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.

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This work introduces a new electrode geometry for making holes with high aspect ratios on AISI 304 using an electrical discharge drilling (EDD) process. In addition to commercially available cylindrical hollow electrodes, an elliptical electrode geometry has been designed, manufactured, and implemented. The principal aim was to improve the removal of debris formed during the erosion process that adversely affects the aspect ratio, dimensional accuracy, and surface integrity. The results were compared and discussed to evaluate the effectiveness of electrode geometry on the machining performance of EDD process with respect to the material removal rate (MRR,) the electrode wear rate (EWR), and the tool wear ratio (TWR). Dimensional features an

In this paper, isobutane (R-600a) is used as a suitable substitute for (R-134a) when changing the length of capillary tube. And the experimental data on capillary tube are obtained under different conditions such as (subcooling and ambient temperatures) on domestic refrigerator (9ft3 size), this data shows that (R-600a) a suitable substitute for (R134a) .The test presented a model for a steady state, two-phase flow in capillary tube for vapour compression system .The numerical model depends on conservation equations (mass, energy and momentum) as wall as the equation of state for refrigerant. The solution methodology was implemented by using finite difference techniques. The system results indicate that it is possible to change the refri

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

Electrochemical machining is one of the widely used non-conventional machining processes to machine complex and difficult shapes for electrically conducting materials, such as super alloys, Ti-alloys, alloy steel, tool steel and stainless steel.  Use of optimal ECM process conditions can significantly reduce the ECM operating, tooling, and maintenance cost and can produce components with higher accuracy. This paper studies the effect of process parameters on surface roughness (Ra) and material removal rate (MRR), and the optimization of process conditions in ECM. Experiments were conducted based on Taguchi’s L9 orthogonal array (OA) with three process parameters viz. current, electrolyte concentration, and inter-electrode gap. Sig