Non-intrusive estimate of spatially varying internal heat flux in coiled ducts: Method of fundamental solutions applied to the reciprocity functional approach

Wall curvature is a widely used technique to passively enhance convective heat transfer that has also proven to be effective in the thermal processing of highly viscous fluids. These geometries produce a highly uneven convective heat-flux distribution at the wall along the circumferential coordinate, thus affecting the performance of the fluid thermal treatment. Although many authors have investigated the forced convective heat transfer in coiled tubes, most of them have presented the results only in terms of heat flux density averaged along the wall circumference. The estimation of the heat exchanger performances requires the proper knowledge of the thermo-fluid dynamic interaction between fluid and device. One of these aspects is related to the estimation of the internal convective heat flux: unfortunately, this quantity is really complicated to measure. One of the most challenging applications requires the solution of the inverse heat conduction problem. This approach deals with the estimation of the local internal properties, given the external temperature measurements, possibly by means of contactless experimental methodologies (i.e. infrared camera imaging). The solution strategy presented here is based on the reciprocity functional approach, which requires the solution of a sequence of auxiliary problems, solved in this paper by means of the method of fundamental solutions. Its adoption permits to obtain a very effective estimation of the local heat flux with a small computational effort.