Invoking the velocity slip and temperature jump, numerical simulation of Darcy–Brinkman–Forchheimer flow model and forced convection in a circular micro/nano channel filled with porous media are presented. Relating the viscosity to the local Knudsen number, Kn, a generalized diffusion coefficient is obtained in such a way that it can model wide range of Kn regimes of flow. The effect of Kn and Darcy coefficient on velocity and temperature distribution is described. It is shown that despite of the fact that in most of previous researches it is assumed that Kn is constant along the channel, the variations of Kn due to the pressure variations, have considerable effects on heat transfer and temperature distribution across the channel cross section.