A high-order moment method is employed to construct the transport model for non-equilibrium gas flow in micro-scale geometries. The motion of a gas in a two-dimensional square micro-cavity is solved using the 26 moment equations for low Reynolds and Mach number flows in the early transition regime. The computed velocity and temperature fields are compared with data obtained from the direct simulation Monte Carlo method. It is found that the 26 moment equations are able to capture the non-equilibrium phenomena in a driven micro-cavity, such as counter-gradient heat transfer, which are not embedded in the Navier-Stokes-Fourier equations.

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