In this paper, we consider a two-phase Stefan problem in one-dimensional space for parabolic heat equation with non-homogenous Dirichlet boundary condition. This problem contains a free boundary depending on time. Therefore, the shape of the problem is changing with time. To overcome this issue, we use a simple transformation to convert the free-boundary problem to a fixed-boundary problem. However, this transformation yields a complex and nonlinear parabolic equation. The resulting equation is solved by the finite difference method with Crank-Nicolson scheme which is unconditionally stable and second-order of accuracy in space and time. The numerical results show an excellent accuracy and stable solutions for two test examples.
The expansion of building blocks at the expense of agricultural land is one of the main problems causing climate change within the urban area of a city. The research came to determine these indicators, as a study was conducted on the expansion of the building blocks in three municipalities in the city of Baghdad for a period of four decades extended in the form of time cycles for the period (1981-2021) and using ArcMap GIS 10.7 technology. Then, the impact of this expansion on temperature rates was evaluated, as they are the most important climatic elements due to their significant effect on the rest of the elements. The results showed a clear, direct relationship between the increase in urban expansion rates and the corresponding r
... Show MoreIn this study, mean free path and positron elastic-inelastic scattering are modeled for the elements hydrogen (H), carbon (C), nitrogen (N), oxygen (O), phosphorus (P), sulfur (S), chlorine (Cl), potassium (K) and iodine (I). Despite the enormous amounts of data required, the Monte Carlo (MC) method was applied, allowing for a very accurate simulation of positron interaction collisions in live cells. Here, the MC simulation of the interaction of positrons was reported with breast, liver, and thyroid at normal incidence angles, with energies ranging from 45 eV to 0.2 MeV. The model provides a straightforward analytic formula for the random sampling of positron scattering. ICRU44 was used to compile the elemental composition data. In this
... Show MoreIn this study, pure polylactic acid (PLA) and composite polylactic acid/ curcumin (PLA / Cur) were prepared by a suspension of ultrasonically agitated micrometer-sized curcumin powder, which was mixed with chloroform solvent under slow mechanical stirring and incorporated into the PLA. The resulting suspension was used to cast free-standing PLA / Cur composite films. The filler content was chosen to be 2.0 wt % curcumin. Physical properties (glass transition, temperature, mechanical and thermodynamic) were analyzed by Positron Annihilation Lifetime Spectroscopy (PALS), which is a unique tool for analyzing the defects of polymer materials. The free volume and holebility of PLA and PLA / Cur were studied 
... Show MoreIn this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth
... Show MoreIn this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform â€double Sumudu â€. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace methodâ€. All results are illustrative numerically and graphically.
In this paper we design a Simulink model which can be evaluate the concentration of Copper, Lead, Zinc, Cadmium, Cobalt, Nickel, Crum and Iron. So, this model would be a method to determine the contamination levels of these metals with the potential for this contamination sources with their impact. The aim of using Simulink environment is to solve differential equations individually and as given data in parallel with analytical mathematics trends. In general, mathematical models of the spread heavy metals in soil are modeled and solve to predict the behavior of the system under different conditions.
In this work, the fractional damped Burger's equation (FDBE) formula = 0,
The Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures
An experimental study was conducted on pressure drop of water flow through vertical cylindrical packed beds in turbulent region and the influence of the operating parameters on its behavior. The bed packing was made of spherical and non-spherical particles (spheres, Rasching rings and intalox saddle) with aspect ratio range 3.46 D/dp 8.486 obtaining bed porosities 0.396 0.84 and Reynolds number 1217 21758. The system is consisted of 5 cm inside diameter Perspex column, 50 cm long; distilled water was pumped through the bed with flow rate 875, 1000, 1125, 1250,1375 and 1500 l/h and inlet water temperature 20, 30, 40 and 50 ˚C. The packed bed system was monitored by using LabVIEW program, were the result
... Show MoreObjective: The aim of this study was to evaluate the effect of pumice, burning investment material
and black sand on the surface roughness of heat cure acrylic resin.
Methodology: Sixty specimens were prepared from pink heat cure acrylic resin, the specimens
where grouped into; 20 specimens which polished with pumice and water (control group); 20
specimens which polished with investment material (after burning it) and water; and 20 specimens
which polished with black sand and water. The average surface roughness of specimens after
polishing procedure had been determined by profilometer (surface roughness tester).
Results: Through the application of ANOVA and LSD tests, the result of this study showed that there
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