Application of an Inverse Heat Conduction Solution with Laplace Transform Technique for a Steel Cooling Processes

Abstract

When we evaluate complicated cooling heat transfer characteristics of high-temperature steel with water, a solution of the inverse heat conduction problem (IHCP) is essential to specify the surface heat flux and surface temperature change with time from the measurement of the inside solid temperatures. In the present study, the analytical solution of the IHCP with the Laplace transform technique proposed by Monde is applied to steel cooling processes. This technique deals uniform and constant thermal properties of the solid, and the measured temperature change at two depths is approximated with half-power polynomials of time. The steel cooling processes show a very high cooling rate and a large temperature drop after quenching. Therefore, the temperature dependence of thermophysical properties could not be negligible, and much better accuracy of the approximate functions is also required for the complicated measured temperature history. We applied modifications to the analysis, such as a simple and explicit treatment of the temperature-depending properties and superimposing approximate functions. The accuracy of the modified technique was assessed for quenching temperature histories in a steel specimen. From the sensibility of approximation parameters constructing the superimposed functions, the optimum parameters were specified for the measured temperature of quenching experiments. The explicit treatment of the thermal properties ensures accurate estimation results for a higher cooling rate, in which the product of the temperature gradient near the surface and the temperature gradient of the thermal conductivity is small.