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.

ABSTRACT Fifty extremely halophilic bacteria were isolated from local high salient soils named Al-Massab Al-Aam in south of iraq and were identified by using numerical taxonomy. Fourty strains were belong to the genus Halobacterium which included Hb. halobium (10%). Hb. salinarium (12.5%), Hb.cutirubrum (17.5%), Hb-saccharovorum (12.5%), Hb. valismortis (10%) and Hb. volcanii (37.5%). Growth curves were determined. Generation time (hr) in complex media and logarithmic phase were measured and found to be 10.37±0.59 for Hb. salinarium. 6.49 ± 0.24 for Hb.cutirubrum. 6.70±0.48 for Hb-valismonis, and 11.24 ± 0.96 for Hb. volcanii

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

To evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult

Current numerical research was devoted to investigating the effect of castellated steel beams without and with strengthening. The composite concrete asymmetrical double hot rolled steel channels bolted back to back to obtain a built-up I-shape form are used in this study. The top half part of the steel is smaller than the bottom half part, and the two parts were connected by bolting and welding. The ABAQUS/2019 program employed the same length and conditions of loading for four models: The first model is the reference without castellated and strengthening; the second model was castellated without strengthened; the third model was castellated and strengthened with reactive powder concrete encased in the

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

The problem of water scarcity is becoming common in many parts of the world, to overcome part of this problem proper management of water and an efficient irrigation system are needed.  Irrigation with a buried vertical ceramic pipe is known as a very effective in the management of irrigation water.  The two- dimensional transient flow of water from a buried vertical ceramic pipe through homogenous porous media is simulated numerically using the HYDRUS/2D software.  Different values of pipe lengths and hydraulic conductivity were selected.  In addition, different values of initial volumetric soil water content were assumed in this simulation as initial conditions.  Different value

Stimulative effect of 10 mW He-Ne laser on the phagocytic activity of human polymorphonuclear leukocytes( PMNs) has been studied in vitro. Normal polymorphonuclear leucocytes were isolated from the human peripheral blood. A mixture of 0.25 ml of Hanks solution, 0.25 ml of serum, 0.25 ml of Candida albicans suspension and 0.25 ml of PMNs suspension was prepared. The samples of mixture of PMNs and Candida were subdivided in 1 ml ependrof tubes and irradiated to He-Ne laser for 1, 3, 5, 10 and 20 min. The diameter of the irradiated area was 0.8 cm. For calculation of Phagocytic index before and after irradiation, the samples were incubated (37°C) at 5, 15, 30, 60 min. The slides of samples were prepared and stained using Giemsa stain. The

This research introduces a developed analytical method to determine the nominal and maximum tensile stress and investigate the stress concentration factor. The required tooth fillets parametric equations and gears dimensions have been reformulated to take into account the asymmetric fillets radiuses, asymmetric pressure angle, and profile shifting non-standard modifications. An analytical technique has been developed for the determination of tooth weakest section location for standard, asymmetric fillet radiuses, asymmetric pressure angle and profile shifted involute helical and spur gears. Moreover, an analytical equation to evaluate gear tooth-loading angle at any radial distance on the involute profile of spur and hel

This work is an experimental investigation for single basin-single slope solar still coupled with an evacuated tube solar collector. The work is carried out under the climatic conditions of Baghdad city (33.2456º North and East latitude, 44.3337º longitude) through certain days of the months of the year 2019 to study the impact of using evacuated tube solar collector on the daily productivity and efficiency under the outdoors climatic conditions. It was found that using the evacuated tube solar collector increase daily productivity from 2.175 kg/  to 2.95 kg/ for 9 hours (35.63 %) for clear days, also an enhancement about 10.97 % in daily efficiency.