Analysis of Gaseous Flow Between Parallel Plates by Second- Order Velocity Slip and Temperature Jump Boundary Conditions

2013 ◽  
Vol 43 (8) ◽  
pp. 734-748 ◽  
Author(s):  
Hari Mohan Kushwaha ◽  
S.K. Sahu
Keyword(s):  
Boundary Conditions ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Second Order ◽  
Parallel Plates ◽  
Gaseous Flow

Effect of Second Order Velocity-Slip/Temperature-Jump on Basic Gaseous Fluctuating Micro-Flows

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. A. Hamdan ◽  
M. A. Al-Nimr ◽  
Vladimir A. Hammoudeh
Keyword(s):  
Boundary Conditions ◽  
Driving Force ◽  
Critical Frequency ◽  
Temperature Jump ◽  
Order Term ◽  
Velocity Slip ◽  
Second Order ◽  
Convection Flow ◽  
Force Frequency ◽  
Jump Model

In this work, the effect of the second-order term to the velocity-slip/temperature-jump boundary conditions on the solution of four cases in which the driving force is fluctuating harmonically was studied. The study aims to establish criteria that secure the use of the first order velocity-slip/temperature-jump model boundary conditions instead of the second-order ones. The four cases studied were the transient Couette flow, the pulsating Poiseuille flow, Stoke’s second problem, and the transient natural convection flow. It was found that at any given Kn number, increasing the driving force frequency, increases the difference between the first and second-order models. Assuming that a difference between the two models of over 5% is significant enough to justify the use of the more complex second-order model, the critical frequencies for the four different cases were found. For the cases for which the flow is induced by the fluctuating wall as in cases 1 and 3, we found that critical frequency at Kn=0.1 to be ω=8. For the cases of flow driven by a fluctuating pressure gradient as in case 2, this frequency was found to be ω=1, at the same Kn number. In case 4, for the temperature-jump model, the critical frequency was found to be ω=7 and for the velocity-slip model the critical frequency at the same Kn number was found to be ω=1.35.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

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.

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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