We present a numerical study of the cooling of a volume of water through the wall of a cylindrical terracotta tube, the pores of which are saturated with water. The internal surface of the wall carries a water film which evaporates by forced convection of hot and dry air. Taking into account the physical properties of the material and that the aspect ratio of the tube used has a maximum value (D/L= 0.32), variations of the thermophysical properties of the air between the entry and the exit of the tube are ignored. The mathematical model describing the physical processes is based on the Darcy equation of fluid flow through a saturated porous material, the equation of Laplace related to pressure and the equation of heat in polar coordinates. One can then describe the space-time evolution of the field of temperature inside the wall as well as the temporal evolution of the average temperature …