The flow of a gas in a grooved nano or micro channel, due to the imposed pressure and temperature gradients in the longitudinal direction, is investigated via a kinetic approach. The solution is valid in the whole range of the Knudsen number, from the free molecular regime through the transition and slip regimes up to the hydrodynamic regime. The flow has common characteristics with the classical Poiseuille and thermal creep problems but the presence of the rectangular grooves that are placed periodically in one of the two stationary walls results to a two-dimensional flow pattern. The problem is modeled by the linearized S model kinetic equation, which is solved for the perturbed distribution function by the discrete velocity method. Maxwell diffuse type reflecting boundary conditions are used to model the gas-surface interaction, while periodic boundary conditions are imposed at the inlet and outlet of the channel. The reported results include overall velocity streamlines and flow rates, which are estimated, in the whole range of the Knudsen number for various values of the depth and the length of the groove and the periodicity length of the channel. Several interesting flow patterns and characteristics are examined in terms of the geometrical parameters of the flow configuration.

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