Heat transfer in rock masses: Application to the Lascaux Cave (France)

Abstract

The conservation of prehistorical painted caves is a major issue for the history of mankind. Alterations, which can appear on walls, mainly result from the thermal convection taking place in caves. The convection in caves depends on the difference between the temperatures of the walls which mainly stem from the heat conduction in rock masses. In literature, this problem is currently solved with a uni-dimensional homogeneous model where the outside air temperature is the only source of energy. Here, based on the literature in other fields, we show that the ground surface temperature cannot be considered as equal to the outside temperature. Radiation, convection and water evaporation indeed figure prominently in the process. The mathematical guideline giving the topsoil temperature is detailed. In addition, we propose a mathematical assumption to ensure energy conservation. A simple experimental setup allowing the circumvention of this complex procedure is also suggested. Then, we apply the widely used uni-dimensional homogeneous thermal diffusion model, with the proposed ground surface temperature calculation, to the Lascaux Cave. The comparison between the measurements in the first meter below the ground surface and the calculated temperatures shows a good agreement. Within the cave, the model successfully predicts the temperature measured by a few thermocouples. For others, there are significant discrepancies, which seem to indicate that the homogeneous hypothesis is not precise enough to describe rock masses. The heterogeneity of the Lascaux Cave massif will thus need to be thermally investigated.