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.

An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Toward a Heated Plate

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Ahmer Mehmood ◽  
Asif Ali
Keyword(s):  
Stagnation Point ◽  
Analytic Solution ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Stagnation Point Flow ◽  
Second Grade ◽  
Heated Plate ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid

We present a purely analytic solution to the steady three-dimensional viscous stagnation point flow of second grade fluid over a heated flat plate moving with some constant speed. The analytic solution is obtained by a newly developed analytic technique, namely, homotopy analysis method. By giving a comparison with the existing results, it is shown that the obtained analytic solutions are highly accurate and are in good agreement with the results already present in literature. Also, the present analytic solution is uniformly valid for all values of the dimensionless second grade parameter α. The effects of α and the Prandtl number Pr on velocity and temperature profiles are discussed through graphs.

scholarly journals A Novel Design of Three-Dimensional MHD Flow of Second-Grade Fluid past a Porous Plate

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Muhammad Shoaib ◽  
Rizwan Akhtar ◽  
Muhammad Abdul Rehman Khan ◽  
Muhammad Afzal Rana ◽  
Abdul Majeed Siddiqui ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Mhd Flow ◽  
Normal Direction ◽  
Second Grade ◽  
Infinite Length ◽  
Second Grade Fluid ◽  
Suction Velocity ◽  
Grade Fluid ◽  
Variable Suction

In this study, a novel theoretical model for three-dimensional (3D) laminar magnetohydrodynamic (MHD) flow of a non-Newtonian second-grade fluid along a plate of semi-infinite length is developed based on slightly sinusoidal transverse suction velocity. The suction velocity involves a steady distribution with a low superimposed perpendicularly varying dispersion. The strength of the uniform magnetic field is incorporated in the normal direction to the wall. The variable suction transforms the fluidic problem into a 3D flow problem because of variable suction velocity in the normal direction to the plane wall. The proposed mathematical modeling and its dynamical analysis are prescribed for the boundary layer flow keeping the magnetic effects without taking into consideration the induced magnetic field. An analytical perturbation technique is employed for the series solutions of the system of ordinary differential equations of velocity profile and pressure. Graphical illustrations are used to analyze the behavior of different proficient parameters of interest. The magnetic parameter is responsible for accelerating the main flow velocity, while controlling the cross flow velocities.

scholarly journals MHD Three-Dimensional Free Convective Flow with Periodic Permeability and Heat Transfer of a Second-Grade Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Atifa Latif ◽  
Muhammad Afzal Rana ◽  
Babar Ahmad ◽  
Muhammad Hussan
Keyword(s):  
Magnetic Field ◽  
Skin Friction ◽  
Flow Direction ◽  
Porous Plate ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Second Grade ◽  
Physical Parameters ◽  
Second Grade Fluid ◽  
Grade Fluid

The present study delivers the mathematical model and theoretical analysis of a three-dimensional flow in a free convection for an electrically conducting incompressible second-grade fluid through a very high porous medium circumscribed by an infinite vertical porous plate subject to a constant suction. A uniform magnetic field along the normal to the surface of plate is applied. Periodic permeability for the medium is assumed, while velocity of free stream is taken to be uniform. Analytic expressions are presented for velocity and temperature fields, pressure, and skin friction components by perturbation technique. The impacts on these physical quantities by the physical parameters existing in the model are discussed and envisioned graphically. It is interesting to note that elastic and permeability parameters are able to control the skin friction along the main flow direction, magnetic field to reduce the pressure, and Reynolds number to control the thermal boundary layer thickness. It is also noted that temperature distribution does not depend upon permeability parameter.

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.

A series solution of the boundary value problem arising in the application of fluid mechanics

2018 ◽  
Vol 28 (10) ◽  
pp. 2480-2490 ◽  
Author(s):  
Yasir Khan
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Transverse Direction ◽  
Hydrodynamic Flow ◽  
Porous Channel ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Content Type ◽  
Grade Fluid

Purpose This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM). Design/methodology/approach The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs. Findings It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number. Originality/value To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

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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