Axial flow in a two-dimensional microchannel induced by a travelling temperature wave imposed at the bottom wall

TY - JOUR

T1 - Axial flow in a two-dimensional microchannel induced by a travelling temperature wave imposed at the bottom wall

AU - Zhang, Chenguang

AU - Wong, Harris

AU - Nandakumar, Krishnaswamy

N1 - Publisher Copyright: © 2018 Cambridge University Press.

PY - 2018/8/10

Y1 - 2018/8/10

N2 - Fluid flow in microchannels has wide industrial and scientific applications. Hence, it is important to explore different driving mechanisms. In this paper, we study the net transport or fluid pumping in a two-dimensional channel induced by a travelling temperature wave applied at the bottom wall. The Navier-Stokes equations with the Boussinesq approximation and the convection-diffusion heat equation are made dimensionless by the height of the channel and a velocity scale obtained by a dominant balance between buoyancy and viscous resistance in the momentum equation. The system of equations is transformed to an axial coordinate that moves with the travelling temperature wave, and we seek steady solutions in this moving frame. Four dimensionless numbers emerge from the governing equations and boundary conditions: the Reynolds number Re, a Reynolds number Rc based on the wave speed, the Prandtl number Pr and the dimensionless wavenumber K. The system of equations is solved by a finite-volume method and by a perturbation method in the limit Re→0. Surprisingly, the leading and first-order perturbation solutions agree well with the computed axial flow for Re ≤ 103. Thus, the analytic perturbation solutions are used to study systematically the effects of Re, Rc, Pr and K on the dimensionless induced axial flow Q. We find that Q varies linearly with Re, and Q/Re versus any of the three remaining dimensionless groups always exhibits a maximum. The global maximum of Q/Re in the parameter space is subsequently determined for the first time. This induced axial flow is driven solely by the Reynolds stress.

AB - Fluid flow in microchannels has wide industrial and scientific applications. Hence, it is important to explore different driving mechanisms. In this paper, we study the net transport or fluid pumping in a two-dimensional channel induced by a travelling temperature wave applied at the bottom wall. The Navier-Stokes equations with the Boussinesq approximation and the convection-diffusion heat equation are made dimensionless by the height of the channel and a velocity scale obtained by a dominant balance between buoyancy and viscous resistance in the momentum equation. The system of equations is transformed to an axial coordinate that moves with the travelling temperature wave, and we seek steady solutions in this moving frame. Four dimensionless numbers emerge from the governing equations and boundary conditions: the Reynolds number Re, a Reynolds number Rc based on the wave speed, the Prandtl number Pr and the dimensionless wavenumber K. The system of equations is solved by a finite-volume method and by a perturbation method in the limit Re→0. Surprisingly, the leading and first-order perturbation solutions agree well with the computed axial flow for Re ≤ 103. Thus, the analytic perturbation solutions are used to study systematically the effects of Re, Rc, Pr and K on the dimensionless induced axial flow Q. We find that Q varies linearly with Re, and Q/Re versus any of the three remaining dimensionless groups always exhibits a maximum. The global maximum of Q/Re in the parameter space is subsequently determined for the first time. This induced axial flow is driven solely by the Reynolds stress.

KW - channel flow

KW - convection

KW - microfluidics

UR - http://www.scopus.com/inward/record.url?scp=85048815939&partnerID=8YFLogxK

U2 - 10.1017/jfm.2018.390

DO - 10.1017/jfm.2018.390

M3 - 文章

AN - SCOPUS:85048815939

SN - 0022-1120

VL - 848

SP - 1040

EP - 1072

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -