Measurement and Modeling of Interface Heat Transfer Coefficients

"The results of preliminary work on the modeling and measurement of the heat transfer coefficients of metal/mold interfaces is reported. The system investigated is the casting of uranium in graphite molds. The motivation for the work is primarily to improve the accuracy of process modeling of prototype mold designs at the Los Alamos Foundry. The evolution in design of a suitable mold for unidirectional solidification is described, illustrating the value of simulating mold designs prior to use. Experiment indicated a heat transfer coefficient of 2 kW/m /K both with and without superheat. It was possible to distinguish between solidification due to the mold and that due to radiative heat loss. This permitted an experimental estimate of the emissivity, ~ = 0.2, of the solidified metal.IntroductionA feature that distinguishes casting processes from welding processes is the presence of an interface with a low heat transfer coefficient between the mold and the casting. Especially when chill casting, the interface delays the start of solidification and increases freezing times significantly. By comparison welds can be assumed to have a very high heat transfer coefficient. The heat transfer coefficient controls such phenomena as folds and laps on the surface of castings which can be crucial to the acceptability of a casting. The time delay for the start of solidification influences the occurrence of cold shut defects. The standard mold material for uranium casting is high quality graphite which is an excellent refractory when used in vacuum and coated with a refractory wash. Graphite is an effective chill material and has a thermal diffusivity approximately twice that of uranium. Experience has shown that practicable superheat without mold pre-heat is not sufficient for avoiding cold shut defects when casting in graphite molds.TheoryIt is possible to calculate the position of the freeze front s, as a function of time, t, the superheat and interface heat transfer coefficient, h, [1]. However, the value of h cannot be obtained explicitly. The Virtual Adjunct Method (VAM) [2] offers a method for extending the standard equation for an insulating mold where s is proportional to the square root of time. By considering the effect of the interface to be equivalent to finite thicknesses of mold and metal, the following quadratic equation is obtained,"