The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

The aim of this paper is to evaluate the rate of contamination in soils by using accurate numerical method as a suitable tool to evaluate the concentration of heavy metals in soil. In particular, 2D –interpolation methods are applied in the models of the spread the metals in different direction.The paper illustrates the importance of the numerical method in different applications, especially nvironment contamination. Basically, there are many roles for approximating functions. Thus, the approximating of function namely the analytical expression may be expressed; the most common type being is polynomials, which are the easy implemented and simplest methods of approximation. In this paper the divided difference formula is used and extended

Enhanced oil recovery is used in many mature oil reservoirs to increase the oil recovery factor. Surfactant flooding has recently gained interest again. To create micro emulsions at the interface between crude oil and water, surfactant flooding is the injection of surfactants (and co-surfactants) into the reservoir, thus achieving very low interfacial tension, which consequently assists mobilize the trapped oil.

In this study a flooding system, which has been  manufactured and described at high pressure. The flooding processes included oil, water and surfactants. 15 core holders has been prepared at first stage of the experiment and  filled with washed sand grains 80-500 mm and then packing the sand to obtain sand packs

A set of hydro treating experiments are carried out on vacuum gas oil in a trickle bed reactor to study the hydrodesulfurization and hydrodenitrogenation based on two model compounds, carbazole (non-basic nitrogen compound) and acridine (basic nitrogen compound), which are added at 0–200 ppm to the tested oil, and dibenzotiophene is used as a sulfur model compound at 3,000 ppm over commercial CoMo/ Al2O3 and prepared PtMo/Al2O3. The impregnation method is used to prepare (0.5% Pt) PtMo/Al2O3. The basic sites are found to be very small, and the two catalysts exhibit good metal support interaction. In the absence of nitrogen compounds over the tested catalysts in the trickle bed reactor at temperatures of 523 to 573 K, liquid hourly space v

In this study, the flow and heat transfer characteristics of Al₂O₃-water nanofluids for a range of the Reynolds number of 3000, 4500, 6000 and 7500 with a range of volume concentration of 1%, 2%, 3% and 4% are studied numerically. The test rig consists of cold liquid loop, hot liquid loop and the test section which is counter flow double pipe heat exchanger with 1m length. The inner tube is made of smooth copper with diameter of 15mm. The outer tube is made of smooth copper with diameter of 50mm. The hot liquid flows through the outer tube and the cold liquid (or nanofluid) flow through the inner tube. The boundary condition of this study is thermally insulated the outer wall with uniform velocity a

Abstract
A two electrode immersion electrostatic lens used in the design
of an electron gun, with small aberration, has been designed using
the finite element method (FEM). By choosing the appropriate
geometrical shape of there electrodes the potential V(r,z) and the
axial potential distribution have been computed using the FEM to
solve Laplace's equation.
The trajectory of the electron beam and the optical properties of
this lens combination of electrodes have been computed under
different magnification conditions (Zero and infinite magnification
conditions) from studying the properties of the designed electron
gun can be supplied with Abeam current of 5.7*10-6 A , electron
gun with half acceptance