New velocity-slip and temperature-jump boundary conditions for Navier–Stokes computation of gas mixture flows in microgeometries

2011 ◽  
Vol 38 (6) ◽  
pp. 417-424 ◽  
Author(s):  
Iman Zahmatkesh ◽  
Mohammad M. Alishahi ◽  
Homayoun Emdad
Keyword(s):  
Boundary Conditions ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Gas Mixture

Three Dimensional Numerical Analysis of Laminar Slip-Flow Heat Transfer in Rectangular Microchannels

2008 ◽  
Author(s):  
H. D. Madhawa Hettiarachchi ◽  
Mihajlo Golubovic ◽  
William M. Worek
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Temperature Jump ◽  
Slip Flow ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Thermal Boundary Condition ◽  
Navier Stokes ◽  
Constant Wall Temperature ◽  
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.

Boundary Conditions for Multi-Component Slip-Flows Based on the Kinetic Theory of Gases

2008 ◽  
Author(s):  
Azad Qazi Zade ◽  
Metin Renksizbulut ◽  
Jacob Friedman
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Gas Flows ◽  
Kinetic Theory Of Gases ◽  
Concentration Jump ◽  
Physical Importance ◽  
Jump Velocity ◽  
Slip Flows

General temperature-jump, velocity-slip, and concentration-jump conditions on solid surfaces in rarefied multi-component gas flows are developed using the kinetic theory of gases. The presented model provides general boundary conditions which can be simplified according to the problem under consideration. In some limiting cases, the results of the current work are compared to the previously available and widely used boundary conditions reported in the literature. The details of the mathematical procedure are also provided to give a better insight about the physical importance of each term in the slip/jump boundary conditions. Also the disagreements between previously reported results are investigated to arrive at the most proper expressions for the slip/jump boundary conditions. The temperature-jump boundary condition is also modified to handle polyatomic gas flows unlike previously reported studies which were mostly concerned with monatomic gases.

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.

Simulation of Flow in Continuum-Transition Regime in Stepped-Microchannels Using Burnett Equations

2008 ◽  
Author(s):  
Reza Kamali ◽  
Saleh Rezaei Ravesh ◽  
Saeid Movahed
Keyword(s):  
Knudsen Number ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Velocity Slip ◽  
Heat Fluxes ◽  
Navier Stokes ◽  
Burnett Equations ◽  
Navier Stokes Equations ◽  
Microfluidic Flows ◽  
Explicit Finite Difference

In present study, the Navier-Stokes equations and the Burnett equations with Maxwell-Smoluchowski slip conditions for some values of Knudsen number are used to resolve the viscous compressible fluid flow of air in the stepped microchannel. An explicit finite difference scheme is employed to develop a two-dimensionl numerical Burnett solver for microfluidic flows and the second order stresses and heat fluxes in the Burnett equations are implemented into the code. Velocity slip/temperature jump conditions on the wall of the channel and on the step within duct are also used. Results are compared with those obtained by using the Navier-Stokes equations with and without the slip-wall conditions using flow in a microchannel. The effects of Knudsen number on the flow and the heat transfer characteristics of the microchannel are also investigated.

Slip Flow Structures in Confined Geometries

2008 ◽  
Author(s):  
Steffen Jebauer ◽  
Justyna Czerwinska
Keyword(s):  
Gas Flow ◽  
Temperature Jump ◽  
Complex Structure ◽  
Slip Flow ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Flow Structures ◽  
Complex Flow ◽  
Vortex Patterns ◽  
Slip Flows

This paper presents various flow structures related to velocity slip and temperature jump in very low Reynolds number gas flow. The structures differ significantly from the ones observed in continuum regime for laminar flow, especially if the geometry has complex structure, which is very often the case in microfluidic devices. We are modelling the flow as a continuum Navier-Stokes gas flow with additional velocity slip and temperature jump boundary conditions for curved surfaces for slip flows with Knudsen numbers Kn < 0.1. For complex channel geometries with obstacles and curved walls vortex patterns are observed that are related to the thermal stress slip flow. This type of flow is induced only when non-uniform temperature distributions inside flow domains are present. The investigated geometries consist of one or more cylinder walls with diameters of up to a few 100 μm placed inside of confined microchannels, with all setups being two-dimensional. In gaseous microdevices the resulting complex flow patterns can be utilised to enhance mixing or heat transfer.

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