In cooling water systems, cooling towers play a critical role in removing heat from the water. Cooling water systems are commonly used in industry to dispose the waste heat. An upward spray cooling water systems was especially designed and investigated in this work. The effect of two nanofluids (Al2O3/ water, black carbon /water) on velocity and temperature distributions along reverse spray cooling tower at various concentrations (0.02, 0.08, 0.1, 0.15, and 0.2 wt.%) were investigated, beside the effect of the inlet water temperature (35 ,40, and 45 ͦ C) and water to air flow ratio (L/G) of 0.5, 0.75, and 1. The best thermal performance was found when the working solution contained 0.1 wt.% for each of Al2O3 and black carbon nanoparticles, with a maximum drop in temperature drops (i, e. range) of (16 ͦ C) and (20 ͦ C), respectively. The temperature of the tower's outlet water was decreased as the inlet working fluid increased, and the thermal efficiency declined with the increasing of the L/G by about 5%. However, the drop in the outlet temperature caused by the nanofluid is more than that of pure water at every point by about 6 ͦ C.
The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.
The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.
A new class of generalized open sets in a topological space, called G-open sets, is introduced and studied. This class contains all semi-open, preopen, b-open and semi-preopen sets. It is proved that the topology generated by G-open sets contains the topology generated by preopen,b-open and semi-preopen sets respectively.