Mathematical Modeling of Surface Heat Flux During Quenching

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G is one of the important industrial processes in which the heat-transfer rate plays a vital role in the development of microstructure and mechanical properties of the quenched product. Immersion quenching is one of the most widely used processes to achieve martensitic and bainitic steels in which the cooling rate has a decisive influence on the material properties. Computer simulation of the quenching process requires the specification of accurate boundary conditions. The surface heat-transfer coefficients or heat fluxes between the quench surface and quenchant are regarded as key parameters for the numerical simulation of the quenching process. Heat transfer during quenching is complex and is controlled by different cooling mechanisms. Quenching of steel in water consists of the following three distinct stages of cooling: (1) the vapor phase, (2) the nucleate boiling, and (3) the convective stage. The parameters that affect the heat transfer during quenching may include surface temperature, surface condition of the specimen, agitation of the quenchant, thermophysical properties of the quenchant, and the materials being quenched. Estimation of the surface heat flux or heat-transfer coefficient from the measured temperature data during quenching is based on the inverse heat-conduction problem. Various algorithms to solve inverse heatconduction problems have been well documented by K. BABU, Research Scholar, and T.S. PRASANNA KUMAR, Professor, are with the Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai 600 036, India. Contact e-mail: [email protected]. Manuscript submitted April 28, 2009. Article published online November 24, 2009. 214—VOLUME 41B, FEBRUARY 2010

Beck[1] and have successfully been implemented by many researchers.[2–9] Prasanna Kumar[3] described a serial solution method for the two-dimensional (2D) inverse heat-conduction problem to estimate multiple heat-flux components and used it to estimate heat-flux components at the metal–mold interface during casting.[4,5] Sarmiento et al. estimated the temperature-dependent heat-transfer coefficient during quenching from the measured cooling curves and compared the results of the two computer programs developed for the computation.[6] The heat-flux transients obtained through the inverse technique were more accurate than the Grossmann technique in determining the quench severity of various quenchants; also, it could be used for heattransfer modeling during quenching.[8] A mathematical model to quantify the heat-transfer coefficient during quenching as a function of nondimensional surface temperature was developed by Prasanna Kumar.[9] Cheng et al.[10] showed that the heat-transfer coefficient had a peak value, and its corresponding temperature interval varied with the cross-section dimension of the work piece, quenchant type, and axial position of the specimen being quenched. Sedighi and McMahon[11] studied the effect of part orientation and quenchant circulation on the heat-transfer rate during the quenching of steels and gave d