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.

Couette flow for a gas with a discrete velocity distribution

1976 ◽  
Vol 76 (2) ◽  
pp. 273-287 ◽  
Author(s):  
Henri Cabannes
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Couette Flow ◽  
Flow Problem ◽  
Kinetic Equations ◽  
Velocity Slip ◽  
Theory Model ◽  
Slip Coefficient ◽  
Slip Coefficients

We consider a kinetic theory model of a gas, whose molecular velocities are restricted to a set of fourteen given vectors. For this model we study the Couette flow problem, the boundary conditions on the walls being the conditions of pure diffuse reflexion. The kinetic equations can be integrated by quadrature under the assumption that the walls have opposite velocities and equal temperatures. The presence on the walls of tangential velocities leads to the consequence that the velocity slip coefficient does not in general vanish when the Knudsen number goes to zero.Considering the same problem again after the suppression of tangential velocities, we obtain formulae for the velocity and temperature slip coefficients which generalize results of Broadwell (1964b), and which agree qualitatively with experiments.

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.

scholarly journals Modeling of Knudsen Layer Effects in the Micro-Scale Backward-Facing Step in the Slip Flow Regime

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 118 ◽  
Author(s):  
Apurva Bhagat ◽  
Harshal Gijare ◽  
Nishanth Dongari
Keyword(s):  
Boundary Conditions ◽  
Flow Regime ◽  
Free Path ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Backward Facing Step ◽  
Micro Scale ◽  
Non Equilibrium

The effect of the Knudsen layer in the thermal micro-scale gas flows has been investigated. The effective mean free path model has been implemented in the open source computational fluid dynamics (CFD) code, to extend its applicability up to slip and early transition flow regime. The conventional Navier-Stokes constitutive relations and the first-order non-equilibrium boundary conditions are modified based on the effective mean free path, which depends on the distance from the solid surface. The predictive capability of the standard `Maxwell velocity slip—Smoluchwoski temperature jump’ and hybrid boundary conditions `Langmuir Maxwell velocity slip—Langmuir Smoluchwoski temperature jump’ in conjunction with the Knudsen layer formulation has been evaluated in the present work. Simulations are carried out over a nano-/micro-scale backward facing step geometry in which flow experiences adverse pressure gradient, separation and re-attachment. Results are validated against the direct simulation Monte Carlo (DSMC) data, and have shown significant improvement over the existing CFD solvers. Non-equilibrium effects on the velocity and temperature of gas on the surface of the backward facing step channel are studied by varying the flow Knudsen number, inlet flow temperature, and wall temperature. Results show that the modified solver with hybrid Langmuir based boundary conditions gives the best predictions when the Knudsen layer is incorporated, and the standard Maxwell-Smoluchowski can accurately capture momentum and the thermal Knudsen layer when the temperature of the wall is higher than the fluid flow.

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