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Micro/nano geometries with specified wall heat flux are widely encountered in electronic cooling and micro-/nano-fluidic sensors. We introduce a new technique to impose the desired (positive/negative) wall heat flux boundary condition in the DSMC simulations. This technique is based on an iterative progress on the wall temperature magnitude. It is found that the proposed iterative technique has a good numerical performance and could implement both positive and negative values of wall heat flux rates accurately. Using present technique, rarefied gas flow through micro-/nanochannels under specified wall heat flux conditions is simulated and unique behaviors are observed in case of channels with cooling walls. For example, contrary to the heating process, it is observed that cooling of micro/nanochannel walls would result in small variations in the density field. Upstream thermal creep effects in the cooling process decrease the velocity slip despite of the Knudsen number increase along the channel. Similarly, cooling process decreases the curvature of the pressure distribution below the linear incompressible distribution. Our results indicate that flow cooling increases the mass flow rate through the channel, and vice versa. [ABSTRACT FROM AUTHOR]