scholarly journals Special function form exact solutions for Jeffery fluid: an application of power law kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Maryam Asgir ◽  
A. A. Zafar ◽  
Abdullah M. Alsharif ◽  
Muhammad Bilal Riaz ◽  
Muhammad Abbas
Keyword(s):  
Classical Model ◽  
Parallel Plates ◽  
Order Model ◽  
Physical Conditions ◽  
Fractional Order Model ◽  
Fluid Parameter ◽  
The Laplace Transform ◽  
The One ◽  
The Mathematical Model ◽  
Validation Of Results

AbstractThis research note’s objective is to elaborate on the study of the unsteady MHD natural convective flow of the Jeffery fluid with the fractional derivative model. The fluid flow phenomenon happens between two vertical parallel plates immersed in a porous medium. The one plate is moving with the time-dependent velocity $U_{0} f(t)$ U 0 f ( t ) , while the other is fixed. The mathematical model is presented with the system of the partial differential equation along with physical conditions. Appropriate dimensionless variables are employed in the system of equations, and then this dimensionless model is transformed into the Caputo fractional-order model and solved analytically by the Laplace transform. The exact expressions for velocity and temperature, which satisfy the imposed initial and boundary conditions, are obtained. Memory effects in the fluid are observed which the classical model fails to elaborate. Interesting results are revealed from the investigation of emerging parameters as Grashof number, Prandtl number, relaxation time parameter, Jeffery fluid parameter, Hartmann number, porosity, and fractional parameter. The results are elucidated with the detailed discussion and the assistance of the graphs. For the sake of validation of results, the corresponding solutions for viscous fluids are also obtained and compared with the solutions already existing in the literature.

scholarly journals Study of electrical R-L circuits composed of resistors and inductors and driven by a voltage of the current source: Simulation with implementing an accurate method

2020 ◽  
Author(s):  
Mohamed Adel ◽  
Hari M. Srivastava ◽  
Mohamed Khader
Keyword(s):  
Current Source ◽  
Numerical Procedure ◽  
Classical Case ◽  
Approximate Solutions ◽  
Accurate Method ◽  
Order Model ◽  
The Third ◽  
Fractional Order Model ◽  
Proposed Model ◽  
The Mathematical Model

In this study, we propose to derive an accurate numerical procedure to solve the mathematical model which describes the electrical R-L circuit composed of resistors and inductors driven by a voltage of current source, which is the fractional-order model for the electrical RL-circuit. Our study depends on the spectral collocation method via the useful properties of the Chebyshev polynomials of the third-kind. Some theorems about the convergence analysis are given. The study concludes by comparing the resulting approximate solutions of the proposed model with the exact solution in the classical case. Illustrative graphical and numerical analysis of the derived results are also included in this study.

scholarly journals ITERATIVE METHOD APPLIED TO THE FRACTIONAL NONLINEAR SYSTEMS ARISING IN THERMOELASTICITY WITH MITTAG-LEFFLER KERNEL

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040040 ◽  
Author(s):  
WEI GAO ◽  
P. VEERESHA ◽  
D. G. PRAKASHA ◽  
BILGIN SENEL ◽  
HACI MEHMET BASKONUS
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Order Model ◽  
Science And Engineering ◽  
One Dimensional ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis ◽  
The One

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

scholarly journals A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel

2021 ◽  
Vol 146 ◽  
pp. 110859
Author(s):  
Ahmed Boudaoui ◽  
Yacine El hadj Moussa ◽  
Zakia Hammouch ◽  
Saif Ullah
Keyword(s):  
Fractional Order ◽  
The Novel ◽  
Order Model ◽  
Fractional Order Model ◽  
Novel Coronavirus

scholarly journals Entropy generation analysis for MHD flow of water past an accelerated plate

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tarek N. Abdelhameed
Keyword(s):  
Magnetic Field ◽  
Entropy Generation ◽  
Transfer Problem ◽  
Finite Difference Methods ◽  
Mhd Flow ◽  
Bejan Number ◽  
Physical Conditions ◽  
Flow Parameters ◽  
The Laplace Transform ◽  
Constant Heating

AbstractThis article examines the entropy generation in the magnetohydrodynamics (MHD) flow of Newtonian fluid (water) under the effect of applied magnetic in the absence of an induced magnetic field. More precisely, the flow of water is considered past an accelerated plate such that the fluid is receiving constant heating from the initial plate. The fluid disturbance away from the plate is negligible, therefore, the domain of flow is considered as semi-infinite. The flow and heat transfer problem is considered in terms of differential equations with physical conditions and then the corresponding equations for entropy generation and Bejan number are developed. The problem is solved for exact solutions using the Laplace transform and finite difference methods. Results are displayed in graphs and tables and discussed for embedded flow parameters. Results showed that the magnetic field has a strong influence on water flow, entropy generation, and Bejan number.

scholarly journals A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

2021 ◽  
Author(s):  
J. Marconi ◽  
P. Tiso ◽  
D. E. Quadrelli ◽  
F. Braghin
Keyword(s):  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Displacement Fields ◽  
Reduced Order ◽  
Total Displacement ◽  
Elastic Forces ◽  
Strain Formulation ◽  
The One ◽  
Definition Of

AbstractWe present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

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