Let us first give a heuristic estimates of boundary layer in steady flows. Consider a particle near the wall to be influenced by viscosity. After traveling a distance x from the edge, it has been under viscous influence for a time of t = x/U . Let U be large. For finite x, t is small so that vorticity is spread sideways to the width (νt) ∼ (νx/U). Let us define this width to be the boundary lay...

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations

Dissipation approximations have been used to calculate the drag on bubbles and drops and the decay rate of free gravity waves on water. In these approximations, viscous effects are calculated by evaluating the viscous stresses on irrotational flows. The pressure is not involved in the dissipation integral, but it enters into the power of traction integral, which equals the dissipation. A viscou...

This paper presents a robust and automated approach to generate unstructured hybrid grids comprised of tetrahedra, prisms, and pyramids for high Reynolds number flow computations. The hybrid mesh generation starts with isotropic tetrahedral grids to enhance the robustness. The tetrahedra near no-slip walls are shifted inward and the resulting gap between the tetrahedra and the walls is filled u...

The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

The classical fluid dynamics boundary condition of no slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However, experiments and molecular dynamics simulations indicate that this is not the case. In this paper we show how flow over a solid substrate with variations of wettability can be described in a continuum framework using the inter...

The present review presents basic concepts of blood rheology related to vascular diseases. Blood flow in large arteries is dominated by inertial forces exhibited at high flow velocities, while viscous forces (i.e., blood rheology) play an almost negligible role. When high flow velocity is compromised by sudden deceleration as at a bifurcation, endothelial cell dysfunction can occur along the ou...

Flow within thick liquid films present owing to capillary effects in the pore space is of key importance in many multiphase flow applications in porous media, for example, drying or oil recovery processes. The viscous resistance to the flow is a key parameter for modelling fluid transport in such situations. It is well known for liquid films wetting the corners of tubes of polygonal cross-secti...

We present an overview of the most common numerical solution strategies for the incompressible Navier–Stokes equations, including fully implicit formulations, artificial compressibility methods, penalty formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular operator splitting methods as special cases of a fully ...

The paper presents analysis of two-dimensional non-Newtonian incompressible viscous flow between parallel plates. The governing problem of momentum equations are reduced to NODE using similarity transformations. The resulting equation is solved using series solution and homotopy analysis method. These methods have advantages over pure numerical methods for obtaining the derived quantities accur...