scholarly journals Homotopy Transforms Analysis Method for Solving Fractional Navier- Stokes Equations with Applications

2020 ◽  
pp. 2048-2054
Author(s):  
Eman Mohmmed Nemah
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Convergent Power Series ◽  
Navier Stokes Equations ◽  
Caputo’S Derivative ◽  
Homotopy Analysis

The presented work includes the Homotopy Transforms of Analysis Method (HTAM). By this method, the approximate solution of nonlinear Navier- Stokes equations of fractional order derivative was obtained.  The Caputo's derivative was used in the proposed method. The desired solution was calculated by using the convergent power series to the components. The obtained results are demonstrated by comparison with the results of Adomain decomposition method, Homotopy Analysis method and exact solution, as explained in examples (4.1) and (4.2). The comparison shows that the used method is powerful and efficient.

Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets

2010 ◽  
Vol 65 (11) ◽  
pp. 961-968 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Nawaz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Tabular Form ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Homotopy Analysis

This investigation describes the effects of heat transfer on magnetohydrodynamic (MHD) axisymmetric flow of a viscous fluid between two radially stretching sheets. Navier-Stokes equations are transformed into the ordinary differential equations by utilizing similarity variables. Solution computations are presented by using the homotopy analysis method. The convergence of obtained solutions is checked. Skin friction coefficient and Nusselt number are given in tabular form. The dimensionless velocities and temperature are also analyzed for the pertinent parameters entering into the problem.

Analytical solution of a two-dimensional stagnation flow in the vicinity of a shrinking sheet by means of the homotopy analysis method

2009 ◽  
Vol 223 (3) ◽  
pp. 133-143 ◽  
Author(s):  
A Kimiaeifar ◽  
G H Bagheri ◽  
M Rahimpour ◽  
M A Mehrabian
Keyword(s):  
Homotopy Analysis Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Stagnation Flow ◽  
Navier Stokes Equations ◽  
Linear Ordinary Differential Equations ◽  
Homotopy Analysis ◽  
Good Agreement

In this article, stagnation flow in the vicinity of a shrinking sheet is studied. A similarity transformation is employed to reduce the Navier—Stokes equations to a set of non-linear ordinary differential equations. These equations are then solved analytically by means of the homotopy analysis method (HAM). The results obtained were shown to compare well with the numerical results available in the literature for the same problem. Close agreement between the two sets of results indicates the accuracy of the HAM. The method can predict the flow field in all vertical distances from the sheet, and is also able to control the convergence of the solution. The numerical solution of the similarity equations is also developed and the results are in good agreement with the analytical results based on the HAM.

Prediction of inverted velocity profile for gas flow in nanochannel

2014 ◽  
Vol 28 (29) ◽  
pp. 1450227
Author(s):  
T. T. Zhang ◽  
Y. R. Ren
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Slip Boundary Conditions ◽  
Interesting Phenomenon ◽  
Navier Stokes Equations ◽  
Velocity Inversion ◽  
Slip Boundary ◽  
Homotopy Analysis

Velocity inversion is an interesting phenomenon of nanoscale which means that the velocity near the wall is greater than that of center. To solve this problem, fluid flow in nanochannel attracts more attention in recent years. The physical model of gas flow in two-dimensional nanochannel was established here. To describe the process with conventional control equations, Navier–Stokes equations combined with high-order accurate slip boundary conditions was used as mathematical model. With the introduction of new dimensionless variables, the problem was reduced to an ordinary differential equation. Then it was analytically solved and investigated using homotopy analysis method (HAM). The results were verified by comparing with other available experiment data. Result shows that the proposed method could predict velocity phenomenon.

scholarly journals Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Mohammad Mehdi Rashidi ◽  
Hamed Shahmohamadi ◽  
Saeed Dinarvand
Keyword(s):  
Fourth Order ◽  
Order Differential Equation ◽  
Stokes Equations ◽  
Approximate Solutions ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Homotopy Analysis

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

scholarly journals Homotopy analysis method for the solution of lubrication of a long porous slider

2016 ◽  
Vol 1 (2) ◽  
pp. 507-516 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Manjunath Jyoti
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Convergent Series ◽  
Navier Stokes ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Similarity Transformations ◽  
Convergence Of Series ◽  
Homotopy Analysis ◽  
Good Agreement

AbstractIn this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

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