The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The solidification process in a multi-tube latent heat energy system is affected by the natural convection and the arrangement of heat exchanger tubes, which changes the buoyancy effect as well. In the current work, the effect of the arrangement of the tubes in a multi-tube heat exchanger was examined during the solidification process with the focus on the natural convection effects inside the phase change material (PCM). The behavior of the system was numerically analyzed using liquid fraction and energy released, as well as temperature, velocity and streamline profiles for different studied cases. The arrangement of the tubes, considering seven pipes in the symmetrical condition, are assumed at different positions in the system, i

The organizations, represented by its Management, are working hard in various ways to identify the environmental disturbances that occur in their environment and to investigate and follow up the movement of these disturbances and to respond to them through the decisions they make in an attempt to keep pace with the work and sustainability of their activities, including those decisions, marketing decisions taken by the environmental disturbulence in the market of the organization, the inability of these organizations to read the indicators of these disturbulence correctly displays their marketing effectiveness to vibration and decline in the negative.The current research is based on a fundamental problem that envi

The current research aims to identify the effect of the hands_on strategy on the life effectiveness skills of the first grade students in the government's daytime middle schools. The Umm al-Mu 'minin school was intentionally chosen to be the research sample of the second Rusafa Directorate for the academic year 2021-2022. Then, two divisions were randomly chosen for the first of the six divisions to represent the experimental group that is studying according to the strategy of the hands_on and the other the control group that is studying according to the usual method. The equivalence of the two research groups was verified by a set of variables. The two groups were found to be equivalent. As for the research tool, the life effectiveness sca

The current research aims to identify the effect of the study hand-on strategy on the achievement of the chemistry subject at the first grade students in the government day schools. The Umm al-Mu 'mineen school was chosen by appointment the intentional, so that its student is the research sample of the second Rusafa Directorate for the academic year (2021-2022). Then, two divisions were randomly selected for the first average out of 6 divisions to represent the experimental group that is studying according to the strategy of the thinker hand and the other the control group that is studying according to the usual method. The equivalence of the two research groups was verified by a set of variables represented by (chronological age, previous

Frictional heat is generated when the clutch starts to engag. As a result of this operation the surface temperature is increased rapidly due to the difference in speed between the driving and driven parts. The influence of the thickness of frictional facing on the distribution of the contact pressure of the multi-disc clutches has been investigated using a numerical approach (the finite element method). The analysis of contact problem has been carried out for a multiple disc dry clutch (piston, clutch discs, separators and pressure plate). The results present the distribution of the contact pressure on all tShe surfaces of friction discs that existed in the friction clutch system. Axisymmetric finite element models have been developed to ac