Table of contents

Similarity solutions of the boundary-layer equations describing mixed convection flow along a vertical plate exist if the difference between the temperature of the plate and the temperature of the ambient fluid is inverse proportional to the distance from the leading edge of the plate. A new solution branch of similarity solutions will be presented and it will be discussed which similarity solution is of physical relevance by a numerical solution of the boundary layer equations. Employing a spatial stability analysis similarity solutions are identified which can be attained as asymptotic limit for large distances from the leading edge of the plate.

The viscous flows in a homogeneous porous medium of permeability k with two two-dimensional holes of an equal radius R₀(≫√k) are investigated experimentally. Center-to-center distance l and the orientation α of the holes with respect to the undisturbed flow are varied, and the flow field around these holes is observed. The volume flux into each hole increases by about 30% in the case of l ≈ 2.5R₀ and α ≈ 30° compared with the flux into a single circular hole, whereas it decreases by about 20% in the case of l ≈ 2.5R₀ and α ≈ 90°. These results suggest that the presence of holes has great influences on the estimation of groundwater flow in natural condition.

The hydrodynamic stability of small disturbances in a non-Newtonian fluid flowing through a circular pipe is studied analytically. Specifically, the time development of the disturbances and the transient disturbance amplification are studied. The non-Newtonian fluid is modelled by a two-constant Jeffrey model characterized by the relaxation time (λ) and a constant (K) representing the ratio of relaxation to retardation times. All the investigations are carried out for streamwise-independent disturbances since they are the most amplified ones in a Newtonian fluid and can be treated analytically. The eigenvalue problem and the initial value problem for the disturbances are studied. Compared to the Newtonian case, the results show that dependent on K and λ, a reduction or an increase of the disturbance transient growth may occur.

We consider the weakly nonlinear spatial evolution of a disturbance consisting of a plane wave and a pair of oblique waves inclined at an angle θ other than 60° superimposed on an inviscid mixing layer, with each wave being slightly amplified on a linear basis. A nonlinear critical layer analysis is employed to derive equations governing the evolution of the instability wave amplitudes, which contain a coupling between the oblique and plane waves as well as the usual interaction within the pair of oblique waves. These equations are discussed and it is shown that, as in related work for other flows, these equations may develop a singularity at a finite distance downstream.