A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Linear Differential Equations ◽  
Analysis Method ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

AbstractThe similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].

scholarly journals The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

2021 ◽  
Author(s):  
Vijay Patel ◽  
Jigisha Pandya
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

scholarly journals The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
F. G. Awad ◽  
Z. G. Makukula ◽  
P. Sibanda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Analysis Method ◽  
Partial Differential ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method ◽  
Good Agreement

The spectral homotopy analysis method is extended to solutions of systems of nonlinear partial differential equations. The SHAM has previously been successfully used to find solutions of nonlinear ordinary differential equations. We solve the nonlinear system of partial differential equations that model the unsteady nonlinear convective flow caused by an impulsively stretching sheet. The numerical results generated using the spectral homotopy analysis method were compared with those found using the spectral quasilinearisation method (SQLM) and the two results were in good agreement.

scholarly journals On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1148
Author(s):  
Stanford Shateyi ◽  
Hillary Muzara
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Coupled System ◽  
Linear Differential Equations ◽  
Nanofluid Flow ◽  
Linear Differential

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Solution of the SEIR model of epidemics using HAM

2014 ◽  
Vol 11 (3) ◽  
pp. 297-310
Author(s):  
Nirmala Ratchagar ◽  
S. Subramanian
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Epidemic Model ◽  
Perturbation Methods ◽  
Analysis Method ◽  
Childhood Diseases ◽  
Seir Model ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Direct Scheme

In this paper, a new semi analytic technique namely the Homotopy Analysis Method (HAM) is applied for SEIR Epidemic model. HAM is different from already existing perturbation methods, and is most suitable for strongly non linear simultaneous differential equations arising in this model. The advantage of this method is that it provides a direct scheme for solving the problem, i.e. without the need for linearization, perturbation, massive computation and any transformation. MATHEMATICA 8.0 is used to carry out computations. Results were discussed graphically, for four childhood diseases.

scholarly journals 7th -Order Caudrey-Dodd-Gibbon Equation and Fisher-Type Equation by Homotopy Analysis Method

2020 ◽  
Vol 5 (2) ◽  
pp. 272-282
Author(s):  
Ankita Sharma ◽  
Rajan Arora
Keyword(s):  
Homotopy Analysis Method ◽  
Type Equation ◽  
Analysis Method ◽  
Nucleation Kinetics ◽  
Reliable Technique ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

In this paper, we first describe the methodology of the Homotopy Analysis Method (HAM) which is an analytical technique and then employ it to some of the non-linear problems which are used in different fields of sciences like plasma physics, fluid dynamics, laser optics, biology, chemical kinetics, nucleation kinetics, physiology, etc. Approximate series solutions have been obtained and the results are compared with the closed form solutions of the equations, which show that this technique gives high accurate results. HAM is a reliable technique, easy to use and is widely applicable to a large class of non-linear differential equations. MATHEMATICA software package has been used for computations.

scholarly journals Approximate Solution of Intuitionistic Fuzzy Differential Equations with the Linear Differential Operator by the Homotopy Analysis Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
S. Melliani ◽  
Z. Belhallaj ◽  
M. Elomari ◽  
L. S. Chadli
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Linear Differential Operator ◽  
Analysis Method ◽  
Intuitionistic Fuzzy ◽  
Homotopy Analysis ◽  
Linear Differential ◽  
Shed Light

In this work, the purpose is to discuss the homotopy analysis method (HAM) for the use of intuitionistic fuzzy differential equations with the linear differential operator. Furthermore, a numerical example is presented to shed light on the capability of the present method, and the numerical results illustrated by adopting the homotopy perturbation method (HPM) are compared with the exact solution to ensure the validity of our outcomes.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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