Revisiting the Temperature Gradient Method

Abstract

Abstract Cooling curve analysis has emerged as a preferred method to characterize the cooling power of quenching media. This methodology is based on measuring the local cooling curve in a laboratory-scale probe using thermocouples. Several methods have been proposed to analyze cooling curves. Among them, the temperature gradient method (TGM) developed by Professor Liščić uses cooling curves measured at the surface and 1.5 mm below the surface of a cylindrical probe (the Liščić-Nanmac probe) to calculate the surface heat flux during quenching. In this work, we measured the thermal response at a location near the surface of cylindrical probes, fabricated with AISI 304 stainless steel, with two different geometries (conical- and hemispherical-end) during quenching from 850°C with water at 60°C, flowing parallel to the probe’s longitudinal axis. Together with the probe geometry, the experimental matrix included two values of water velocity (0.2 and 0.6 m/s). The data was used to estimate the surface heat flux and thermal response at the probe surface by solving a one-dimensional inverse heat conduction problem (IHCP) without phase change. The TGM was then applied to re-estimate the surface heat flux using the cooling curves at the subsurface (measured) and at the surface (estimated by solving the IHCP). The surface thermal gradient computed solving the IHCP is higher and, therefore, the surface heat flux estimated solving the IHCP is also higher than the value calculated with the TGM. The hemispherical-end probe delays the rupture of the vapor film, producing low values of the surface temperature at the time of maximum heat extraction; this results in extremely high values of the heat-transfer coefficient, which precludes the use of this geometry in conjunction with the TGM. The thermal profiles are parabolic, which restricts the maximum depth at which a subsurface thermocouple may be placed to use the TGM confidently.