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. Karsts are landscapes formed from the dissolution of soluble rocks. The chemical erosion due to rainwater results in the formation of an extensive network of caves traversed by air and water flows. Understanding heat transfer in karst is a key issue in many fields, as diverse as study of underground biota or paleoclimate reconstruction. The present work focuses on heat transfer in ventilated caves for which the airflow is driven by the temperature contrast between the cave and the external atmosphere. In winter, the air inside the massif is hotter (and thus lighter) than the air outside. This situation results in an upward airflow as in a chimney. The airflow is reversed in summer (colder and thus heavier air inside the massif). Assuming a simplified geometry, we investigate by numerical simulations the propagation of thermal perturbations inside a single ventilated conduit. The results of the numerical simulations are tested against field data from a mine and two caves. We show that in ventilated caves, the airflow can propagate the annual temperature fluctuations over distances from the entrance ranging from a few tens to a few hundreds of meters. In extreme cases, it could go up to kilometers. Our study provides first estimates to identify climate sensitive regions for speleothem science and/or ecosystemic studies. A numerical model was developed to investigate heat transfer inside ventilated caves driven by chimney effect The airflow can propagate annual temperature fluctuations over a few tens to a few hundreds of meters from the cave entrance (over kilometers in extreme cases) The distance of propagation (the convection length) is approximately proportional to the airflow rate and inversely proportional to the square root of the cave diameter