Melting trajectory of the asymmetrically-heated conical thermal head for ice-melting probes

The development of ice-melting probes is driven by the scientific need to explore the subglacial aquatic environments, such as the subglacial lakes in Antarctica and subglacial water on some extraterrestrial planets. However, during the downward melting, a deviation of the melting trajectory might occur. If left unaddressed, the accumulated deviation will eventually lead to missing the probe's target. Therefore, it is necessary to build a theoretical model to describe the deviation for predicting the future melting trajectory and building the deviation correction system. The deviation comes from any asymmetric heating condition on the melting head. Generally, the Close-Contact Melting (CCM) theory is used to model the probe's melting process without any deviation, and there is only one attempt so far that applies the CCM theory to asymmetric heating conditions. Based on this initial attempt, we successfully expanded the CCM theory with asymmetric temperature profiles to conical thermal heads. Additionally, we simplified the model solving which leads to fewer influence factors compared to existing studies. The model indicates that the melting trajectory of a conical head is linear under asymmetric heating conditions, and the inclination angle of the trajectory is related to the ratio between the head's temperatures on each side and the head's cone angle. To validate the theoretical results, laboratory experiments have also been conducted with an innovative optical positioning method.