Plane Couette-Poiseuille Flow Research Articles

A special form of Galerkin's method applied to heat transfer in plane Couette-Poiseuille flows

The heat-transfer problem for plane Couette-Poiseuille flows is solved by a Galerkin's procedure for which the system of representing functions has a close relation to the governing equation. A coordinate transformation brings the principal part of the partial differential equation into a standard form, for which the eigenfunctions can be determined once and for all. The resulting system of ordinary differential equations has strong diagonal dominance and is integrated by a predictor corrector method for stiff equations. The accuracy of the method is examined by a comparison of the eigen-functions of Galerkin's operator with those of the exact problem. The dimensionless temperature field has been computed for various pressure gradients.

The spectrum of small perturbations in plane couette-poiseuille flow

The spectrum of small perturbations of plane Couette-Poiseuille flow is studied. The perturbations are classified according to their behavior at large wave numbers. The changes in the spectrum are traced as the transition is made from Poiseuille to Couette flow at fixed Reynolds number. The behavior of the perturbations is considered as a function of the Reynolds number.

Stability of plane Couette-Poiseuille flow in the presence of a magnetic field

Within the framework of the linear theory, a study was made of the hydrodynamic stability of the Couette-Poiseuille flow of a viscous conducting fluid in a transverse magnetic field. The total spectrum of small perturbations was studied for characteristic Hartmann numbers. A classification of perturbations was made in accordance with the behavior of their phase velocity with large wave numbers. Dependences of the critical Reynolds number and of the critical wave number on a parameter characterizing the relationship between the parts of the flow, determined by the motion of plates and by the pressure gradient, were obtained. The character of the asymptotic dependences at large Hartmann numbers was clarified. The article gives an example of a neutral curve formed by two branches of the neutral fluctuations.

Stability of Plane Couette-Poiseuille Flow with Uniform Crossflow

The stability of plane Couette-Poiseuille flow between porous walls is considered. Injection of fluid through one wall and suction through the opposite wall leads to a nonparallel flow that satisfied the Navier-Stokes equations. Neutral stability diagrams are presented for Poiseuille flow and for Couette-Poiseuille flow. In both cases crossflow produces a significant increase in the critical Reynolds number.

Stability of Plane Couette-Poiseuille Flow

The stability of plane Couette-Poiseuille flow has been computed by a new numerical method. Results show that the unstable mode associated with Poiseuille flow is always stable for Couette flow.

Instability due to viscosity stratification

The principal aim of this paper is to show that the variation of viscosity in a fluid can cause instability. Plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosities between two horizontal plates is considered, and it is found that both plane Poiseuille flow and plane Couette flow can be unstable, however small the Reynolds number is. The unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability, and are brought out by the viscosity stratification.

Stability of plane Couette–Poiseuille flow

The stability of a two-dimensional Couette-Poiseuille flow is investigated. The primary unidirectional flow is between two infinite parallel plates, one of which moves relative to the other. The results for the case of Poiseuille flow agree with Lin's results and all flows for which the plate velocity exceeds 70% of the maximum velocity of the Poiseuille component of flow are found to be stable for all finite Reynolds numbers. Results of intermediate cases are also obtained.