Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Hettiarachchi, Hiroshan; Golubovic, Mihajlo; Worek, William M.; Minkowycz, W. J.

doi:10.1016/j.ijheatmasstransfer.2008.02.049

Cited by 76 publications

(51 citation statements)

References 26 publications

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“…A schematic representation of the previous state for slip velocity values is illustrated in Figure 2; moreover it highlights the difference between the no-slip and the slip boundary conditions. Mathematically, the Maxwell model is described for the dimensionless slip velocity U s as follows [1,7,12,14] …”

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

“…where U w denotes the velocity on the wall surface, K n is the Knudsen number and ∂Us ∂n the transverse velocity gradient, i.e., the derivative of the tangential slip velocity normal to the wall surface (denoted by vector n) [12]. Further, σ u is the tangential momentum accommodation coefficient (equal to unity in this study) [13,19], which actually models the momentum exchange of the gas molecules impinging on the solid boundaries.…”

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

“…The second term includes the values of the dimensionless Reynolds Re and Eckert E c numbers, along with the ideal gas constant γ and the tangential to the wall surface derivative of the temperature. It actually represents the slip velocity contribution induced by the thermal creep; it appears usually to be relatively small, due to the second-order in Knudsen number as well as due to the fact that in common engineering problems there is a small temperature change across the wall surfaces; therefore, in this study it is neglected [12]. The temperature jump boundary conditions are defined similarly to the slip velocity ones as [12] …”

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

“…Despite the main concept of the aforementioned conditions was initially proposed by Navier [1], the first corresponding mathematical model was introduced by Maxwell in 1879 [7]; according to this approach the values of slip velocity and temperature are defined with the corresponding normal to the boundary surface gradients [3]. Since then, various studies have been conducted on the prediction of the attitude of rarefied gases,focusing on the utilization of two-or three-dimensional computational fields, structured or unstructured grids, various geometries, etc., [8,9,10,11,12,13]. Furthermore, significant efforts have been exerted for the development of higher-order spatial schemes to increase the accuracy of the final steady-state solution at the region of the solid wall boundaries [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Klothakis¹,

Lygidakis²,

Nikolos³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. During the last decades considerable efforts have been exerted for the development of micro air vehicles as well as microelectromechanical systems in general, for a wide range of applications. However, such systems involve microscale rarefied gas flows, which appear to be significantly different comparing to flows at macroscale and continuum regime; it is this the reason the Navier-Stokes equations fail to simulate such phenomena without further modification. To this end, the enhancement of the in-house academic Computational Fluid Dynamics solver Galatea to encounter such simulations is reported in this study. In case of rarefied gas flows and particularly for fluids in slip flow regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip conditions as well as temperature jump ones have to be included instead. Furthermore, to increase accuracy at the same region the second-order accurate spatial slip model of Beskok and Karniadakis has been incorporated, which avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered. Due to oscillations that might appear, especially during the initial steps of the iterative procedure, a normalization scheme is additionally employed, to allow for the gradual increase of the corresponding slip/jump values. Galatea has been validated against a benchmark test case concerning rarefied laminar flow (inside the slip flow regime) over a wing with a NACA0012 airfoil in different angles of attack. The obtained results were compared with those of a reference solver, and with those obtained with the paralleld open-source kernel SPARTA, based on the Direct Simulation Monte-Carlo method. According to this last approach, the flow domain is divided into a finite number of computational cells, while the required sample macroscopic flow properties are retrieved assuming intermolecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by Galatea and SPARTA as well.

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Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

Section: Velocity Slip and Temperature Jump Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Klothakis¹,

Lygidakis²,

Nikolos³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Its applications are found in a wide range of areas, such as electronic systems, biochemical processes, computer chips, micro-electromechanical systems, optoelectronics, and chemical separations. In micro-and nano-sized channels, one of the major difficulties in the flow prediction is due to the rarefaction effects that occur when the channel dimensions are comparable to the mean free path of the fluid molecules [1]. The continuum assumption is no longer valid and the gas exhibits non-continuum effects, such as velocity slip and temperature jump, at the channel walls.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional simulation of slip-flow and heat transfer in a microchannel using the lattice Boltzmann method

Sousa¹,

Hadavand²,

Nabovati³

2010

Advanced Computational Methods and Experiments in Heat Transfer XI

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In micro-and nano-flows, since the molecular mean free path is comparable to the system's characteristic length, the effect of rarefaction should be considered. In this category of flows, the continuum assumption is no longer valid; therefore, heat transfer, velocity profile and pressure drop markedly and depart from those which are common to macro-flows. Rarefaction may occur in various applications, such as in zero gravity flights and vacuum devices. This phenomenon can occur at the wall surfaces when the Mach number is sufficiently small, which is the case of interest in this study. In these conditions, at the solid-fluid interfaces, the fluid has a slip velocity and a temperature jump is also present. Three-dimensional, thermally developing incompressible laminar flows in a square microchannel with constant temperature walls are studied numerically using the lattice Boltzmann method. The effect of rarefaction on the velocity and temperature distributions and on the Nusselt number is analysed. The LBM predictions are compared with those obtained using the Navier-Stokes equations with the slip condition for the same configuration. The results indicate that an increase of the slip velocity yields an increasing Nusselt number, whereas an increase of the temperature jump has the opposite effect on the Nusselt number values; therefore, the combined result of these two competing effects may yield an increase or decrease on the Nusselt number.

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Effects of Viscous Dissipation and Rarefaction on Parallel Plates with Constant Heat Flux Boundary Conditions

Kushwaha

Sahu

2014

Chem Eng & Technol

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The effect of viscous dissipation and rarefaction on heat transfer characteristics of hydrodynamically and thermally fully developed flow between parallel plates with constant heat flux conditions is analyzed. Three different types of heat flux boundary conditions, i.e., both plates kept at different constant heat fluxes, both plates kept at equal constant heat fluxes, and one plate insulated, are applied. In all cases, closed form expressions are obtained for the temperature distribution and Nusselt number. Viscous dissipation, rarefaction, and heat flux ratio are found to influence the heat transfer substantially. The present predictions are verified for the cases which neglect the microscale and viscous heating effect. The obtained results are in good agreement with other analytical results.

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Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Cited by 76 publications

References 26 publications

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Three-dimensional simulation of slip-flow and heat transfer in a microchannel using the lattice Boltzmann method

Effects of Viscous Dissipation and Rarefaction on Parallel Plates with Constant Heat Flux Boundary Conditions

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