scholarly journals Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1

2001 ◽  
Vol 124 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou ◽  
Olga Simek
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Flow Regime ◽  
Wall Temperature ◽  
Slip Flow ◽  
Constant Wall Temperature ◽  
Slip Flow Regime ◽  
Axial Heat ◽  
Axial Heat Conduction

We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0⩽Kn⩽0.1, and most of the transition regime 0.1<Kn⩽10, where Kn, the Knudsen number, is defined as the ratio between the molecular mean free path and the channel height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0⩽Kn⩽0.2, and a stochastic molecular simulation technique known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in the range 0.02<Kn<2. Inclusion of the effects of axial heat conduction in the continuum model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Kn⩽0.1, but also remains a good approximation beyond its expected range of applicability. We also show that the Nusselt number decreases monotonically with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Kn=0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.

Slip-Flow Constant-Wall-Temperature Nusselt Number in Circular Tubes in the Presence of Axial Heat Conduction

2001 ◽  
Author(s):  
Olga Simek ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Wall Temperature ◽  
Slip Flow ◽  
Small Scale ◽  
Constant Wall Temperature ◽  
Circular Tubes ◽  
Axial Heat ◽  
Axial Heat Conduction

Abstract We present an investigation of slip-flow constant-wall-temperature convective heat transfer in circular tubes under hydrodynamically and thermally fully developed conditions. Our analysis includes the contribution of axial heat conduction (finite Peclet number) which is important in small scale flows, and has not been included in previous investigations of slip-flow heat transfer. The Nusselt number is found to decrease with increasing Knudsen number for all Peclet numbers in the fully accommodating case, as expected. The effect of axial heat conduction is found to be most important at Kn = 0, and results in an increase in the Nusselt number of the order of 15%; as Kn increases, the effect of axial heat conduction decreases.

scholarly journals Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Stéphane Colin
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Flow Regime ◽  
Convective Heat ◽  
Temperature Jump ◽  
Numerical Models ◽  
Slip Flow ◽  
Velocity Slip ◽  
Constant Wall Temperature ◽  
Slip Flow Regime

Accurate modeling of gas microvection is crucial for a lot of MEMS applications (microheat exchangers, pressure gauges, fluidic microactuators for active control of aerodynamic flows, mass flow and temperature microsensors, micropumps, and microsystems for mixing or separation for local gas analysis, mass spectrometers, vacuum, and dosing valves…). Gas flows in microsystems are often in the slip flow regime, characterized by a moderate rarefaction with a Knudsen number of the order of 10−2–10−1. In this regime, velocity slip and temperature jump at the walls play a major role in heat transfer. This paper presents a state of the art review on convective heat transfer in microchannels, focusing on rarefaction effects in the slip flow regime. Analytical and numerical models are compared for various microchannel geometries and heat transfer conditions (constant heat flux or constant wall temperature). The validity of simplifying assumptions is detailed and the role played by the kind of velocity slip and temperature jump boundary conditions is shown. The influence of specific effects, such as viscous dissipation, axial conduction and variable fluid properties is also discussed.

Roughness Effect on the Heat Transfer Coefficient for Gaseous Flow in Microchannels

2010 ◽  
Author(s):  
Metin B. Turgay ◽  
Almila G. Yazicioglu ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Nusselt Number ◽  
Flow Regime ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Roughness Height ◽  
Working Fluid ◽  
Axial Conduction ◽  
Slip Flow Regime

Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.

Effects of Axial Heat Conduction in the Wall on Convection in Microtubes

2003 ◽  
Author(s):  
Zhi-Xin Li ◽  
Wei Wang ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Boundary Condition ◽  
Thermal Conductivity Ratio ◽  
Convective Boundary ◽  
Axial Heat ◽  
Axial Heat Conduction

Single-phase convective heat transfer in microtubes was numerically studied with consideration on the heat conduction in the tube wall. It indicates that the Nusselt numbers of the fully developed laminar convective heat transfer in microtubes with convective boundary condition outside the tube vary from 3.66 to 4.36, which represent the conventional results for isothermal and constant heat flux boundaries respectively. The Nusselt number depends on the parameters of thermal conductivity ratio (k*), diameter ratio (D*), and Biot number. One-dimensional thermal resistance model could underestimate the Nusselt number if the axial heat conduction in the wall can not be ignored. Discrepancies between the experimental results for the Nusselt number based on 1-D model and the standard values might be misunderstood as being caused by novel phenomena at microscales.

Gas Microflows in the Slip Flow Regime: A Review on Heat Transfer

2010 ◽  
Author(s):  
Ste´phane Colin
Keyword(s):  
Heat Transfer ◽  
Flow Regime ◽  
Temperature Jump ◽  
Numerical Models ◽  
Slip Flow ◽  
Velocity Slip ◽  
Constant Heat Flux ◽  
Gas Analysis ◽  
Constant Wall Temperature ◽  
Slip Flow Regime

Accurate modeling of gas microvection is crucial for a lot of MEMS applications (micro-heat exchangers, pressure gauges, fluidic microactuators for active control of aerodynamic flows, mass flow and temperature micro-sensors, micropumps and microsystems for mixing or separation for local gas analysis, mass spectrometers, vacuum and dosing valves…). Gas flows in microsystems are often in the slip flow regime, characterized by a moderate rarefaction with a Knudsen number of the order of 10−2–10−1. In this regime, velocity slip and temperature jump at the walls play a major role in heat transfer. This paper presents a state of the art review on convective heat transfer in microchannels, focusing on rarefaction effects in the slip flow regime. Analytical and numerical models are compared for various microchannel geometries and heat transfer conditions (constant heat flux or constant wall temperature). The validity of simplifying assumptions is detailed and the role played by the kind of velocity slip and temperature jump boundary conditions is shown. The influence of specific effects, such as viscous dissipation, axial conduction and variable fluid properties is also discussed.

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