A vertical straight circular adiabatic vertical long tube, open at its lower and upper ends, is heated at its base on a short portion. The flow is studied with the hypothesis of no pressure drop between the entrance and the exit. Direct resolution of Navier Stokes equations is done by finite volumes. The numerical solutions are then compared to a one dimensional model and to two asymptotic models. The first asymptotic model is inspired from boundary layer approximations whereas the second one is more a linear perturbation of the Navier Stokes Boussinesq equations. For moderate values of the Grashof number, pressure, starting from zero decreases over the heated part to a minimum and increases on the adiabatic tube to zero. For larger values of Grashof, a local maximum in pressure appears, this pressure hump may even be positive. The four model agree, for moderate Grashof. When increasing the Grashof, only the two asymptotic models recover the behavior obtained from the numerical simulations.