Papers by ABDELHALIM EBAID
Zeitschrift für Naturforschung, Jul 1, 2011
Although the decomposition method and its modified form were used during the last two decades by ... more Although the decomposition method and its modified form were used during the last two decades by many authors to investigate various scientific models, a little attention was devoted for their applications in the field of fluid mechanics. In this paper, the Adomian decomposition method (ADM) is implemented for solving the nonlinear partial differential equation (PDE) describing the peristaltic flow of a power-law fluid in a circular cylindrical tube under the effect of a magnetic field. The numerical solutions obtained in this paper show the effectiveness of Adomian's method over the perturbation technique.
International journal of engineering research and technology, Mar 14, 2014
The peristaltic motion of a Carreau fluid in an asymmetric channel with partial slip is studied u... more The peristaltic motion of a Carreau fluid in an asymmetric channel with partial slip is studied under long wave length and low Reynolds number assumptions which are also used to solve the problem. Applying perturbation technique, the expressions for stream function, axial velocity, axial pressure gradient, pressure rise, shear stress and frictional forces have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping is examined for different wave forms. The results of the current paper reveal that the size of the trapping bolus increases by Carreau fluid (n=0.398) to Newtonian fluid (n=1).
Journal of theoretical and applied mechanics, Dec 1, 2016
The exact solutions of a nonlinear differential equations system, describing the boundary layer f... more The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.
Acta Astronautica, Nov 1, 2017
Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendenta... more Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendental equation in terms of the eccentric anomaly of a planet which orbits the Sun. Determining the position of a planet in its orbit around the Sun at a given time depends upon the solution of Kepler's equation, which we will solve in this paper by the Adomian decomposition method (ADM). Several properties of the periodicity of the obtained approximate solutions have been proved in lemmas. Our calculations demonstrated a rapid
Asian research journal of mathematics, Nov 27, 2020
Delay differential equations (DDEs) are generalization of the ordinary differential equation (ODE... more Delay differential equations (DDEs) are generalization of the ordinary differential equation (ODEs), which is suitable for physical system that also depends on the past data. In this paper, the Reproducing Kernel Hilbert Spaces (RKHS) method is applied to approximate the solution of a general form of first, second and third order fractional DDEs (FDDEs). It is a relatively new analytical technique. The analytical and approximate solutions are represented in terms of series in the RKHS.
Zeitschrift für Naturforschung, 2011
alexandria engineering journal, Mar 1, 2023
Zeitschrift für Naturforschung, Dec 1, 2010
In this paper, suitable transformations and a so-called exp-function method are used to obtain di... more In this paper, suitable transformations and a so-called exp-function method are used to obtain different types of exact solutions for some nonlinear evolution equations with variable coefficients and nonlinear terms of any orders. The Korteweg-de Vries equation and the Burgers equation with nonlinear terms of any orders are chosen to show how to apply the exp-function method for these kinds of nonlinear equations. These exact solutions are in full agreement with the previous results obtained by Ebaid and by Zhu.
Waves in Random and Complex Media, Mar 30, 2023
International Journal of Analysis and Applications, 2021
The Ambartsumian equation in view of the q-calculus is investigated in this paper. This equation ... more The Ambartsumian equation in view of the q-calculus is investigated in this paper. This equation is of practical interest in the theory of surface brightness in the Milky Way. Two approaches are applied to obtain the closed form solution. The first approach implements a direct series assumption while the second approach is based on the Adomian decomposition method. The two approaches lead to a unique power series of arbitrary powers. Furthermore, the convergence of the obtained series is theoretically proven. In addition, we showed that the present solution reduces to the results in the relevant literature when the quantum calculus parameter tends to 1.
Thermal Science, 2019
This paper presents the solution of the initial boundary-value problem for the system of 1-D ther... more This paper presents the solution of the initial boundary-value problem for the system of 1-D thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method.
