Some exact solutions of two-dimensional Navier–Stokes equations by generalizing the local vorticity

Tanvir Akbar,Qazi Muhammad Zaigham Zia

doi:10.1177/1687814019831893

Tanvir Akbar, Qazi Muhammad Zaigham Zia

Open Access

https://doi.org/10.1177/1687814019831893

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Abstract

This article is proposed to discuss the solutions of two-dimensional equations of motion for viscous fluid. Different situations for the solution have been investigated while employing inverse solution methods. On assuming the stream functions in a certain form without prescribing boundary conditions, the expressions for streamlines and velocity components are explicitly presented. Moreover, a series of graphical results for streamlines and velocity components are plotted.

Highlights

Navier–Stokes equations describing the physical interests of scientific and engineering research are considered to be worthwhile
Different physical models have been exploited in literature to deal with assorted physical situations.[1,2,3,4,5,6,7,8,9,10]. These equations are a challenging system of nonlinear equations in the presence of viscous flows
No general analytical method exists for attacking this system for an arbitrary viscous flow problem

Summary

Introduction

Navier–Stokes equations describing the physical interests of scientific and engineering research are considered to be worthwhile. They all obtained exact solutions of some interesting problems by assuming vorticity to be related to stream function c with the relation r2c = K(c À Uy), where K We investigate the exact solutions while generalizing the local vorticity to satisfy the following expression r2c = K(c + ax + by), where a( 61⁄4 0) and b are real constants.

Results

Conclusion