Estimation of the local heat-transfer coefficient in the laminar flow regime in coiled tubes by the Tikhonov regularisation method

Wall curvature is a widely used technique to passively enhance convective heat transfer that has proven to also 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 the Nusselt number averaged along the wall circumference. A procedure to estimate the local convective wall heat flux in coiled tubes is presented and tested in this paper: the temperature distribution maps on the external coil wall were employed as input data of the inverse heat conduction problem in the wall under a solution approach based on the Tikhonov regularisation method with the support of the fixed-point iteration technique to determine a proper regularisation parameter. The investigation was focused on the laminar flow regime.