scholarly journals Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation

2007 ◽  
Vol 43 (6) ◽  
Author(s):  
Fredrik Huthoff ◽  
Denie C. M. Augustijn ◽  
Suzanne J. M. H. Hulscher
Keyword(s):  
Analytical Solution ◽  
Flow Velocity

On the Role of Enduring Contact in Powder Lubrication

2005 ◽  
Vol 128 (1) ◽  
pp. 168-175 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Analytical Solution ◽  
Flow Velocity ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Kinetic Regime ◽  
Governing Equations ◽  
Wide Range ◽  
Fraction Distribution ◽  
Powder Lubrication

This paper is devoted to a study of the enduring contact between granules of powder lubricants in an effort to better understand the flow characteristics of powder lubricants. Appropriate formulation of the governing equations is reported that can be used for prediction of the flow velocity, pseudo temperature, and volume fraction distribution of powders for a wide range of operating speeds. A set of parametric simulations and a limiting analytical solution is presented for predicting the behavior of a powder lubricant under low operating speeds when the enduring contact tends to dominate the kinetic regime. The limiting solution shows that below a certain sliding speed the volume fraction remains unchanged due to the effect of the enduring contact. It is also shown that below this limiting speed the enduring contact plays a major role and should not be neglected.

A Single Probe Transient Moving Line Source Method for Determining Thermal Conductivity, Thermal Diffusivity, and Superficial Flow Velocity of a Porous Material With Flow

2011 ◽  
Author(s):  
Kevin D. Woods ◽  
Alfonso Ortega
Keyword(s):  
Thermal Conductivity ◽  
Thermal Diffusivity ◽  
Analytical Solution ◽  
Porous Material ◽  
Flow Velocity ◽  
Empirical Data ◽  
Line Source ◽  
Single Probe ◽  
Moving Line Source ◽  
Moving Line

This paper presents a method to determine the effective thermal conductivity and thermal diffusivity of a porous material, as well as the superficial flow velocity of fluid flowing through the porous matrix using a single probe transient moving line source method. The method transforms the transient analytical solution for a moving line source using differentiation to produce three independent equations to solve for the three unknowns. Empirical data are presented from a laboratory scale test apparatus for three test cases with known properties and flow rates to validate the method. The method is then applied to field data from a standing column well used in ground source heat pump systems to obtain the thermal and flow properties of the ground formation. The properties are inserted into the transient analytical solution for a moving line source and superimposed over the empirical data showing agreement between the model and the data. The method is more accurate than traditional methods for estimating thermal properties when flow conditions are present, and the implementation of the method does not require any additional thermal data.

Effects of flow velocity and depth on the rates of reaeration and bod removal in a shallow open channel

1997 ◽  
Vol 35 (8) ◽  
pp. 57-67
Author(s):  
Horng-Guang Leu ◽  
C. F. Ouyang ◽  
Tze-Yi Pai
Keyword(s):  
Analytical Solution ◽  
Flow Velocity ◽  
Open Channel ◽  
Rate Coefficient ◽  
Removal Rate ◽  
Sedimentation Coefficient ◽  
Inverse Correlation ◽  
Flow Conditions ◽  
Batch Tests ◽  
Bod Removal

This study developed an analytical solution of reaeration rate coefficient (K2) and modified the equation of BOD removal in a shallow artificial open channel. A series of well-controlled batch tests were carried out to measure the K2 and BOD removal rate in the channel at different flow conditions. The results of these tests indicated that measured K2 within the developing zone of the laminar boundary layer is better described by the analytical solution of this study than by the five semi-empirical formulae mentioned in this paper. On the other hand, a resuspension-sedimentation coefficient, Rs, was added to the BOD removal equation to describe the variation in BOD due to varied flow conditions. Based on the results of the experimental data the following conclusions in the BOD removal process were reached. It was found that a direct correlation exists between the flow velocity to depth ratio (U/h) and the deoxygenation rate coefficient (K1), but there is an inverse correlation between U/h and Rs as well. This modified BOD removal equation can predict BOD removal rate at different travel times or known downstream distances in an open channel under varied flow conditions.

Optimal Shapes of Straight Fins and Finned Heat Sinks

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Matti Lindstedt ◽  
Kaj Lampio ◽  
Reijo Karvinen
Keyword(s):  
Numerical Model ◽  
Analytical Solution ◽  
Flow Velocity ◽  
Power Electronics ◽  
Heat Sink ◽  
Base Plate ◽  
Heat Sinks ◽  
Optimal Shapes ◽  
Cool Power

Finned heat sinks are used to cool power electronics components. We present optimization results for single rectangular, triangular, and trapezoidal fins. After that, we minimize the mass of an existing heat sink consisting of a base plate and a fin array by optimizing the geometrical variables and component locations on the base plate. An analytical solution is used with rectangular fins and a numerical model with trapezoidal fins. Whereas the triangle is the best shape for single fins, in a heat sink flow velocity coupled with geometry favors trapezoids over triangles and rectangles.

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