scholarly journals Unsteady Flows of a Generalized Fractional Burgers’ Fluid between Two Side Walls Perpendicular to a Plate

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jianhong Kang ◽  
Yingke Liu ◽  
Tongqiang Xia
Keyword(s):  
Unsteady Flows ◽  
Maxwell Fluid ◽  
Second Grade ◽  
Burgers Fluid ◽  
Double Fourier Transform ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Side Walls ◽  
Generalized Maxwell Fluid ◽  
Stokes Second Problem

The unsteady flows of a generalized fractional Burgers’ fluid between two side walls perpendicular to a plate are studied for the case of Rayleigh-Stokes’ first and second problems. Exact solutions of the velocity fields are derived in terms of the generalized Mittag-Leffler function by using the double Fourier transform and discrete Laplace transform of sequential fractional derivatives. The solution for Rayleigh-Stokes’ first problem is represented as the sum of the Newtonian solutions and the non-Newtonian contributions, based on which the solution for Rayleigh-Stokes’ second problem is constructed by the Duhamel’s principle. The solutions for generalized second-grade fluid, generalized Maxwell fluid, and generalized Oldroyd-B fluid performing the same motions appear as limiting cases of the present solutions. Furthermore, the influences of fractional parameters and material parameters on the unsteady flows are discussed by graphical illustrations.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

scholarly journals MHD Peristaltic Flow of Fractional Jeffrey Model through Porous Medium

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoyi Guo ◽  
Jianwei Zhou ◽  
Huantian Xie ◽  
Ziwu Jiang
Keyword(s):  
Porous Medium ◽  
Pressure Rise ◽  
Maxwell Fluid ◽  
Peristaltic Flow ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Viscoelastic Parameters ◽  
Special Cases ◽  
Generalized Second Grade Fluid

The magnetohydrodynamic (MHD) peristaltic flow of the fractional Jeffrey fluid through porous medium in a nonuniform channel is presented. The fractional calculus is considered in Darcy’s law and the constitutive relationship which included the relaxation and retardation behavior. Under the assumptions of long wavelength and low Reynolds number, the analysis solutions of velocity distribution, pressure gradient, and pressure rise are investigated. The effects of fractional viscoelastic parameters of the generalized Jeffrey fluid on the peristaltic flow and the influence of magnetic field, porous medium, and geometric parameter of the nonuniform channel are presented through graphical illustration. The results of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid, are also deduced as special cases. The comparison among them is presented graphically.

scholarly journals On rate type fluid flow induced by rectified sine pulses

2021 ◽  
Vol 7 (2) ◽  
pp. 1615-1627
Author(s):  
Kehong Zheng ◽  
◽  
Fuzhang Wang ◽  
Muhammad Kamran ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Flow Characteristics ◽  
Unsteady Motion ◽  
Second Grade ◽  
Engineering Mathematics ◽  
Parameter Ratio ◽  
Fourier Sine Transform ◽  
Grade Fluid ◽  
Side Walls ◽  
Rate Type ◽  
Mathematics And Physics

<abstract><p>This investigation aims to present the unsteady motion of second grade fluid in an oscillating duct induced by rectified sine pulses. Some of the most dominant means for solving problems in engineering, mathematics and physics are transform methods. The objective is to modify the domain of the present problem to a new domain which is easier for evaluation. Such modifications can be done by different ways, one such way is by using transforms. In present work Fourier sine transform and Laplace transform techniques are used. The solution thus obtained is in form of steady state, with combination of transient solution which fulfills all required initial and boundary conditions. The influence of various parameters of interest for both developing and retarding flows on the flow characteristics will also be sketched and discussed. Also, the problem is reduced to the flow model where side walls are absent by bringing the aspect ratio parameter (ratio of length to width) to zero.</p></abstract>

Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate

2005 ◽  
Vol 42 (4) ◽  
pp. 395-405 ◽  
Author(s):  
Tasawar Hayat ◽  
Masood Khan
Keyword(s):  
Porous Plate ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Flows of a generalized second grade fluid in a cylinder due to a velocity shock

2019 ◽  
Vol 60 ◽  
pp. 720-730 ◽  
Author(s):  
Itrat Abbas Mirza ◽  
Muhammad Saeed Akram ◽  
Imran Siddique
Keyword(s):  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

scholarly journals Analytic solution of Stokes second problem for second-grade fluid

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
S. Asghar ◽  
S. Nadeem ◽  
K. Hanif ◽  
T. Hayat
Keyword(s):  
Analytical Solution ◽  
Laplace Transformation ◽  
Material Parameter ◽  
Analytic Solution ◽  
Second Grade ◽  
Perturbation Techniques ◽  
Second Grade Fluid ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Second Problem

Using Laplace transformation and perturbation techniques, analytical solution is obtained for unsteady Stokes' second problem. Expressions for steady and transient solutions are explicitly determined. These solutions depend strongly upon the material parameter of second-grade fluid. It is shown that phase velocity decreases by increasing material parameter of second-grade fluid.

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