scholarly journals MHD and Thermal Radiation Effects of a Nanofluid over a Stretching Sheet using HAM

2019 ◽  
Vol 8 (4) ◽  
pp. 3489-3496
Keyword(s):  
Nusselt Number ◽  
Homotopy Analysis Method ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Analysis Method ◽  
Partial Differential ◽  
Shooting Technique ◽  
Linear Partial Differential Equations ◽  
Homotopy Analysis

In the present paper, we made an attempt to identify the governing conditions of heat and flow of a nanofluid over a flat plate using Homotopy analysis method (HAM). The arrangement of coupled nonlinear differential (CND) conditions is obtained from the partial differential conditions which will be determined by the homotopy analysis method (HAM). These methods will be useful to draw the conclusion based on the numerical and Graphical results of various parameters such as speed (velocity), concentration and temperature for different values of developing parameters shown in figures. Variations of skin-friction coefficient, Sherwood number and local Nusselt number have shown alongside. Finally conclusions have been drawn based on both diagrams and numerical results, it indicates that the non-linear partial differential equations are changed into a system of CN ODE’s and solved mathematically by using HAM method with shooting technique.

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 Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Victor Fabian Morales-Delgado ◽  
José Francisco Gómez-Aguilar ◽  
Huitzilin Yépez-Martínez ◽  
Dumitru Baleanu ◽  
Ricardo Fabricio Escobar-Jimenez ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Homotopy Analysis

Radiation and Mass Transfer Effects on the Magnetohydrodynamic Unsteady Flow Induced by a Stretching Sheet

2010 ◽  
Vol 65 (3) ◽  
pp. 231-239 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Qasim ◽  
Zaheer Abbas
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Unsteady Flow ◽  
Homotopy Analysis Method ◽  
Local Nusselt Number ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Transfer Effects ◽  
Homotopy Analysis ◽  
Transfer Flow

This investigation deals with the influence of radiation on magnetohydrodynamic (MHD) and mass transfer flow over a porous stretching sheet. Attention has been particularly focused to the unsteadiness. The arising problems of velocity, temperature, and concentration fields are solved by a powerful analytic approach, namely, the homotopy analysis method (HAM). Velocity, temperature, and concentration fields are sketched for various embedded parameters and interpreted. Computations of skin friction coefficients, local Nusselt number, and mass transfer are developed and examined.

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

2010 ◽  
Vol 65 (11) ◽  
pp. 935-949 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian ◽  
Abbas Saadatmandi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Analysis Method ◽  
Partial Differential ◽  
Integer Order ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

scholarly journals Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 691-700
Author(s):  
Dr. K.V.Tamil Selvi , Et. al.
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Temperature Fields ◽  
Analysis Method ◽  
Partial Differential ◽  
Convective Boundary ◽  
Homotopy Analysis

In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

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