In this paper, the problem of developing turbulent flow in rectangular duct is investigated by obtaining numerical results of the velocity profiles in duct by using large eddy simulation model in two dimensions with different Reynolds numbers, filter equations and mesh sizes. Reynolds numbers range from (11,000) to (110,000) for velocities (1 m/sec) to (50 m/sec) with (56×56), (76×76) and (96×96) mesh sizes with different filter equations. The numerical results of the large eddy simulation model are compared with k-ε model and analytic velocity distribution and validated with experimental data of other researcher. The large eddy simulation model has a good agreement with experimental data for high Reynolds number with the first, seco

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.

تتطلب عملية التنمية الاقتصـادية في الدول النامية مبالغ كبيرة من رؤوس الأمـوال اللازمة لتنفيذ البرامج والخطط الاقتصادية، ولما كانت الاسـتثمارات التي تنفذها هذه الدول خلال حقبة معينة، تزيد على ما تم  تحقيقه من موارد مالية محلية، فلابد أنْ يمول الفرق من خلال انسياب صافٍ لرأس المال الأجنبي (قروض ومساعدات) إلى الداخل خلال المدة نفسها، لغـرض سَدّ الفجوة في المـوارد المحلية المعدة للاسـتثمار، وعانت بعض د

A pseudo-slug flow is a type of intermittent flow characterized by short, frothy, chaotic slugs that have a structure velocity lower than the mixture velocity and are not fully formed. It is essential to accurately estimate the transition from conventional slug (SL) flow to pseudo-slug (PSL) flow, and from SL to churn (CH), by precisely predicting the pressure losses. Recent research has showed that PSL and CH flows comprise a significant portion of the conventional flow pattern maps. This is particularly true in wellbores and pipelines with highly deviated large-diameter gas-condensate wellbores and pipelines. Several theoretical and experimental works studied the behavior of PSL and CH flows; however, few models have been suggested to pre

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.