Numerical study on the rotating electro-osmotic flow of third grade fluid with slip boundary condition

2020 ◽  
Vol 75 (7) ◽  
pp. 649-655
Author(s):  
Juan Song ◽  
Shaowei Wang ◽  
Moli Zhao ◽  
Ning Li
Keyword(s):  
Boundary Condition ◽  
Velocity Profile ◽  
Slip Boundary Condition ◽  
Third Grade ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Osmotic Flow ◽  
Slip Boundary ◽  
Grade Fluid ◽  
Electro Osmotic Flow

AbstractConsidering the slip boundary condition, the rotating electro-osmotic flow of a third grade fluid in a channel formed by two parallel plates is investigated in the present study. The charge distribution is treated with the Debye–Hückel approximation analytically. Based on the finite difference method, the velocity profile for rotating electro-osmotic flow of third grade fluid is obtained numerically. It is shown that the non-Newtonian parameter of third grade fluid and the velocity slip factor play the important roles for the rotating electro-osmotic flow. The increasing non-Newtonian parameter slows down the flow and decreases the velocity magnitude, and the increasing slip parameter β has the similar influence on the velocity profile. Furthermore, the effect of the inclusion of third grade on the velocity profile is more conspicuous in the area near the walls.

scholarly journals Electro-osmotic flow of a third-grade fluid past a channel having stretching walls

2019 ◽  
Vol 8 (1) ◽  
pp. 56-64 ◽  
Author(s):  
Mamata Parida ◽  
Sudarsan Padhy
Keyword(s):  
Differential Equation ◽  
Boltzmann Equation ◽  
Linear Partial Differential Equation ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Osmotic Flow ◽  
Grade Fluid ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electro Osmotic Flow

Abstract The electro-osmotic flow of a third grade fluid past a channel having stretching walls has been studied in this paper. The channel height is taken much greater than the thickness of the electric double layer comprising of the Stern and diffuse layers. The equations governing the flow are obtained from continuity equation, the Cauchy’s momentum equation and the Poisson-Boltzmann equation. The Debye-Hückel approximation is adopted to linearize the Poisson-Boltzmann equation. Suitable similarity transformations are used to reduce the resulting non-linear partial differential equation to ordinary differential equation. The reduced equation is solved numerically using damped Newton’s method. The results computed are presented in form of graphs.

scholarly journals Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Velocity Profile ◽  
Nonlinear Boundary ◽  
Slip Boundary Condition ◽  
First Grade ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Governing Equations ◽  
Slip Boundary

In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.

scholarly journals Weak Solution for 3D-Stochastic Third Grade Fluid Equations

Water ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 3211
Author(s):  
Adilson Almeida ◽  
Fernanda Cipriano
Keyword(s):  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Navier Slip ◽  
Slip Boundary ◽  
Sample Paths ◽  
Stochastic Solution ◽  
Grade Fluid ◽  
Differential Type

This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain O, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space H2(O), and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in L∞(0,T;H2(O)).

Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy-Brinkman-Forchheimer model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lijun Zhang ◽  
Muhammad Mubashir Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Temperature Profile ◽  
Fluid Model ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Solution Technique ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Transform Method ◽  
Content Type ◽  
Grade Fluid

Purpose The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study. Design/methodology/approach A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme. Findings The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study. Originality/value The obtained results are new and presented for the first time in the literature.

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