Three-Dimensional Steady Vapor Bubbles in Rectangular Microchannels

Slip-flow and heat transfer in rectangular microchannels are studied numerically for constant wall temperature (T) and constant wall heat flux (H2) boundary conditions under thermally developing flow. Navier-Stokes and energy equations with velocity slip and temperature jump at the boundary are solved using finite volume method in a three dimensional cartesian coordinate system. A modified convection-diffusion coefficient at the wall-fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is stabilized. The effect of rarefaction on heat transfer in the entrance region is analyzed in detail. The velocity slip has an increasing effect on the Nusselt (Nu) number whereas temperature jump has a decreasing effect, and the combined effect could result increase or decrease in the Nu number. For the range of parameters considered, there could be high as 15% increase or low as 50% decrease in fully developed Nu is plausible for T thermal boundary condition while it could be high as 20% or low as 35% for H2 thermal boundary condition.

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PRESSURE DROP FOR THREE-DIMENSIONAL RECTANGULAR MICROCHANNELS

10.1615/ihtc16.ctm.023173 ◽

2018 ◽

Author(s):

Liangbin Su ◽

Hao Ma ◽

Peng Liang ◽

Niya Ma ◽

Xiaoru Ning ◽

...

Keyword(s):

Pressure Drop ◽

Three Dimensional ◽

Rectangular Microchannels

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Numerical simulation of pressure drop for three-dimensional rectangular microchannels

Engineering Computations ◽

10.1108/ec-07-2017-0275 ◽

2018 ◽

Vol 35 (6) ◽

pp. 2234-2254 ◽

Cited By ~ 4

Author(s):

Zhipeng Duan ◽

Peng Liang ◽

Hao Ma ◽

Niya Ma ◽

Boshu He

Keyword(s):

Reynolds Number ◽

Pressure Drop ◽

Laminar Flow ◽

Friction Factor ◽

Three Dimensional ◽

Numerical Data ◽

Rectangular Microchannels ◽

Content Type ◽

Aspect Ratios ◽

Rectangular Channels

Purpose The purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios. Design/methodology/approach Using a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product fappRe is referenced as a semi-theoretical fundamental analysis for numerical simulations. Findings The accurate and reliable results of fappRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of fappRe are significantly extended to other different aspect ratios and the novel values of fappRe are presented in the tables. The characteristics of fappRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed. Originality/value From the reliable data, it is shown that the values of fappRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

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Numerical Investigation to Derive Correlations for Hydrodynamic Entrance Length in Very Low Reynolds Number Regime in Rectangular Microchannels

Journal of Fluids Engineering ◽

10.1115/1.4047232 ◽

2020 ◽

Vol 142 (9) ◽

Author(s):

Dustin R. Ray ◽

Debendra K. Das

Keyword(s):

Three Dimensional ◽

Numerical Data ◽

Reynolds Numbers ◽

Maximum Error ◽

Entrance Length ◽

Fully Developed Flow ◽

Rectangular Microchannels ◽

Mean Error ◽

Aspect Ratios ◽

Laminar Flow Model

Abstract A three-dimensional laminar flow model was used for 37 Reynolds numbers (0.1, 0.2…1, 2…10, 20…100, and 200…1000) through six rectangular microchannels (aspect ratios: 1, 0.75, 0.5, 0.25, 0.2, and 0.125) to develop correlations for hydrodynamic entrance length. The majority of the Reynolds numbers are in the low regime (Re < 100) to fulfill the need to determine the hydrodynamic entrance length for microchannels. Examination of the fully developed flow condition was considered using the velocity or fRe criteria. Numerical results from the present simulations were validated by comparing the fRe results. Two new correlations were developed from a vast amount of numerical data (222 simulations). The velocity criterion correlations predict entrance length with a mean error of 4.67% and maximum error of 10.28%. The fRe criterion generated better correlations and were developed as a function of aspect ratio to predict entrance length with a mean error less than 2% and maximum error of 5.75% for 0.1 ≤ Re ≤ 1000 and 0 ≤ α ≤ ∞.

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THE EFFECT OF TEMPERATURE ON FRICTION CHARACTERISTICS OF INCOMPRESSIBLE FLOW IN LONG RECTANGULAR MICROCHANNELS

Modern Physics Letters B ◽

10.1142/s0217984905010104 ◽

2005 ◽

Vol 19 (28n29) ◽

pp. 1639-1642

Author(s):

C. S. CHEN ◽

M. H. LIN

Keyword(s):

Incompressible Flow ◽

Three Dimensional ◽

Numerical Procedure ◽

Effect Of Temperature ◽

Governing Equations ◽

Rectangular Microchannels ◽

Friction Characteristics ◽

Fast Speed

This paper develops an efficient three-dimensional numerical procedure to predict incompressible flow in long microchannels. The major advantage of the present numerical procedure is its fast speed due to the parabolic character of the governing equations.

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Mathematical Modeling of Constrained Vapor Bubbles

1st International Conference on Microchannels and Minichannels ◽

10.1115/icmm2003-1072 ◽

2003 ◽

Cited By ~ 6

Author(s):

Vladimir S. Ajaev ◽

G. M. Homsy

Keyword(s):

Steady State ◽

Three Dimensional ◽

Liquid Interface ◽

Vapor Bubbles ◽

Dimensional Model ◽

Type Analysis ◽

Steady Regime ◽

Mass Fluxes ◽

Steady State Solutions ◽

Vapor Liquid

We develop a mathematical model of a long vapor bubble in a micro-channel with given temperature distributions on the walls. We assume that the shape of the bubble is dominated by capillary forces everywhere except near the walls of the channel and use a lubrication-type analysis to find the local vapor-liquid interface shapes and mass fluxes near the walls. Both two- and three-dimensional steady-state solutions are found such that evaporation near the heated bottom is balanced by condensation in colder areas of the vapor-liquid interface. The total length in this steady regime is found from the integral mass balance and investigated as a function of heating conditions. Steady-state conditions can no longer be satisfied when the intensity of heating is above a certain level. In this regime the bubble is expanding. We investigate such expansion in the framework of a two-dimensional model in the limit of small capillary number.

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Three-Dimensional Numerical Simulation for Annular Condensation in Rectangular Microchannels

Nanoscale and Microscale Thermophysical Engineering ◽

10.1080/15567260802625882 ◽

2009 ◽

Vol 13 (1) ◽

pp. 13-29 ◽

Cited By ~ 29

Author(s):

Jiafeng Wu ◽

Yongping Chen ◽

Mingheng Shi ◽

Panpan Fu ◽

G.P. Peterson

Keyword(s):

Numerical Simulation ◽

Three Dimensional ◽

Rectangular Microchannels

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The orbit of Pluto over a long interval of time

Symposium - International Astronomical Union ◽

10.1017/s0074180900105509 ◽

1966 ◽

Vol 25 ◽

pp. 227-229 ◽

Cited By ~ 1

Author(s):

D. Brouwer

Keyword(s):

Periodic Orbit ◽

Numerical Integration ◽

Restricted Problem ◽

Three Dimensional ◽

The Third ◽

Circular Restricted Problem ◽

Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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