This paper considers the nonlinear homogeneous fractional Burger's equation as a type of nonlinear fractional partial differential equations (FPDE). Our goal in this paper is to show that an initial value problem (IVP) can be modified with a second initial condition when (α ∈ ( 1,2 ]) as the velocity of the movement, and the obtained solution agrees with the nature of the wave with space and time for the problem. The Caputo fractional derivative is used in all the fractional derivatives. Also, the algorithm of the Laplace transform decomposition method (LTDM) for fractional PDEs is presented. The approximate solution converges to the exact solution in Theorem 1. Also, a numerical simulation is made to confirm the theoretical results. In addition, the solution is displayed graphically for three values of (α ) that belong to the interval ( 1,2 ] to study the effects of changing the value of the fractional order derivative on the wave solutions of the time-fractional Burger PDE. The time interval is extended in each graph to check the effect of time on the number and shape of the waves in addition to changing the fractional order. Finally, a comparison of the obtained solutions is made.
This study delves into the realm of advanced cooling techniques by examining the performance of a two-stage parallel flow indirect evaporative cooling system enhanced with aspen pads in the challenging climate of Baghdad. The objective was to achieve average air dry bulb temperatures (43 oC) below the ambient wet bulb temperatures (24.95 oC) with an average relative humidity of 23%, aiming for unparalleled cooling efficiency. The research experiment was carried out in the urban environment of Baghdad, characterized by high temperature conditions. The investigation focused on the potential of the two-stage parallel flow setup, combined with the cooling capability of aspen pads, to surpass the limitat
... Show MoreIn this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel
... Show MoreThe current study was conducted with the aim of fortifying meat burger with the protein isolate extracted from defatted sweetened and unsweetened apricot kernels. The antimicrobial activity of defatted apricot kernels and protein isolates of sweetened and unsweetened kernels against some pathogenic microbes was studied, and it was characterized by its effect on gram-positive bacteria more than gram-negative bacteria. As for its effect on yeast, the inhibition diameter was 4.5 mm at a concentration of 200 mg for the unsweetened protein isolate. As for its effect on mold, the inhibition percentage was between 56.05 65.21% for all samples at a concentration of 100 mg. The sweetened and unsweetened protein isolate was used in the manufact
... Show MoreIn this paper, a time–space fractional order inverse source problem to determine the temperature solution and the time‐dependent source term from heat moment to the time–space fractional heat equation with an initial condition, homogeneous Dirichlet boundary conditions, and integral overdetermination condition is investigated. Two unconditionally stable finite difference schemes are proposed to find a numerical solution of the direct problem. Namely, method I is based on the approximation of the time‐fractional derivative via Laplace transformation, whereas method II is based on finite difference approximation. The inverse problem is solved iteratively
To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which shows the reliability and applicability of the proposed approach.
Abstract
The aim of this work is to create a power control system for wind turbines based on fuzzy logic. Three power control loop was considered including: changing the pitch angle of the blade, changing the length of the blade and turning the nacelle. The stochastic law was given for changes and instant inaccurate assessment of wind conditions changes. Two different algorithms were used for fuzzy inference in the control loop, the Mamdani and Larsen algorithms. These two different algorithms are materialized and developed in this study in Matlab-Fuzzy logic toolbox which has been practically implemented using necessary intelligent control system in electrical engineerin
... Show MoreThis article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.
One and two-dimensional hydraulic models simulations are important to specify the hydraulic characteristics of unsteady flow in Al-Gharraf River in order to define the locations that facing problems and suggesting the necessary treatments. The reach in the present study is 58200m long and lies between Kut and Hai Cities. Both numerical models were simulated using HEC-RAS software, 5.0.4, with flow rates ranging from 100 to 350 m3/s. Multi-scenarios of gates openings of Hai Regulator were applied. While the openings of Al-Gharraf Head Regulator were ranged between 60cm to fully opened. The suitable manning roughness for the unsteady state was
... Show MoreA particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)