Gaseous Slip Flow Mixed Convection in Vertical Microducts With Constant Axial Energy Input

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Arman Sadeghi ◽  
Mostafa Baghani ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Cross Sections ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Slip Boundary Conditions ◽  
First Order ◽  
Slip Boundary

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.

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.

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

2019 ◽  
Vol 29 (5) ◽  
pp. 1786-1814 ◽  
Author(s):  
A.A. Avramenko ◽  
N.P. Dmitrenko ◽  
I.V. Shevchuk ◽  
A.I. Tyrinov ◽  
V.I. Shevchuk
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Rotation Rate ◽  
Second Order ◽  
Temperature Profiles ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Slip Boundary

Purpose The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions. Design/methodology/approach The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other. Findings The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions. Originality/value The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

scholarly journals FEATURES OF HEAT TRANSFER IN A FLAT POROUS MICROCHANNEL WITH THE SECOND ORDER SLIP BOUNDARY CONDITIONS

2021 ◽  
Vol 43 (2) ◽  
pp. 5-12
Author(s):  
A.A. Avramenko ◽  
N.P. Dmitrenko ◽  
Yu.Yu. Kovetska ◽  
O.I. Skitsko
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Second Order ◽  
Hydrodynamic Resistance ◽  
First Order ◽  
Slip Boundary ◽  
Velocity Jump ◽  
The Heat Transfer Coefficient

The results of the study of heat transfer under forced convection in a flat porous microchannel taking into account the boundary conditions of slippage of the first and second order are considered. The simulation showed that with decreasing porosity the flow velocity in the central part of the microchannel and the slipping velocity on the wall decrease due to the increase in hydrodynamic resistance. Taking into account the influence of the boundary conditions of the second order shows that the magnitude of the velocity jump on the wall varies depending on the value of the parameter A2. The jump decreases with a positive value of A2, with a negative value - increases in comparison with the case A2 = 0 (first order boundary conditions). Qualitatively similar effects of porosity and second-order boundary conditions were also observed with respect to temperature profiles. The results of the calculation of the relative Nusselt number showed that the decrease in porosity contributes to the intensification of heat transfer. The dynamics of the change in the heat transfer coefficient with an increase in the Knudsen number indicates that an increase in the Prandtl number also leads to an improvement in the thermal interaction of the flow with the channel wall. The analysis of taking into account the boundary conditions of the second order showed that at small values of the Prandtl number (Pr ≤ 1) the influence of the parameter A2 was not observed. At A2 < 0 the effects of the boundary conditions of the second order lead to an increase in the relative Nusselt number, whereas at A2> 0 the value of the normalized Nusselt number decreases in comparison with the case A2 = 0 (boundary conditions of the first order).

Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Leila Issa ◽  
Issam Lakkis
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Reduced Order ◽  
Low Mach Number ◽  
First Order ◽  
Slip Boundary

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

Method of Submerged Stokeslets for Slip Flow About Ensembles of Particles

2008 ◽  
Vol 8 (7) ◽  
pp. 3790-3801
Author(s):  
Shunliu Zhao ◽  
Alex Povitsky
Keyword(s):  
Boundary Conditions ◽  
Self Assembly ◽  
Slip Flow ◽  
Chemical Vapor ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Singularity Method ◽  
Low Reynolds Number Flows ◽  
Micro Pump

A boundary singularity method with submerged Stokeslets is applied to the low Reynolds number flows about a set of spheres. Newtonian fluid is considered with no slip or partial slip boundary conditions at the wall. The validity of the method for Stokes flows about representative sets of spheres is investigated. The considered cases include (i) a uniform flow about a stationary set of particles typical for filtration and chemical vapor deposition, (ii) a flow induced by particles moving toward each other typical for self-assembly processes and (iii) a flow induced by spinning particles typical for micro-pump applications. The dependence of the flowfield on the number of Stokeslets is investigated in order to establish the needed number of Stokeslets. Comparison of flow field for the no-slip (Kn = 0) and partial-slip boundary conditions (Kn = 0.1) shows that the partial slip at the particles' surface significantly affect the velocity field and pressure distribution.

Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Boundary Conditions ◽  
Friction Factor ◽  
Knudsen Number ◽  
Velocity Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
First Order ◽  
Slip Boundary

In this paper, first, the Navier–Stokes equations for incompressible fully developed flow in microchannels and microtubes with the first-order and second-order slip boundary conditions are analytically solved. Then, the compressible Navier–Stokes equations are numerically solved with slip boundary conditions. The numerical methodology is based on the control volume scheme. Numerical results reveal that the compressibility effect increases the velocity gradient near the wall and the friction factor. On the other hand, the increment of velocity gradient near the wall leads to a much larger slip velocity than that for incompressible flow with the same value of Knudsen number and results in a corresponding decrement of friction factor. General correlations for the Poiseuille number (fRe), the Knudsen number (Kn), and the Mach number (Ma) containing the first-order and second-order slip coefficients are proposed. Correlations are validated with available experimental and numerical results.

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.

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