The fluid flow and heat transfer inside a saturated porous impermeable conduit at constant surface heat flux was modeled analytically and numerically. The present model was depicted the fluid flow and the temperature distribution through both of the entrance region and the fully developed region. The Nusselt number was found in both regions subjected to constant surface heat flux boundary condition. The present modeling was developed by using; the Continuity, Momentum and Energy equations. The equations were in two dimensions-cylindrical coordinate, both of Darcy model and Forchheimer model were studied, and the Nusselt number was found ,analytically and numerically by using finite deference scheme, according to the conditions of constant surface heat flux, as approximately decaying exponentially along the conduit length until it reaches to the value (8). Furthermore, the temperature profile was depicted.