The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

The research aims to demonstrate the impact of internal audit in Iraqi economic units on enhancing social performance reports, through the statistical models used, as a survey list (for the independent variant) of the search, which contains five axes of each axis, contains a set of The questions were prepared on the basis of the standards issued by the Institute of Internal Auditors (IIA) and were distributed to a sample of internal auditors, as for (for the approved variable) the researcher obtained numerical data represented by the financial statements of the research sample and used statistical models such as model (Kolmakrov-Smirnov) is a good match (goodness of fit) which assumes that the data is distributed naturally as wel

The Mauddud Formation was one of the important and widespread Lower Cretaceous period formations in Iraq. It has been studied in three wells (EB. 55, EB. 58, and EB. 59) within the East Baghdad Oil Field, Baghdad, central Iraq. 280 thin sections were studied by microscope to determine fauna, the formation composed of limestone and dolomitized limestone in some parts which tends to be marl in some parts, forty species and genus of benthic foraminifera have been identified beside algae and other fossils, three biozones have been identified in the range which is: Orbitolina qatarica range zone (Late Albian), Orbitolina sefini range zone (Late Albian – Early Cenomanian) and Orbitolina concava range zone (Early Cenomanian), The age of

In this paper, we introduce and study the essential and closed fuzzy submodules of a fuzzy module X as a generalization of the notions of essential and closed submodules. We prove many basic properties of both concepts.

Summary
This research is included in the study of one of the most important rules of jurisprudence, which is (necessity descends the status of necessity, controls and applications) branching from the major rule (hardship brings facilitation) and since the jurisprudential rule is defined as knowledge of a total or majority rule that applies to all its parts. He has to know all the branches that fall under him, which leads to understanding Sharia, controlling jurisprudential issues and linking them to its rules, so that no contradiction occurs, and he has the jurisprudential faculty that he promotes in consideration and diligence. And what is meant by need: is what is lacking in terms of expansion and raising the distress that often lea

Countries have faced the challenges of high levels of public debt and seek to define the optimum limits to reduce risks to which the financial system can be exposed and its impact on the economy as a whole. Hence the importance of research in studying the impact of internal and external public debt components on indicators of stability of the financial system for the period 2005-2017 for the purpose of knowing the extent of the financial stability indicators response to the high level of the public debt from its optimum ratio, as the aim of the research is to estimate and analyze the dynamic relationship of short and long term between the components of public debt and indicators of financial stability using the (ARDL) model that

The values of fmgerprint angles were studied in 57 females and 44 males from Najaf province in the m iddle of Iraq. Some results of tlus sample were compared with the results of Southern provinces sample from Iraq i population.

The  rCS\tlts  revealed that the mean of  maximum fingerprint angle (MFA) and also the mean of absolute fingerprint angle (AFA) between samples in the studied provinces did nnt differ significantly. However, the unilateral analysis revealed only one significant diOerence in LS of  the male samples (r-2.89,  P<O.Ol), while the bilateral analysis revealed two significant differences, wluch occurred in Rl and R3 of the right hand.

As lbr the compari son between sexes of the

Bentonite is widely used in industrial applications. The present study reports the effect of adding different weights of ZnO to the Iraqi bentonite, on surface area, pore volume and real density. These surface properties were evaluated for pure and modified bentonite. The modification was made by adding different ZnO weights such as; ( 0.5%, 1%, 5%, 10% ). The effect of heat exposing for all modified clay samples at 500 ?C have been also evaluated. The results show that the addition of 0.5% ZnO leads to increase the surface area percentage about 36%, increase pore volume percentage about 5.48% and increase the real density percentage about 27.116%. When the samples exposed to 500 ?C, their surface area and pore volumes have been decreased a

we applied the direct product concept on the notation of intuitionistic fuzzy semi d-ideals of d-algebra with investigation some theorems, and also, we study the notation of direct product of intuitionistic fuzzy topological d-algebra.