In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

       In this study, a simulation model inside a channel of rectangular section with high of (0.16 m) containing two rectangular obstruction plates were aligned variable heights normal to the direction of flow, use six model of the obstructions height of (0.059, 0.066, 0.073, 0.08 and 0.087 m) were compared with the flow behavior of the same duct without obstructions. To predict the velocity profile, pressure distribution, pressure coefficient and turbulence kinetic energy flow of air, the differential equations which describe the flow were approximated by the finite volumes method for two dimensional, by using commercial software package (FLUENT) with standard of k-ε model two dimensions turbulence flow.

In this study, a different design of passive air Solar Chimney(SC)was tested by installing it in the south wall of insulated test room in Baghdad city. The SC was designed from vertical and inclined parts connected serially together, the vertical SC (first part) has a single pass and Thermal Energy Storage Box Collector (TESB (refined paraffin wax as Phase Change Material(PCM)-Copper Foam Matrix(CFM))), while the inclined SC was designed in single pass, double passes and double pass with TESB (semi refined paraffin wax with copper foam matrix) with selective working angle ((30^o, 45^o and 60^o). A computational model was employed and solved by Finite Volume Method (FVM) to simulate the air i

An experimental and numerical study has been carried out to investigate the heat transfer by natural convection in a three dimensional annulus enclosure filled with porous media (silica sand) between two inclined concentric cylinders with (and without) annular fins attached to the inner cylinder under steady state condition; The experiments were carried out for a range of modified Rayleigh number (0.2 ≤Ra*≤ 11) and extended to Ra* =500 for numerical study, annulus inclination angle of (δ = 0˚, 30˚, 60˚ and 90˚). The numerical study was to write the governing equation under an assumptions used Darcy law and Boussinesq’s approximation and then solved numerically using finite difference approximation. It was found that the averag

Numerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case  on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th

        In this study multi objective optimization is utilized to optimize a turning operation to reveal the appropriate level of process features. The goal of this work is to evaluate the optimal combination of cutting parameters like feed, spindle speed, inclination angle and workpiece material to have a best surface quality Taguchi technique L9 mixed orthogonal array, has been adopted to optimize the roughness of surface. Three rods of length around (200 mm) for the three metals are used for this work. Each rod is divided into three parts with 50 mm length. For brass the optimum parametric mix for minimum Ra is A1, B1 and C3, i.e., at tool inclination angle (5), feedrate of 0.01, spindle speed of 120

The mechanical function of the heart is governed by the contractile properties of the cells, the mechanical stiffness of the muscle and connective tissue, and pressure and volume loading conditions on the organ. Although ventricular pressures and volumes are available for assessing the global pumping performance of the heart, the distribution of stress and strain that characterize regional ventricular function and change in cell biology must be known. The mechanics of the equatorial region of the left, ventricle was modeled by a thick-walled cylinder. The tangential (circumferential) stress, radial stress and longitudinal stress in the wall of the heart have been calculated. There are also significant torsional shear in the wall during b