Rayleigh Problem in Slip Flow With Modified Initial Conditions

1967 ◽  
Vol 34 (4) ◽  
pp. 833-836 ◽  
Author(s):  
K. C. Reddy
Keyword(s):  
Temperature Jump ◽  
Initial Conditions ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Conditions ◽  
Flow Conditions ◽  
Slip Boundary ◽  
Rayleigh Problem ◽  
Molecule Flow ◽  
The Continuum

The initial conditions of the linearized Rayleigh problem in slip flow are modified so as to satisfy the free molecule flow conditions at the start of the motion. Approximate initial profiles for velocity and temperature are chosen which would yield correct values of velocity slip, temperature jump, and so on, at the start of the motion. The continuum solutions with the modified initial conditions and slip boundary conditions are found to be uniformly valid for all times of motion and agree well with the results of the kinetic theory analyses of the problem.

Zero Mass Flux Dependent on Radiative Magnetohydrodynamics Carreau Nanofluid Over a Radially Surface with Temperature Jump and Slip Flow: A Hybrid Nanofluid Analysis

2021 ◽  
Vol 10 (1) ◽  
pp. 118-127
Author(s):  
Amit Parmar ◽  
Rakesh Choudhary ◽  
Krishna Agrawal
Keyword(s):  
Mass Flux ◽  
Temperature Jump ◽  
Slip Flow ◽  
Velocity Slip ◽  
Concentration Profiles ◽  
Fluid Temperature ◽  
Slip Parameter ◽  
First Order ◽  
Zero Mass ◽  
Carreau Nanofluid

The present study explores the slip flow and heat transfer induced by a radially surface with MHD Carreau nanofluid. In addition, the effects of temperature jump, non-linear radiation and the dependent zero mass flux also taken into account. This study also considers the cross-diffusion effect on temperature and concentration governing profiles. Appropriate transformations are engaged in order to acquire nonlinear differential equations (ODEs) from the partial differential system, their solutions are obtained by Runge-Kutta 4th order with shooting scheme in MATLAB. The impact of pertinent flow parameters such as first and second order velocity slip parameter, temperature jump, magnetic parameter, heat source, radiation parameter, melting surface parameter, temperature ratio parameter on dimensionless velocity, temperature and concentration profiles achieved graphically as well as local skin friction, Nusselt number and Sherwood number are demonstrated in the form of Table. first order velocity slip parameter (slip1) on f′, Θ and Φ profile fields. With an increment in the velocity slip first order parameter (slip1) we have perceived a fall in the momentum boundary layer and concentration profiles and a growth in the fluid temperature field.

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.

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

scholarly journals Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 142
Author(s):  
Xin He ◽  
Kai Zhang ◽  
Chunpei Cai
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Boundary Layer Flow ◽  
Velocity Slip ◽  
Linear Stability Theory ◽  
Resonance Phenomenon ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Layer Flow

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

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.

scholarly journals Slip Flow of Kerosene Oil Based SWCNT Nanofluid over Stretching Sheet with Radiation and Suction/Injection Effects

2021 ◽  
Vol 6 (3) ◽  
pp. 860-877
Author(s):  
Susheela Chaudhary ◽  
Kiran Kunwar Chouhan ◽  
Santosh Chaudhary
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Skin Friction Coefficient ◽  
Single Wall Carbon Nanotubes ◽  
Local Skin ◽  
Slip Boundary ◽  
Similarity Transformations

Present study numerically investigates a two dimensional steady laminar boundary layer nanofluid flow of single-wall carbon nanotubes (SWCNTs) immersed into kerosene oil, due to a linearly stretched sheet. Flow is subjected to the slip boundary condition and suction/injection effects. Employing suitable similarity transformations, governing PDEs of the arising problem are converted into coupled nonlinear non-dimensional ordinary differential equations. A set of obtained ODEs with assisting boundary conditions is solved numerically by applying finite element method (FEM). Effect of pertinent factors, velocity slip parameter, suction/injection parameter and solid volume fraction parameter on non-dimensional velocity and temperature profiles are characterized graphically. In addition, physical emerging parameters, local Nusselt’s number and local skin friction coefficient are computed and presented via table. Furthermore, derived numerical values of shear stress and heat flux at the surface are compared with previously published results.

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.

Hydromagnetic flow and heat transfer with various nanoparticle additives past a wedge with high order velocity slip and temperature jump

2017 ◽  
Vol 95 (5) ◽  
pp. 440-449 ◽  
Author(s):  
Qianfang Liu ◽  
Jing Zhu ◽  
Bandar Bin-Mohsin ◽  
Liancun Zheng
Keyword(s):  
Heat Transfer ◽  
Temperature Jump ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
High Order ◽  
Solid Particles ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Fundamental Equations

Nanofluid slip flow with distinct solid particles past a wedge with convective surface and high order slip is discussed in this paper. The wedge model is modified by considering the effects of Brownian motion and thermophphoresis together with the high order velocity slip and temperature jump. In this study, the governing fundamental equations are first transformed into third-order ordinary differential equations and solved by using the homotopy analysis method (HAM). Through error analysis and comparison with previous research, the effectiveness of HAM is ascertained, and the crucial influence of nanoparticles and high-order slip on the fluid skin-friction coefficient and heat transfer coefficient is analyed. Thermophphoresis parameter and suction/injection parameter are found to cause an increase in velocity and temperature. The rate of heat transfer in the Cu–water nanofluid is found to be higher than the others.

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