Quantification of the Surface Temperature Discrepancy Caused by Subsurface Thermocouples and Methods for Compensation
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IN recent years, design and control of many industrial processes have increasingly relied on computational modeling. Doing so has minimized the necessity to conduct ‘‘trial and error’’ experiments to comprehend the effects of various parameters and to develop controls that would ensure final product quality. Such is the case in metallurgical processing, wherein strict control in all processing stages, such as during water quenching, is critical in determining product outcomes. Water quenching, in particular, plays an important role in metallurgical manufacturing operations as a means of controlling the temperature during processing and the final alloy microstructure. Thus, accurate quantification of the heat-transfer boundary conditions (heat fluxes or heat-transfer coefficients) is critical in establishing proper control. However, the complex nature of boiling water heat transfer renders any accurate analysis of the boundary conditions during water quenching difficult. As a result, researchers are increasingly turning to inverse heat conduction (IHC) models to quantify the surface heat fluxes during boiling water heat transfer. G.A. FRANCO, M.A.Sc. Candidate, and E. CARON, Postdoctoral Candidate, are with the Centre for Metallurgical Process Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4. Contact e-mail: [email protected] M.A. WELLS, Associate Professor, formerly with the Centre for Metallurgical Process Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4, is with the Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Canada N2L 3G1. Manuscript submitted June 7, 2007. Article published online December 4, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B
The IHC models can estimate the heat-transfer boundary condition at a surface by using the thermal history at a known interior location. Thermal histories are typically obtained by installing thermocouples (TCs) at the base of holes drilled close to the sample surface (subsurface TCs), and collecting temperature-time data during a quench test. Thermocouples typically consist of two wires welded together at each end to form the TC junction. The wires are separated and surrounded by an insulating material to ensure that only the measurements at the TC junction are recorded. The thermal properties of the insulating material, which forms the bulk of the TC volume, are often different compared to the sample in which it is embedded. In particular, the thermal conductivity of metallic samples is significantly higher than the TC insulating material. Thus, the TC will, in essence, form a cavity in the sample that is of much lower thermal conductivity than the surrounding material. This can then create a disturbance in the local temperature field, particularly when the TC is oriented parallel to the direction of heat flux. The temperature disturbance caused by an embedded thermocouple is illustrated in Figure 1. Contour lines from top to bottom represent isotherms of increasing temperature. As
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