Natural convection effects in the heat transfer from a buried pipeline

In the present paper, the effect of the buoyancy on the heat transfer from a buried pipeline is investigated. The soil surrounding the pipe is modelled as a porous medium saturated by water, and the Darcy's law is assumed. Reference is made to a time-varying temperature distribution on the soil surface, and uniform and constant temperature on the pipe wall. The steady state regime is investigated as particular case. The heat power per unit length is evaluated for different values assumed by the Darcy-Rayleigh number, thus revealing that, for high values of Ra, the natural convection effects are non trivial. A comparison with the case of pure conduction is made for the limiting case of a vanishing value of Ra, revealing an excellent agreement.