Symmetry Analysis of Boundary Layer Equations of an Upper Convected Maxwell Fluid with Magnetohydrodynamic Flow

2011 ◽  
Vol 66 (5) ◽  
pp. 321-328
Author(s):  
Gözde Deǧer ◽  
Mehmet Pakdemirli ◽  
Yiǧit Aksoy
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Similarity Solutions ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Boundary Layer Equations

Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted.

scholarly journals Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

2019 ◽  
Vol 24 (1) ◽  
pp. 53-66
Author(s):  
O.J. Fenuga ◽  
S.J. Aroloye ◽  
A.O. Popoola
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Momentum Boundary Layer

Abstract This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

MHD Flow of Dusty Fluid Past a Stretching Sheet with Slip Effect Using Carreau Model

2018 ◽  
Vol 387 ◽  
pp. 135-144 ◽  
Author(s):  
Mahesha ◽  
S.M. Upadhya ◽  
G.K. Ramesh ◽  
Oluwole Daniel Makinde
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Heat Transport ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Slip Effect ◽  
Regular Boundary ◽  
Carreau Model ◽  
Dimensionless Velocity ◽  
The Impact

This examination manages the impact of magnetic field on the flow and heat transport of an incompressible Carreau liquid over an extending sheet with particle fluid suspension. The significant conditions are first improved under regular boundary layer suppositions, and afterward changed into conventional differential conditions by reasonable transformations. The changed conventional nonlinear differential conditions which are explained numerically by Matlab bvp4c package. The impacts of specific parameters on the dimensionless velocity and temperature are exhibited in graphical structures.

Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet

2015 ◽  
Vol 32 (2) ◽  
pp. 175-184 ◽  
Author(s):  
T. Javed ◽  
A. Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Maxwell Fluid ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Parameter Ratio ◽  
Two Dimensional Flow

AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

scholarly journals Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Tesfaye Kebede ◽  
Eshetu Haile ◽  
Gurju Awgichew ◽  
Tadesse Walelign
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Analytic Approximation

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

2009 ◽  
Vol 33 (5) ◽  
pp. 601-606 ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer ◽  
K. Vajravelu ◽  
J. R. Cannon ◽  
Robert A. Van Gorder
Keyword(s):  
Boundary Layer ◽  
Stretching Sheet ◽  
Similarity Solutions ◽  
Boundary Layer Equations ◽  
Nonlinearly Stretching Sheet

scholarly journals MHD Flow of Thermally Radiative Maxwell Fluid Past a Heated Stretching Sheet with Cattaneo–Christov Dual Diffusion

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
K. Loganathan ◽  
Nazek Alessa ◽  
Ngawang Namgyel ◽  
T. S. Karthik
Keyword(s):  
Stretching Sheet ◽  
Heated Surface ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Physical Parameters ◽  
Liquid Temperature ◽  
Transfer Rates ◽  
Magnetic Field Parameter ◽  
The Magnetic Field

This study explains the impression of MHD Maxwell fluid with the presence of thermal radiation on a heated surface. The heat and mass transmission analysis is carried out with the available of Cattaneo–Christov dual diffusion. The derived PDE equations are renovated into ODE equations with the use of similarity variables. HAM technique is implemented for finding the solution. The importance of physical parameters of fluid velocity, temperature, concentration, skin friction, and heat and mass transfer rates are illustrated in graphs. We found that the fluid velocity declines with the presence of the magnetic field parameter. On the contrary, the liquid temperature enhances by increasing the radiation parameter. In addition, the fluid velocity is low, and temperature and concentration are high in Maxwell fluid compared to the viscous liquid.

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