Determination of Thermal Boundary Conditions Using Piecewise Hermite Polynomials During the Air Transfer Step of an Industrial Quenching Process

The study herein presents the identification of the thermal boundary conditions during the air travel step before quenching by immersion under an industrial environment. The experimental characterization was done with quench probes instrumented with multiple in-body thermocouples and tested in situ to account for the uneven cooling during the air transfer. A fast-converging numerical approach using an exhaustive search algorithm was developed to solve the inverse heat transfer problem thus estimating the unknown thermal boundary conditions. The approach reconstructs the surface temperature based on the Hermite polynomials whose control points were determined as per the system movements and the underlying physics. The solver considers near-solution starting values obtained from converting the test data at subsurface locations into mathematical expressions, thereby bounding the solution domain. The proposed methodology minimizes the root mean square error (RMSE), it produces RMSE < 2 °C and peak max/min errors <3.5 °C confirming the accuracy of the procedure. Findings demonstrate the need to consider the heterogeneous conditions even for specimens that qualify for lumped capacitance analysis (Bi < 0.1). The irradiative effects can produce a difference in heat flux magnitude in the range of 10-35% between surfaces. This tendency has appeared for values of the Bi number between 0.05 and 0.08.