Global existence of solutions for the second grade fluid equations in a thin three-dimensional domain

2016 ◽  
Vol 101 (1-2) ◽  
pp. 69-95
Author(s):  
Bouthaina Abdelhedi
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Global Existence Of Solutions ◽  
Fluid Equations ◽  
Grade Fluid ◽  
Dimensional Domain

Global existence of the 3D rotating second grade fluid system

2020 ◽  
pp. 1-32
Author(s):  
Basma Jaffal-Mourtada
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Fluid System ◽  
Forcing Term ◽  
First Case ◽  
Grade Fluid

We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components.

scholarly journals Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

2016 ◽  
Vol 21 (2) ◽  
pp. 359-376
Author(s):  
N.A. Khan ◽  
F. Naz
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensional ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Grade Fluid ◽  
Suction Or Injection

AbstractThis investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

scholarly journals Three-Dimensional Couette Flow of a Second-Grade Fluid Along Periodic Injection/Suction

Coatings ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 553 ◽  
Author(s):  
Muhammad Afzal Rana ◽  
Yasar Ali ◽  
Babar Ahmad ◽  
Muhammad Touseef Afzal Rana
Keyword(s):  
Transverse Direction ◽  
Flow Direction ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Main Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Suction Velocity ◽  
Grade Fluid ◽  
Main Flow Direction

This work explores the three-dimensional laminar flow of an incompressible second-grade fluid between two parallel infinite plates. The assumed suction velocity comprises a basic steady dispersal with a superimposed weak transversally fluctuating distribution. Because of variation of suction velocity in transverse direction on the wall, the problem turns out to be three-dimensional. Analytic solutions for velocity field, pressure and skin friction are presented and effects of dimensionless parameters emerging in the model are discussed. It is observed that the non-Newtonian parameter plays dynamic part to rheostat the velocity component along main flow direction.

scholarly journals Hm Convergence of the Second-Grade Fluid Equations to Euler Equations in ℝd

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hui Zhou
Keyword(s):  
Euler Equation ◽  
Euler Equations ◽  
Initial Velocity ◽  
Viscosity Coefficient ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Filter Parameter ◽  
Fluid Equations ◽  
Grade Fluid

In this paper, we investigate an approximation of the Euler equation by the second-grade fluid equations in ℝdd=2,3. The convergence in Hm of a sequence of solutions to the second-grade fluid equations in a uniform interval is proven as both the viscosity coefficient ν and filter parameter α tend to zero with an initial velocity in Hm.

Magnetohydrodynamic Three-Dimensional Flowof a Second-Grade Fluid with Heat Transfer

2010 ◽  
Vol 65 (8-9) ◽  
pp. 683-691 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Nawaz
Keyword(s):  
Heat Transfer ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Second Grade ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Ion Slip ◽  
Grade Fluid ◽  
Layer Flow

An analysis has been carried out for the heat transfer on steady boundary layer flow of a secondgrade fluid bounded by a stretching sheet. The magnetohydrodynamic nature of the fluid is considered in the presence of Hall and ion-slip currents. The nonlinear mathematical problem is computed by a powerful tool, namely, the homotopy analysis method (HAM). A comparative study between the present and existing limiting results is carefully made. Convergence regarding the obtained solution is discussed. Skin friction coefficients and Nusselt number are analyzed. Effects of embedded parameters on the dimensionless velocities and temperature are examined

Soret-Dufour effects on MHD rotating flow of a viscoelastic fluid

2014 ◽  
Vol 24 (2) ◽  
pp. 498-520 ◽  
Author(s):  
T. Hayat ◽  
R. Naz ◽  
S. Asghar ◽  
A. Alsaedi
Keyword(s):  
Mass Transfer ◽  
Temperature Profile ◽  
Three Dimensional ◽  
Concentration Field ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Content Type ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Dufour Number

Purpose – The purpose of this paper is to study the heat and mass transfer with Soret-Dufour effects for the magnetohydrodynamic three-dimensional flow of second grade fluid in the rotating frame of reference. Design/methodology/approach – Series solution is obtained by homotopy analysis method. Findings – Increase in Soret number, Schmidt number and Dufour number, the heat transfer increases and mass transfer decreases. Effects of Prandtl and Eckert numbers are qualitatively similar as they assist the temperature profile and reduce the concentration of species. Increase in the length of the channel versus height increases the temperature profile but decreases the concentration field. Increase in the second grade fluid parameter causes reduction in both the temperature and concentration fields. The heat flux values at the lower plate are smaller than the values at the upper plate, whereas the situation is opposite in the case of mass transfer. Originality/value – These findings will be useful for the fluid flow in porous channel.

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