In this study, the steady incompressible flow of a non-Newtonian sodium alginate (SA) fluid conveying copper nanoparticles (Cu) which flow within two vertical parallel plates is investigated by using the homotopy perturbation analytical scheme to solve the coupled nonlinear ordinary equations arising from the mechanics of the fluid. The developed analytical solutions are used to investigate the...

The various industrial and engineering applications of flow of fluid between parallel plates have continued to generate renewed interests. In this work, a comparative study of approximate analytical methods is carried out using differential transformation,homotopy perturbation, Adomian decomposition, variation of parameter and variational iteration methods for the analysis of a steady two-dimen...

An analytically exact solution for the problem of low Mach number (i.e. incompressible) incident vorticity scattering at a hard to pressure release (Z = 0) wall transition is obtained using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition, which results in a pressure-velocity field which is qualitatively different for low...

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

This paper presents an analytical approach for representing the flow through the glottis. Based on the polygonal line approximation of the coronal section of the glottis, the velocity field of incompressible, inviscid flow can be conveniently represented using the method of conformal mapping. In this method, the actual physical domain is conformally connected to the canonical domain configured ...

The Euler equations for inviscid incompressible fluid flow have a Hamiltonian structure in Eulerian coordinates, the Hamiltonian operator, though, depending on the vorticity. Conservation laws arise from two sources. One parameter symmetry groups, which are completely classified, yield the invariance of energy and linear and angular momenta. Degeneracies of the Hamiltonian operator lead in thre...

We consider uniformly rotating incompressible Euler and NavierStokes equations. We study the suppression of vertical gradients of Lagrangian displacement (”vertical” refers to the direction of the rotation axis). We employ a formalism that relates the total vorticity to the gradient of the back-to-labels map (the inverse Lagrangian map, for inviscid flows, a diffusive analogue for viscous flows...

We study the inviscid multilayer Saint-Venant (or shallow-water) system in the limit of small density contrast. We show that, under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation, the system is well-posed on a large time interval, despite the singular limit. By studying the asymptotic limit, we provide a rigorous justification of th...

Many works have considered two-dimensional free-surface flow over the edge of a plate, forming waterfall, and with uniform horizontal far upstream. The is assumed to be steady irrotational, whilst fluid inviscid incompressible. Gravity also taken into account. In particular, amongst these works, numerical solutions for supercritical flows been computed, utilising conformal mappings as well seri...

An approximate solution is developed for two-dimensional, steady, inviscid supersonic flow over an airfoil. This approximation produces accurate results for a wide range of Mach numbers and airfoil thicknesses. It is used as the starting point for a rapidly convergent iterative numerical solution of the exact equations. A co-ordinate system consisting of the principal characteristics and stream...