Secondary flow in a Hele-Shaw cell

1968 ◽  
Vol 31 (2) ◽  
pp. 379-395 ◽  
Author(s):  
B. W. Thompson
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Secondary Flow ◽  
Separation Distance ◽  
Large Separation ◽  
Outer Expansion ◽  
Hele Shaw Cell

Riegels (1938) investigated the breakdown of Hele-Shaw flow in a Hele-Shaw cell with unusually large separation distance 2h* between the walls. A theoretical outer expansion for the velocity was constructed in the case where the obstacle is a circular cylinder, using an intuitive inner boundary condition that seems to be correct in the limit h* → 0, but without explicit matching with the inner expansion.An inner expansion has now been found, and it shows that the solution in the inner layer forces terms into the outer expansion that are larger than those found by Riegels whenever h* is finite and not zero.

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

1953 ◽  
Vol 49 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Boundary Condition ◽  
Thermal Properties ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
The Moon ◽  
Non Linear

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

An approximate method in high-frequency scattering

1962 ◽  
Vol 58 (4) ◽  
pp. 662-670
Author(s):  
A. Sharples
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Integral Representation ◽  
Sound Wave ◽  
High Frequency ◽  
Correction Term ◽  
Scattering Coefficient ◽  
Extended Form ◽  
Geometrical Acoustics ◽  
Plane Sound

ABSTRACTThe diffraction of a high-frequency plane sound wave by a circular cylinder is investigated when the boundary condition on the cylinder is expressed by means of an equation of the form The special feature of this investigation is that an extended form of the Kirchhoff-Fresnel theory of diffraction is used to find an integral representation for the scattering coefficient. In order to avoid the complicated analysis which would be necessary to evaluate the integrals concerned, the more natural geometrical acoustics approach is used to find the first correction term in the scattering coefficient. Numerical results are given for large and small values of the impedance Z.

Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

Numerical Simulation of Fluid Slip at a Hydrophobic Surface

Volume 4 ◽  
2004 ◽  
Author(s):  
Takao Fujita ◽  
Keizo Watanabe
Keyword(s):  
Boundary Condition ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Drag Reduction ◽  
Hydrophobic Surface ◽  
Friction Reduction ◽  
Water Repellent ◽  
Two Dimensional ◽  
Hydrophobic Property ◽  
Flow Past

Laminar drag reduction is achieved by using a hydrophobic surface. In this method, fluid slip is applied at the hydrophobic surface. An initial experiment to clarify for a laminar skin friction reduction was conducted using ducts with a highly water-repellent surface. The surface has a fractal-type structure with many fine grooves. Fluid slip at a hydrophobic surface has been analyzed by applying a new wet boundary condition. In this simulation, an internal flow is assumed to be a two-dimensional laminar flow in a rectangular duct and an external flow is assumed to be a two-dimensional laminar flow past a circular cylinder. The VOF technique has been used as the method for tracking gas-liquid interfaces, and the CSF model has been used as the method for modeling surface tension effects. The wet boundary condition for the hydrophobic property on the surface has been determined from the volume ratio in contact with water near the surface. The model with a stable gas-liquid interface and the experimental results of flow past a circular cylinder at Re = 250 without growing the Karman vortex street are made, and these results show that laminar drag reduction occurring due to fluid slip can be explained in this model.

Numerical Investigation of Slip Flow and Heat Transfer in Rotating Rectangular Microchannels

2012 ◽  
Author(s):  
Pratanu Roy ◽  
N. K. Anand ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Convective Heat Transfer ◽  
Secondary Flow ◽  
Convective Heat ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Fluid Temperature ◽  
Slip Boundary ◽  
Flow And Heat Transfer

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The pseudo forces namely the centrifugal force and the Coriolis force arising as a consequence of the rotating reference frame change the flow pattern significantly from the parabolic profile in a non-rotating channel. The convective heat transfer process is also influenced by the secondary flow introduced by the rotational effect. Moreover, if the microchannel wall is hydrophobic, slip flow can occur inside the channel when the conventional no slip boundary condition is no longer valid. In this work, we have numerically investigated the flow and heat transfer inside a straight rotating rectangular microchannel in the slip flow regime. A pressure based finite volume technique in a staggered grid was applied to solve the steady incompressible Navier-Stokes and energy equations. It has been observed that, depending on the rotational velocity, different slip velocities are induced at the channel walls. The average fluid temperature increases with the increase of rotation as convective heat transfer mechanism is increased due to the secondary flow. However, the slip boundary condition has a negligible effect on the temperature profiles.

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