A novel configuration of Knudsen pump is numerically studied in this paper. The pumping element consists of two facing isothermal ratchet surfaces at different temperatures. Since the main practical difficulty associated with traditional Knudsen pumps which refers to the necessity to accurately control the temperature gradient imposed along the walls of the device, the possibility of independently heating or cooling two distinct surfaces can be considered as a turnaround point in the design simplification of such new generation pumps. The micrometric dimensions of the pump provide the necessary conditions for obtaining rarefied gas inside the device and the asymmetric saw-tooth-like surfaces provide the optimal geometrical conditions in order to create temperature inequalities along the flow that finally engender a macroscopic gas movement. The rarefied flow is numerically investigated by Direct Simulation Monte Carlo (DSMC) in a large range of Knudsen number. The mass flowrate reaches a maximum value for a Knudsen number around 0.1 and becomes negative for a Knudsen number close to unity. A bidirectional flow depending on the Knudsen number value is observed and described. The temperature distributions, flow patterns and generated flow rate are investigated for different Knudsen numbers and also with different accommodation coefficients on vertical and inclined walls of the ratchet surfaces. The results are sensitive to the local boundary conditions.