On the Derivation of Pressure Field Distribution at the Entrance of a Rectangular Capillary

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Prashant R. Waghmare ◽  
Sushanta K. Mitra
Keyword(s):  
Aspect Ratio ◽  
Field Distribution ◽  
High Aspect Ratio ◽  
Pressure Field ◽  
Capillary Flow ◽  
Control Volume ◽  
Equivalent Radius ◽  
Circular Capillary ◽  
Entrance Pressure ◽  
Correct Expression

In capillary flow, integral momentum approach is used to derive the governing equation, which requires an expression for the pressure field at the inlet of the capillary. Generally, the pressure field for circular capillary is deduced with hemispherical control volume. This expression has been extended for other noncircular capillaries with an equivalent radius approximation. In case of high aspect ratio channels, the semicylindrical control volume needs to be considered. In the present study, the correct expression for the entrance pressure field for high aspect ratio capillaries is derived with such appropriate control volume.

A Titanium Based Flat Heat Pipe

2008 ◽  
Author(s):  
Changsong Ding ◽  
Gaurav Soni ◽  
Payam Bozorgi ◽  
Brian Piorek ◽  
Carl D. Meinhart ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Aspect Ratio ◽  
Heat Pipe ◽  
Carrying Capacity ◽  
High Aspect Ratio ◽  
Capillary Flow ◽  
Titanium Substrate ◽  
Heat Pipes ◽  
Working Fluid ◽  
Wick Structure

We are developing innovative heat pipes based on Nano-Structured Titania (NST) with a potential for high heat carrying capacity and high thermal conductivity. These heat pipes have a flat geometry as opposed to a cylindrical geometry found in conventional heat pipes. The flatness will enable a good contact with microprocessor chips and thus reduce the thermal contact resistance. We refer to it as a Thermal Ground Plane (TGP) because of its flat and thin geometry. It will provide the ability to cool the future generations of power intensive microprocessor chips and circuit boards in an efficient way. It also brings the potential to function in high temperature (>150°C) fields because of its high yield strength and compatibility [1]. The TGP is fabricated with Titanium. It adopts the recently developed high aspect ratio Ti processing techniques [2] and laser packaging techniques. The three main components of the TGP are 1) a fine wick structure based on arrays of high aspect ratio Ti pillars and hair like structures of Nano-Structured Titania (NST), 2) A shallow Ti cavity welded onto the wick structure and 3) the working fluid, water, sealed between the cavity and the wick. The heat carrying capacity and the thermal conductivity of a heat pipe are generally determined by the speed of capillary flow of the working fluid through its wick. The TGP wick has the potential to generate high flow rates and to meet the growing challenges faced by electronics cooling community. The TGP wick structure, developed by etching high aspect ratio pillars in a titanium substrate and growing nano scale hairs on the surface of the pillars, is super hydrophilic and capable of wicking water at velocities ∼ 10−2 m/s over distances of several centimeters. The thermal conductivity of the current TGP device was measured to be k = 350 W/m·K. The completed TGP device has the potential of attaining a higher conductivity by improving the wicking material and of carrying higher power density. Washburn equation [3] for dynamics of capillary flow has been employed to explain the results of our experiments. The experiment shows a good agreement with Washburn equation.

The Effect of a Translating High Aspect Ratio Particle in a Plane Slider Bearing

1983 ◽  
Vol 105 (3) ◽  
pp. 396-404 ◽  
Author(s):  
M. T. Languirand ◽  
J. A. Tichy
Keyword(s):  
Aspect Ratio ◽  
Theoretical Analysis ◽  
High Aspect Ratio ◽  
Pressure Field ◽  
Stokes Equations ◽  
Velocity Fields ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Experimental Apparatus ◽  
Initial Starting

An approximate solution of Stokes equations is presented to determine the pressure and velocity fields in an infinite slider bearing containing a two-dimensional high aspect ratio particle of arbitrary cross-section. The particle may translate in two directions as well as rotate about its centroid. The fluid field is divided into four regions: upstream, above, below, and downstream of the particle. The governing Stokes equations are applied to each region and solved through specific continuity requirements and pressure matching conditions. For illustrative purposes, this method of analysis is applied to a plane slider bearing containing a rectangular particle which can translate in one direction. Approximate solutions are given for the pressure and velocity fields. The solution reveals a pressure drop which develops in the pressure field at the particle location. The magnitude of this drop is shown to be dependent on a particle size, velocity, and location. It is shown that the particle has a major effect on the bearing pressure field when it is able to significantly obstruct the flow of the lubricant. To support the theoretical analysis, experimental research is performed. An experimental apparatus is used to measure the transient pressure in a slider bearing as a high aspect ratio two-dimensional rectangular particle is passed through the fluid film. The apparatus measures pressure at a particular location in the bearing and simultaneously measures the particle’s displacement with respect to its initial starting location. Results are given to demonstrate the effect of particle velocity on the pressure field in the bearing. The experimental results presented are in good agreement with analytical results obtained from the theoretical analysis.

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