scholarly journals Analytical Solution of Unsteady Boundary Layer Flow of a Nanofluid Past a Stretching Inclined Sheet With Effects of Magnetic Field

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdulhakeem Yusuf ◽  
Gbolahan Bolarin ◽  
Samson T Adekunle
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Numerical Method ◽  
Magnetic Parameter ◽  
Mathematical Formulation ◽  
Adomian Decomposition Method ◽  
Convective Heating ◽  
Adomian Decomposition ◽  
Inclined Sheet

 Flow of a nanofluid in a boundary layer in an inclined moving sheet at angle  is considered analytically. The Mathematical formulation consists of the Magnetic parameter, thermophoresis, and Brownian motion. Previously published work considered convective boundary condition. The present study considered an inclined stretching sheet at angle in one dimension and considered thermal conditions of non convective heating and heat flux. Solutions to  momentum,  temperature and concentration distribution depends on seven parameters, Magnetic parameter M, Lewis number Le, Prandtl number Pr, thermophoresis parameter Nt, the Brownian motion parameter Nb, unsteady parameter c and Grashof numbers Gr and Gc. The non linear coupled Differential equations were solved using the improved Adomian decomposition method and a good agreement was established with the numerical method (Shooting technique). Analytical result is also presented graphically to illustrate the effect of the earlier listed parameters on Momentum, temperature and nanofraction boundary layers. Momentum boundary layer increases with increase in Grashof numbers, angle of inclination and unsteady parameter..Keywords— Adomian Decompostion Method (ADM), Nanofluid, Inclined sheet, magnetic field effects, Numerical Method (NM). 

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

ADOMIAN DECOMPOSITION METHOD FOR MAGNETOHYDRODYNAMIC FLOW OF BLOOD INDUCED BY PERISTALTIC WAVES

2017 ◽  
Vol 17 (01) ◽  
pp. 1750007 ◽  
Author(s):  
G. C. SHIT ◽  
N. K. RANJIT ◽  
A. SINHA
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Decomposition Method ◽  
Flow Characteristics ◽  
Adomian Decomposition Method ◽  
Velocity Slip ◽  
Wave Number ◽  
Axial Velocity Component ◽  
Adomian Decomposition ◽  
Small Change

The present investigation deals with the application of Adomian decomposition method (ADM) to blood flow through an asymmetric non-uniform channel induced by peristaltic wave in the presence of magnetic field and the velocity slip at the wall. The ADM is applied with an aim to avoid any simplifications and restrictions, which changes non-linearity of the problem as well as to provide analytical solution. The blood flowing through the vessel is assumed to be Newtonian and incompressible with constant viscosity. The analytical expressions for the axial velocity component, streamlines and wall shear stress are presented. The numerical results of these physical quantities are obtained for different values of the Reynolds number, wave number and Hartmann number. The results obtained for different values of the parameters involved in the problem under consideration show that the flow is appreciably influenced by the presence of slip velocity as well as magnetic field. From this study, we conclude that the assumption of long wavelength and low Reynolds number overestimates the flow characteristics even for a small change in the parameters.

scholarly journals Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Krishnendu Bhattacharyya ◽  
G. C. Layek
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Lewis Number ◽  
Nanoparticle Volume Fraction ◽  
Layer Flow ◽  
Wall Mass

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

Solution methodology of convection boundary layer problems using Adomian decomposition method

2012 ◽  
Vol 227 (7) ◽  
pp. 1554-1565
Author(s):  
MJ Javanmardi ◽  
K Jafarpur ◽  
M Mahzoon
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Convection Boundary Layer ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Convection Boundary ◽  
Boundary Layer Problems

Adomian decomposition method has been applied to some convection boundary layer problems. It is shown that the method is excellent in solving nonlinear partial differential equations. Comparison of the results so obtained and those from conventional methods proves the technique to be powerful and to give nearly exact solutions. Since most physical problems are governed by nonlinear ordinary or partial differential equations, application of this method may be advised to simplify the method of solution.

scholarly journals Approximate analytical solution of the MHD Powell-Eyring fluid flow near accelerated plate

2017 ◽  
Vol 13 (4-1) ◽  
pp. 416-420 ◽  
Author(s):  
Fawzia Mansour Elniel ◽  
Zainal Abdul Aziz ◽  
Faisal Salah ◽  
Shaymaa Mustafa
Keyword(s):  
Magnetic Field ◽  
Sensitivity Analysis ◽  
Shear Stress ◽  
Fluid Flow ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Material Parameters ◽  
Non Linear Equation ◽  
Adomian Decomposition

 In this article, the non-linear equation of unsteady flow of Powell-Eyring fluid is solved by using Adomian Decomposition Method (ADM). The fluid is assumed to be flowing under the effect of magnetic field. The model is developed for the case of constant accelerated plate. Sensitivity analysis is performed to show the effects of material parameters on the velocity profile and shear stress at the wall. The results confirmed the suitability of ADM in solving nonlinear equations. 

Entropy analysis of Poiseuille nanofluid flow in a porous channel with slip and convective boundary conditions under magnetic field

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
S. Das ◽  
S. Chakraborty ◽  
R. N. Jana
Keyword(s):  
Magnetic Field ◽  
Entropy Generation ◽  
Poiseuille Flow ◽  
Magnetic Parameter ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Convective Heating ◽  
Bejan Number ◽  
Content Type ◽  
Hydrodynamic Slip

Purpose This study aims to expose the flow phenomena and entropy generation during a; magnetohydrodynamic (MHD) Poiseuille flow of water-based nanofluids (NFs) in a porous channel subject to hydrodynamic slip and convective heating boundary conditions. The flow caused by the uniform pressure; gradient between infinite parallel plates is considered steady and fully developed. The nanoparticles; namely, copper, alumina and titanium oxide are taken with pure water as the base fluid. Viscous dissipation and Joule heating impacts are also incorporated in this investigation. Design/methodology/approach The reduced governing equations are solved analytically in closed form. The physical insights of noteworthy parameters on the important flow quantities are demonstrated through graphs and analyzed elaborately. The thermodynamic analysis is performed by calculating entropy generation; rate and Bejan number. A graphical comparison between solutions corresponding to NFs and regular fluid in the channel is also provided. Findings The analysis of the results divulges that entropy generation minimization can be achieved by an appropriate combination of the geometrical and physical parameters of thermomechanical systems. It is reported that ascent in magnetic parameter number declines the velocity profiles, while the inverse pattern is witnessed with augmentation in hydrodynamic slip parameters. The temperature dissemination declines with the growth of Biot numbers. It is perceived that the entropy generation rate lessens with an upgrade in magnetic parameter, whereas the reverse trend of Bejan number is perceived with expansion in magnetic parameter and Biot number. The important contribution of the result is that the entropy generation rate is controlled with an appropriate composition of thermo-physical parameter values. Moreover, in the presence of a magnetic field and suction/injection at the channel walls, the shear stresses at the channel walls are reduced about two times. Practical implications In various industrial applications, minimizing entropy generation plays a significant role. Miniaturization of entropy is the utilization of the energy of thermal devices such as micro heat exchangers, micromixers, micropumps and cooling microelectromechanical devices. Originality/value An attentive review of the literature discloses that quite a few studies have been conducted on entropy generation analysis of a fully developed MHD Poiseuille flow of NFs through a permeable channel subject to the velocity slip and convective heating conditions at the walls.

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