AIMS mathematics, 2023
The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few ... more The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few months, China faced a new wave of this pandemic which increases the risk of its spread to the rest of the world. Therefore, there has become an urgent demand to know the expected behavior of this pandemic in the coming period. In this regard, there are many mathematical models from which we may obtain accurate predictions about the behavior of this pandemic. Such a target may be achieved via updating the mathematical models taking into account the memory effect in the fractional calculus. This paper generalizes the power-law growth model of the COVID-19. The generalized model is investigated using two different definitions in the fractional calculus, mainly, the Caputo fractional derivative and the conformable derivative. The solution of the first-model is determined in a closed series form and the convergence is addressed. At a specific condition, the series transforms to an exact form. In addition, the solution of the second-model is evaluated exactly. The results are applied on eight European countries to predict the behavior/variation of the infected cases. Moreover, some remarks are given about the validity of the results reported in the literature.
Zeitschrift für Naturforschung, Jun 1, 2014
No doubt, the exact solution of any physical system is considered optimal when it is available. S... more No doubt, the exact solution of any physical system is considered optimal when it is available. Such exact solution is of great importance not only in validating the accuracy of the approximate solution obtained for the same problem but also to derive the correct physical interpretation of the involved physical phenomena. In this paper, the system of linear and nonlinear partial differential equations describing the peristaltic flow of a nanofluid in a channel with compliant walls has been solved exactly. These exact solutions have been implemented to explore the exact effects of Prandtl number Pr, thermophoresis parameter N T , Brownian motion parameter N B , and Eckert number Ec on the temperature, the nanoparticle concentration profiles, and the heat transfer coefficient Z(x). In addition, the exact results have been compared with a very recent work via the homotopy analysis method for the same problem. Although these comparisons showed that the published approximate results coincide with the current exact analysis, a few remarkable differences have been detected for the behaviour of the heat transfer coefficient.
Communications in Theoretical Physics, Mar 1, 2017
Applied Mathematics and Computation, Nov 1, 2006
The problem of peristaltic transport of an incompressible viscous fluid in an asymmetric channel ... more The problem of peristaltic transport of an incompressible viscous fluid in an asymmetric channel through a porous medium is analyzed. The flow is investigated in a wave frame of reference moving with velocity of the wave under the assumptions of long-wavelength and low-Reynolds number. An explicit form of the stream function is obtained by using Adomian decomposition method. The analysis showed that transport phenomena are strongly dependent on the phase shift between the two walls of the channel. It is indicated that the axial velocity component U in fixed frame increases with increasing the permeability parameter. In the case of high permeability parameter (as K ! 1), our results are in agreement with Mishra and Ramachandra Rao [M. Mishra, A. Ramachandra Rao, Peristaltic transport of a Newtonian fluid in an asymmetric channel, ZAMP 53 (2003) 532] and Eytan and Elad [O. Eytan, D. Elad, Analysis of intra-uterine fluid motion induced by uterine contractions, Bull. Math. Biol. 61 (1999) 221]. The results given in this paper may throw some light on the fluid dynamic aspects of the intra-uterine fluid flow through a porous medium.
International Journal of Thermal Sciences, 2009
An approximate analytical solution for the temperature distribution and interface motion is deter... more An approximate analytical solution for the temperature distribution and interface motion is determined for the freezing of blood-perfused tissue around a cylindrical cryoprobe. The solution is based on an improved quasi-steady model in which assumed temperature profiles in the frozen and unfrozen tissue are used to determine the interface motion. The approximate solution satisfies all temperature boundary conditions as well as the transient heat equations at the interface. Due to blood perfusion in the unfrozen tissue, a steady state is reached where the interface becomes stationary. The solution converges to the exact steady state interface location. Improvement over the quasi-steady solution and the accuracy of the present theory are verified by comparison with numerical solutions for the limiting case of zero blood perfusion and metabolic heat production. Results show that a typical quasi-steady error of 73% is reduced to 8% using the present theory. Parametric charts are presented to evaluate the effect of the governing parameters on interface location.
Mathematics, Jul 27, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Fractal and fractional, Feb 2, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Mathematics, May 22, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Advances and Applications in Fluid Mechanics, Apr 22, 2017
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Papers by ABDELHALIM EBAID