Temperature distribution inside and around a lava tube

We propose a model describing the thermal effects of a lava tube. The tube is a circular cylinder, embedded in a solid medium and filled with a Newtonian liquid flowing under the gravity force. Steady-state conditions are considered. The velocity field in the tube, evaluated by the Navier–Stokes equation, is introduced into the heat equation taking into account the viscous dissipation. The temperature distribution is evaluated both inside the tube and in the surrounding solid medium. Under the assumption that the lava tube is embedded in a solid half-space, the surface heat flow due to the presence of the tube is calculated. It is shown that heat flow measurements at the Earth’s surface can give information on the depth, size and temperature of the buried lava tube.