Journal Published Online: 09 October 2018
Volume 8, Issue 2

Mathematical Modeling of the Thermal Response of Laboratory-Scale Probes



Experiments for cooling curve analysis of laboratory-scale quenched probes produce a wetting front that advances at a finite velocity along the longitudinal axis of the probe as cooling progresses. The wetting front velocity depends on probe material and geometry as well as the type of quenchant, its temperature, and agitation. Because of the wetting front, the mathematical model of the direct heat conduction problem to compute the evolution of the thermal field within the probe may be characterized as a moving front boundary problem. In this work, cooling curves at three subsurface locations along the length of conical-end cylindrical probes, fabricated with AISI 304 stainless steel, during quenching from 850°C with water at 60°C flowing parallel to the probe’s longitudinal axis were measured. A fourth thermocouple located at the geometrical center of the probe was used to validate the model. Two values of free-stream water velocity (0.2 and 0.6 m/s) were studied. As a first approximation, the measured cooling curves were used to estimate the corresponding surface heat flux histories by solving three separate 1-D inverse heat conduction problems. Then, the thermal field evolution within the probe was computed by solving a 2-D axis-symmetrical heat transfer model. The boundary condition at the probe surface was modeled with a composite mapping of the surface heat flux histories. The surface heat flux history estimated for the lower section of the cylindrical part of the probe was applied as a boundary condition for the probe tip. It was found that the cooling curve at the lowest thermocouple position was overestimated; thus, the surface heat flux history for the probe tip was divided by 1.2 to correctly model the thermal response. The model was successfully validated by comparing measured and computed cooling curves for the thermocouple located at the probe’s geometrical center.

Author Information

Hernández-Morales, B.
Facultad de Química, Departamento de Ingeniería Metalúrgica, Universidad Nacional Autónoma de México, Ciudad de México, México
Cruces-Reséndez, R.
Facultad de Química, Departamento de Ingeniería Metalúrgica, Universidad Nacional Autónoma de México, Ciudad de México, México
Vergara-Hernández, H. J.
Instituto Técnológico de México/I.T. Morelia, División de Estudios de Posgrado e Investigación, Morelia, Michoacán, México
Pages: 16
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Stock #: MPC20180030
ISSN: 2379-1365
DOI: 10.1520/MPC20180030