mouthwashes. Materials and Methods. Four hundred and forty pieces of Elasto-Force and Super Elasto-Force elastomeric chains were divided into two control and eight experimental groups. The pieces were stretched to 25 mm on pins mounted on an acrylic block and stored in distilled water at 37°C. The experimental groups were immersed in four different types of mouthwash for one minute twice a day throughout the test period. Ten continuous thermocycles per day between cold and hot water baths (5–55°C) were carried out. Forces were measured at six-time intervals (in

The objective of this study is to demonstrate the corrosion behavior of dental alloys Co-Cr-Mo, Ni-Cr-Mo and Ti-Al-V in artificial saliva at pH=4 and 37oC enriched with ethyl alcohol at 8% percentage. The linear and cyclic polarizations were investigated by electrochemical measurements. Laser surface modification was achieved for the three dental alloys to improve corrosion resistance. The results show that corrosion resistance of Co-Cr-Mo and Ni-Cr-Mo alloys only were increased after laser treatment due to the fact that laser radiation has caused a smoother surface, in addition to the decrement in corrosion current densities (icorr) for Co-Cr-Mo and Ni-Cr-Mo alloys and the reverse scan in cyclic polarization became in the wider range of

          Potentiostatic polarization and weight loss methods have been used to investigate the corrosion behavior of carbon steel in sodium chloride solution at different concentrations (0.1, 0.4 and 0.6) M under the influence of temperatures ( 293, 298, 303, 308 and 313) K. The inhibition efficiency of the amoxicillin drug on carbon steel in 0.6 M NaCl has also been studied based on concentration and temperature. The corrosion rate showed that all salt concentrations ( NaCl solution) resulted in corrosion of carbon steel in varying ratio and 0.6 M of salt solution  was the highest rate (50.46 g/m².d). The results also indicate that the rate of corrosion increases at a temperature of 313 K.. Potentiodynamic polarization studi

Objective This study evaluated the effects of adding titanium oxide (TiO2) nanofillers on the tear strength, tensile strength, elongation percentage, and hardness of room-temperature-vulcanized (RTV) VST50F and high-temperature-vulcanized (HTV) Cosmesil M511 maxillofacial silicone elastomers. Methods Two types of maxillofacial elastomers, VST50F RTV and Cosmesil M511 HTV, were used. Nano-TiO2 powder was applied as a nanofiller. A total of 120 specimens were fabricated, 60 each of VST50F and Cosmesil M511. The specimens of each type of elastomer were divided into three equal groups on which tests were conducted for tear strength, tensile strength, and hardness i.e., 20 specimens were used for each test. Each group of 20 specimens was further