The Effect of Magnetic Field on Compressible Boundary Layer by Homotopy Analysis Method

2021 ◽  
Vol 88 (1-2) ◽  
pp. 125
Author(s):  
R. Madhusudhan ◽  
Achala L. Nargund ◽  
S. B. Sathyanarayana
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Adverse Pressure Gradient ◽  
Analysis Method ◽  
Boundary Layer Region ◽  
Homotopy Analysis ◽  
Curve Singularities ◽  
Large Injection ◽  
Layer Region

We analyse the effect of applied magnetic field on the flow of compressible fluid with an adverse pressure gradient. The governing partial differential equations are solved analytically by Homotopy analysis method (HAM) and numerically by finite difference method. A detailed analysis is carried out for different values of the magnetic parameter, where suction/ injection is imposed at the wall. It is also observed that flow separation is seen in boundary layer region for large injection. HAM is a series solution which consists of a convergence parameter h which is estimated numerically by plotting <em>h</em> curve. Singularities of the solution are identified by Pade approximation.

scholarly journals Falkner-Skan Flow of a Maxwell Fluid with Heat Transfer and Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Qasim ◽  
S. Noreen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Prandtl Number ◽  
Comparative Study ◽  
Homotopy Analysis Method ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Analysis Method ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi…eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted.

A Mathematical Study on Non-Linear MHD Boundary Layer Past a Porous Shrinking Sheet with Suction

2019 ◽  
Vol 2 (2) ◽  
pp. 32-48
Author(s):  
V. Ananthaswamy ◽  
K. Renganathan
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Dimensionless Temperature ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Approximate Analytical Expression ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Homotopy Analysis ◽  
Good Agreement

In this paper we discuss with magneto hydrodynamic viscous flow due to a shrinking sheet in the presence of suction. We also discuss two dimensional and axisymmetric shrinking for various cases. Using similarity transformation the governing boundary layer equations are converted into its dimensionless form. The transformed simultaneous ordinary differential equations are solved analytically by using Homotopy analysis method. The approximate analytical expression of the dimensionless velocity, dimensionless temperature and dimensionless concentration are derived using the Homotopy analysis method through the guessing solutions. Our analytical results are compared with the previous work and a good agreement is observed.

scholarly journals Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

2019 ◽  
pp. 1-7
Author(s):  
S. Alao ◽  
R. A. Oderinu ◽  
F. O. Akinpelu ◽  
E. I. Akinola
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Analysis Method ◽  
Viscous Boundary Layer ◽  
New Approach ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Adomian Polynomial

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

Analytical simulation of nanoparticle-embedded blood flow control with magnetic field influence through spectra homotopy analysis method

2021 ◽  
pp. 2150226
Author(s):  
Ebenezer Olubunmi Ige ◽  
Funmilayo Helen Oyelami ◽  
Emmanuel Segun Adedipe ◽  
Iskander Tlili ◽  
M. Ijaz Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Stagnation Point ◽  
Homotopy Analysis Method ◽  
Mathematical Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact ◽  
Field Influence

Nanoparticles-based infusion strategies are presently being employed for a range of clinical interventions either for in vivo or in vitro applications while imposition of magnetic field is also identified as an important technique for fluid manipulation during nanoparticles-based propulsion. The impact of magnetic field to control of the transport of nanoparticles-based blood flow is demonstrated numerically over an elaborate variant of transport mechanisms. Mathematical formulations were undertaken and stability analysis of the mathematical problem was a scrutinized by generation of eigen values using the Lyapunov scheme. The numerical solution based on Chebysehev pseudo-spectra and spectra homotopy analysis method (SHAM) was implemented to handle the combination on nonlinear ordinary differential equations derived from the transport models. We observed that far-field of the stagnation point, nanoparticles specie dispersion increased with higher thermal diffusivity, while the decrease in concentration profile around the vicinity of stagnation point depicts clustering of nanoparticles-embedded blood flow. The observations revealed that higher magnitude of thermophoretic parameters constitute significantly to increase in momentum as well as energy fields during transport of nanoparticles-containing blood flow under magnetic field influence. These findings showed the potentials of magnetic-field for control of suspended particles in transport medium which could be harnessed to manipulate transport of nanoparticles-containing fluids in microfluidic platforms with intricate configurations.

scholarly journals Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. Rashidi ◽  
E. Momoniat ◽  
B. Rostami
Keyword(s):  
Boundary Layer ◽  
Viscoelastic Fluid ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Homotopy Analysis ◽  
Energy Equations

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region inℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated.

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