Estimation of transient temperature distribution during quenching, via a parabolic model

A material-independent model to estimate the transient temperature distribution in a test probe quenched by immersion is presented in this study. This model is based on the assumption that, under one-dimensional unsteady heat conduction, the radial temperature distribution at the end of an interval belongs to the equation of a parabola. The model was validated using AISI 304 stainless steel test probes (Φ8×40 mm and Φ12×60 mm) quenched from 850 to 900 °C in water and in water-based NaNO₂ solutions at 25 °C and in canola oil at 50 °C. Additionally, square test probes (20×20×100 mm) were quenched from 550 °C in water. The test probes were equipped with embedded thermocouples for temperature-versus-time data logging at the core, one-quarter thickness and 1 mm below the surface. In each experiment, the data recordings from the core and near-surface thermocouples were employed for the temperature calculations while the data from the one-quarter thickness thermocouple were employed for model validity verifications. In all cases, the calculated temperature distributions showed good correlations with the experimentally obtained values. Based on the results of this work, it is concluded that this approach constitutes a simple, quick and efficient tool for estimating transient surface and radial temperature distributions and represents a useful resource for quenchant cooling rate calculations and heat transfer characterizations.