An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases

1964 ◽  
Vol 7 (6) ◽  
pp. 681-694 ◽  
Author(s):  
R.G. Deissler
Keyword(s):  
Boundary Conditions ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Rarefied Gases

Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Tim Ameel
Keyword(s):  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Order Approximation ◽  
Slip Flow ◽  
Order Effect ◽  
Second Order ◽  
First Order ◽  
Slip Regime ◽  
Energy Equations

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, first-order boundary conditions are found to over predict the effects of slip and temperature jump, while the effect of the second-order terms is most significant at the upper limit of the slip regime. The second-order terms are found to provide a correction to the first-order approximation. For airflows, the maximum second-order correction to the Nusselt number is on the order of 50%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.

Isothermal Microtube Heat Transfer With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Order Model ◽  
First Order ◽  
Second Order Model

Two analytical models are presented in which the continuum momentum and energy equations, coupled with second-order slip flow and temperature jump boundary conditions, are solved. An isothermal boundary condition is applied to a microchannel with a circular cross section. The flow is assumed to be hydrodynamically fully developed and thermal field is either fully developed or thermally developing from the tube entrance. A traditional first-order slip boundary condition is found to over predict the slip velocity compared to the second-order model. Heat transfer increases at the upper limit of the slip regime for the second-order model. The maximum second-order correction to the first-order Nusselt number is on the order of 18% for air. The second-order effect is also more significant in the entrance region of the tube. The Nusselt number decreases relative to the no-slip value when slip and temperature jump effects are of the same order or when temperature jump effects dominate. When temperature jump effects are small, the Nusselt number increases relative to the no-slip value. Comparisons to a previously reported model for an isoflux boundary condition indicate that the Nusselt number for the isoflux boundary condition exceeds that for the isothermal case at all axial locations.

Numerical Modeling of Micro Fin Arrays Using Slip Flow and Temperature Jump Boundary Conditions

2008 ◽  
Author(s):  
C. B. Sobhan ◽  
Muhsin M. Ameen ◽  
Praveen P. Abraham
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Slip Flow ◽  
Convection Heat Transfer ◽  
Transient State ◽  
Velocity Slip ◽  
Operating Pressure ◽  
Parametric Studies ◽  
Explicit Finite Difference

A numerical investigation of natural convection heat transfer from a rectangular fin array of microscale dimensions, where a “down and up” flow pattern occurs, is carried out. The stream function vorticity formulation is used in the analysis and the governing equations of the transient two dimensional field are solved using an explicit finite difference scheme. The dimensions of the domain are such that the problem falls under the slip flow regime. The non continuum effects are modeled through Maxwell’s velocity slip and Smoluchowski’s temperature jump boundary conditions. The steady state velocity and temperature distributions in the field are obtained by marching through the transient state. The average heat transfer coefficient and the Nusselt Number are calculated. The influence of the fin spacing, fin height and operating pressure on the performance of the fin array is studied through parametric studies and some conclusions are drawn regarding the significance of non continuum effects in the micro scale dimensions considered.

Experimental uncertainties analysis as a tool for friction factor determination in microchannels

2008 ◽  
Vol 222 (5) ◽  
pp. 817-827 ◽  
Author(s):  
M Lorenzini ◽  
G L Morini ◽  
T Henning ◽  
J Brandner
Keyword(s):  
Boundary Conditions ◽  
Slip Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Second Order ◽  
Limiting Factor ◽  
Total Uncertainty ◽  
Rarefied Flows ◽  
Error Propagation Analysis ◽  
Poiseuille Number

The constant growth of the studies on microchannel flows has brought under question the validity of the relations for heat transfer and fluid flow, which are usually employed at the macroscales. Rarefied flows in the slip-flow region have attracted much attention and solutions have been developed using first- and second-order boundary conditions. These models need to be experimentally validated through careful test in order to be able to use them for more complex problems and engineering applications. In the current work the error propagation analysis is applied to a set of error-free measurements artificially generated in order to assess the influence of the uncertainty on each of the measured quantities on the determination of the Poiseuille number for rarefied flows: it is shown that the most limiting factor is the accuracy on the tube diameter, while flowrate and pressure drop errors can be kept contained provided the measurement ranges for the transducers are suitably chosen. The total uncertainty is also calculated and the limit of the investigable Reynolds numbers defined. The possibility of experimentally evidencing the differences between first- and second-order boundary conditions is investigated and it is concluded that this is the case only for highly rarefied flows ( Kn > 0.5).

Constant Wall Temperature Nusselt and Poiseuille Numbers in Rectangular Microchannels

2007 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Wall Temperature ◽  
Rectangular Channel ◽  
Slip Flow ◽  
Second Order ◽  
Constant Wall Temperature ◽  
Axial Conduction ◽  
Accommodation Coefficients

Slip flow convective heat transfer and friction loss characteristics are numerically evaluated for constant wall temperature rectangular microchannels. The effects of rarefaction, accommodation coefficients, aspect ratio, second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work are each considered. Second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work effects have not been studied previously for rectangular channel slip flows. The effects of each of these parameters on the numerically computed convective heat transfer rate and friction loss are evaluated through the Nusselt number and Poiseuille number respectively. The numerical results are obtained using a continuum-based computational fluid dynamics algorithm that includes second-order slip flow and temperature jump boundary conditions. Numerical results for the three-dimensional, fully developed Nusselt and Poiseuille numbers are presented as functions of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, aspect ratio, Brinkman number, and Peclet number. Effects of rarefaction, accommodation coefficients, and aspect ratio are consistent with previously reported analytical results for rectangular channel constant wall temperature flows. The effects of second-order slip terms, axial conduction and viscous dissipation are also shown to significantly affect the Nusselt and Poiseuille numbers.

scholarly journals Evaluation of Nusselt number for a flow in a microtube using second-order slip model

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 103-109 ◽  
Author(s):  
Barbaros Cetin ◽  
Ozgur Bayer
Keyword(s):  
Nusselt Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Slip Model ◽  
Brinkman Number ◽  
Constant Property ◽  
Axial Conduction ◽  
Closed Form Solutions ◽  
Constant Wall Heat Flux

In this paper, the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order slip model is used for the slip-flow and temperature jump boundary conditions for the implementation of the rarefaction effect. Closed form solutions for the temperature field and the fully-developed Nusselt number is derived as a function of Knudsen number, Brinkman number and Peclet number.

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