Modeling Heat Transfer for Assessing the Convection Length in Ventilated Caves

The present study focuses on heat transfer in ventilated caves for which the airflow is driven by the temperature contrast between the cave and the external atmosphere. We use a numerical model that couples the convective heat transfer due to the airflow in a single karst conduit with the conductive heat transfer in the rock mass. Assuming dry air and a simplified geometry, we investigate the propagation of thermal perturbations inside the karst massif. We perform a parametric study to identify general trends regarding the effect of the air flowrate and conduit size on the amplitude and spatial extent of thermal perturbations. Numerical results support the partition of a cave into three regions: (a) a short (few meters) diffusive region, where heat mainly propagates from the external atmosphere by conduction in the rock mass; (b) a convective region where heat is mainly transported by the air flow; (c) a deep karst region characterized by quasi-constant temperatures throughout the year. Numerical simulations show that the length of the convective region is approximately proportional to the amplitude of the flowrate annual fluctuations divided by the square root of the cave radius. This result is tested against field data from a mine tunnel and two caves. Our study provides first estimates to identify climate sensitive regions for speleothem science and/or ecosystemic studies.