A new efficient technique for solving fractional coupled Navier–Stokes equations using q-homotopy analysis transform method

Pramana ◽  
2019 ◽  
Vol 93 (1) ◽  
Author(s):  
Amit Prakash ◽  
P Veeresha ◽  
D G Prakasha ◽  
Manish Goyal
Keyword(s):  
Stokes Equations ◽  
Efficient Technique ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Homotopy Analysis

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

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.

scholarly journals A reliable algorithm for time-fractional Navier-Stokes equations via Laplace transform

2019 ◽  
Vol 8 (1) ◽  
pp. 695-701 ◽  
Author(s):  
Amit Prakash ◽  
Doddabhadrappla Gowda Prakasha ◽  
Pundikala Veeresha
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Fractional Derivative ◽  
Series Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow ◽  
Analysis Scheme ◽  
Homotopy Analysis

Abstract In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme. Fractional derivative is considered in Caputo sense. The proposed technique is a blend of q-homotopy analysis scheme and transform of Laplace. It executes well in efficiency and provides h-curves that show convergence range of series solution.

scholarly journals Three-Dimensional Hydro-Magnetic Flow Arising in a Long Porous Slider and a Circular Porous Slider with Velocity Slip

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 748 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Amna Anjum ◽  
Muhammad Kahshan
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Frictional Resistance ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Convergent Series ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Homotopy Analysis ◽  
Lift And Drag

The current research explores the injection of a viscous fluid through a moving flat plate with a transverse uniform magneto-hydrodynamic (MHD) flow field to reduce sliding drag. Two cases of velocity slip between the slider and the ground are studied: a long slider and a circular slider. Solving the porous slider problem is applicable to fluid-cushioned porous sliders, which are useful in reducing the frictional resistance of moving bodies. By using a similarity transformation, three dimensional Navier–Stokes equations are converted into coupled nonlinear ordinary differential equations. The resulting nonlinear boundary value problem was solved analytically using the homotopy analysis method (HAM). The HAM provided a fast convergent series solution, showing that this method is efficient, accurate, and has many advantages over the other existing methods. Solutions were obtained for the different values of Reynolds numbers (R), velocity slip, and magnetic fields. It was found that surface slip and Reynolds number had substantial influence on the lift and drag of the long and the circular sliders. Moreover, the effects of the applied magnetic field on the velocity components, load-carrying capacity, and friction force are discussed in detail with the aid of graphs and tables.

NEW ANALYTICAL SOLUTION OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 23 (26) ◽  
pp. 3147-3155 ◽  
Author(s):  
MOHAMMAD MEHDI RASHIDI ◽  
GANJI DOMAIRRY
Keyword(s):  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Differential Transform ◽  
Conditions At Infinity

The purpose of this study is to implement a new analytical method (the DTM-Padé technique, which is a combination of the differential transform method (DTM) and the Padé approximation) for solving Navier–Stokes equations. In this letter, we will consider the DTM, the homotopy perturbation method (HPM) and the Padé approximant for finding analytical solutions of the three-dimensional viscous flow near an infinite rotating disk. The solutions are compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that the application of the Padé approximants in the DTM and HPM is an appropriate method in solving the Navier–Stokes equations with the boundary conditions at infinity. On the other hand, the convergence of the obtained series from DTM-Padé is greater than HPM-Padé.

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.

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