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

To explore driving mechanisms in microchannels, we studied the transport of fluid in a two-dimensional channel induced by a traveling temperature wave applied at the bottom wall. The Boussinesq approximation is used for the buoyancy effect. The system of equations is transformed to the coordinate moving with the temperature wave so time dependence is removed. 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<=1000. Thus, the analytic perturbation solutions are used to study systematically the effects of Re, Rc, Pr, and K on the axial flow Q. We find that Q varies linearly with Re, and Q/Re versus any of the three remaining dimensionless numbers always exhibits a maximum. The global maximum of Q/Re in the parameter space is determined for the first time. This axial flow exerts no net stress on channel walls and is driven solely by the Reynolds stress.