scholarly journals The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Limei Cao ◽  
Xinhui Si ◽  
Liancun Zheng ◽  
Huihui Pang
Keyword(s):  
Lewis Number ◽  
Maxwell Fluid ◽  
Elastic Parameter ◽  
Group Method ◽  
Physical Parameters ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Runge Kutta Method ◽  
Stretching Plate

AbstractIn this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/ injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

An Initial Value Method for the Solution of MHD Boundary-Layer Equations

1970 ◽  
Vol 21 (1) ◽  
pp. 91-99 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Boundary Layer ◽  
Iteration Process ◽  
Physical Parameters ◽  
Point Boundary ◽  
Initial Value ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

SummaryAn initial value method is introduced in this paper for the solution of the two-point non-linear ordinary differential equations resulting from an analysis of the MHD boundary-layer flow originally treated by Greenspan and Carrier. By using this method, the iteration process is eliminated. The method is seen to be applicable to the solution of similar two-point boundary value problems where certain physical parameters appear either in the differential equation or in the boundary conditions and solutions for a range of the parameter are sought.

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.

Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes

1988 ◽  
Vol 110 (3) ◽  
pp. 655-661 ◽  
Author(s):  
M. V. Karwe ◽  
Y. Jaluria
Keyword(s):  
Numerical Study ◽  
Hot Extrusion ◽  
Physical Parameters ◽  
Manufacturing Processes ◽  
Heated Plate ◽  
Governing Equations ◽  
Moving Plate ◽  
Boundary Layer Equations ◽  
Temperature And Flow Fields ◽  
Finite Difference Techniques

The heat transfer arising due to the movement of a continuous heated plate in processes such as hot rolling and hot extrusion has been studied. Of particular interest were the resulting temperature distribution in the solid and the proper imposition of the boundary conditions at the location where the material emerges from a furnace or die. These considerations are important in the simulation and design of practical systems. A numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance. The boundary layer equations, as well as full governing equations including buoyancy effects, are solved employing finite difference techniques. The effect of various physical parameters, which determine the temperature and flow fields, is studied in detail. The significance of these results in actual manufacturing processes is discussed.

Heat transfer in nano fluid from a stretching (shrinking), porous and heated sheet of variable thickness

2021 ◽  
pp. 095440622199070
Author(s):  
Azhar Ali ◽  
Dil Nawaz Khan Marwat ◽  
Aftab Alam
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Variable Thickness ◽  
Lewis Number ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Nano Fluid ◽  
Special Cases ◽  
Classical Models ◽  
New Variables

Heat transfer in Nano fluid from a stretching (shrinking) and porous sheet of variable thickness is investigated in this paper. A set of unseen transformations is generated and the new variables are consequently used for the solution of partial differential equations under consideration. The classical models of heat transfer in Nano fluids from rigid/porous and stretching/shrinking sheets with Brownian motion and thermophoresis effects will be the special case of current study. The set of generalized similarity variables is introduced into the systems of boundary layer equations and boundary conditions and a system of coupled and non-linear ODE’s is formed. The final ODE’s are characterized by several dimensionless parameters and their effects are examined on field quantities. The governing parameters are: suction (injection), stretching (shrinking) parameters, Brownian motion number ( Nb), Thermophoresis number ( Nt) and Lewis number ( Le). The numerical observations are shown in different graphs and tables, whereas, effects of physical parameters are seen on the rate of heat transfer [Formula: see text] and mass transfer [Formula: see text], defined at the surface of the sheet. Moreover, the new results are presented in the respective sections. The remarkable aspects of the present simulations are scrutinized, however, special cases of current simulations give the previous problems, which are highlighted in the consequent sections.

scholarly journals MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions

2020 ◽  
Vol 9 (1) ◽  
pp. 457-469
Author(s):  
Bidyut Mandal ◽  
Krishnendu Bhattacharyya ◽  
Astick Banerjee ◽  
Ajeet Kumar Verma ◽  
Anil Kumar Gautam
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Soret Effect ◽  
Lewis Number ◽  
Continuous Group ◽  
Governing Equations ◽  
Soret Number ◽  
Stretching Plate

AbstractThis work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

scholarly journals Bioconvection of Micropolar Fluid in an Annulus

2020 ◽  
Vol 5 (2) ◽  
pp. 237-247
Author(s):  
D. Srinivasacharya ◽  
I. Sreenath
Keyword(s):  
Differential Equations ◽  
Outer Cylinder ◽  
Lewis Number ◽  
Coupled System ◽  
Linearization Method ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Successive Linearization Method ◽  
Fully Coupled

This paper deals with the bioconvection of microploar fluid in an annulus containing microorganisms in which the outer cylinder is rotating. A mathematical model, with a fully coupled system of partial differential equations presenting the velocity, total mass, momentum, thermal energy, mass diffusion, and motile microorganisms is presented. A suitable transformations is adopted to reduce the governing non-linear governing to a set of non-linear ordinary differential equations and then linearized by means of successive linearization method. The resulign linearized equaions are solved using Chebyshev collocation method. The illustrating analysis of influences of the various flow governing physical parameters such as the micropolar coupling number, the bioconvection Schmidt-number, Prandtl number, Lewis number and bioconvection Peclet-number and Reynolds number on motile microorganism distribution are studied and is presented. Also, the density number of motile microorganism is examined for various governing parameters along with slip parameter of motile microorganism.

Soret and Dufour Effects in the Flow of Williamson Fluid over an Unsteady Stretching Surface with Thermal Radiation

2015 ◽  
Vol 70 (4) ◽  
pp. 235-243 ◽  
Author(s):  
Tasawar Hayat ◽  
Yusra Saeed ◽  
Sadia Asad ◽  
Ahmed Alsaedi
Keyword(s):  
Thermal Radiation ◽  
Energy Equation ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Soret And Dufour Effects ◽  
Williamson Fluid ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Unsteady Stretching Surface ◽  
Biot Numbers

AbstractThis paper looks at the simultaneous effects of heat and mass transfer in the flow of Williamson fluid over an unsteady stretching surface. The effects of thermal radiation and viscous dissipation are considered in an energy equation. Besides, the energy and concentration equations are coupled with the combined effects of Soret and Dufour. The convective conditions for both temperature and mass concentration are employed. The transformation procedure reduces the time-dependent boundary layer equations of momentum, energy, and concentration to the non-linear ordinary differential equations. Through graphs and numerical values, the velocity, temperature, and concentration fields are discussed for different physical parameters. It is found that the thermal and concentration Biot numbers have an increasing impact on both temperature and concentration fields, respectively.

Effects of the magnetic field on a non-Newtonian conducting fluid past a stretching plate

1994 ◽  
Vol 72 (5-6) ◽  
pp. 290-292 ◽  
Author(s):  
K. A. Helmy
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Elastic Parameter ◽  
Conducting Fluid ◽  
Parameter Method ◽  
Similarity Parameter ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Stretching Plate ◽  
The Magnetic Field

The boundary-layer flow past a stretching plate in a viscoelastic conducting fluid in the presence of a magnetic field is considered. The solution for the boundary-layer equations is obtained using the similarity parameter method. An analytic solution for the temperature distribution of the plate undergoing cooling in this fluid and in the boundary layer is developed. The effect of the visco-elastic parameter k0 and the magnetic field on the flow velocity is investigated. The effect of the magnetic field on the convergence of the solution is also discussed.

scholarly journals Influence of Magnetic Field on Thermal Radiation and Particle Shapes of Copper-Water Nanofluid Considering Marangoni Boundary Layer

2020 ◽  
Vol 5 (5) ◽  
pp. 957-970
Author(s):  
KM Kanika ◽  
Santosh Chaudhary ◽  
Mohan Kumar Choudhary
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Physical Parameters ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Different Shapes ◽  
Layer Flow ◽  
Marangoni Boundary Layer ◽  
Particle Shapes

This problem aims to address hydrodynamic Marangoni boundary layer flow of incompressible nanofluid along different shapes of particle like sphere, tetrahedron, column and lamina with exponential temperature. Choosing appropriate transformations, the governing equations are reduced to non-linear ordinary differential equations and then solved by using a perturbation technique. Impacts in velocity and temperature profiles for the relevant considering parameters namely nanoparticle volume fraction, magnetic parameter, empirical shape factor and radiation parameter are evaluated and shown through graphs. Moreover, computational values for influences of physical parameters on local surface heat flux are presented in table.

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