Analytical Approach to Fractional Navier–Stokes Equations by Iterative Laplace Transform Method

2019 ◽  
pp. 179-188
Author(s):  
Rajendra K. Bairwa ◽  
Jagdev Singh
Keyword(s):  
Laplace Transform ◽  
Analytical Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Navier Stokes Equations

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

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.

Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability

2010 ◽  
Vol 65 (12) ◽  
pp. 1033-1038 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yıldırım ◽  
Sefa Anıl Sezer
Keyword(s):  
Series Solution ◽  
Analytical Approach ◽  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Rectangular Channel ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Remarkable Improvement ◽  
Homotopy Perturbation ◽  
Expanding Or Contracting Walls

In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.

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.

scholarly journals A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Abdul-Sattar J. Al-Saif ◽  
Assma J. Harfash
Keyword(s):  
Analytical Solutions ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Good Convergence ◽  
Flow Problems ◽  
Approximate Analytical Solutions

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

scholarly journals MHD Flow of an Incompressible Viscous Fluid through Convergent or Divergent Channels in Presence of a High Magnetic Field

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Reza Hosseini ◽  
Sadegh Poozesh ◽  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Homogeneous Magnetic Field ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Electrically Conducting ◽  
Non Linear

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM). The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme). The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.

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