Nonstationary hot wire method with silica-coated probe for measuring thermal conductivities of molten metals
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I. INTRODUCTION
THE mathematical modeling of heat flow in high-temperature processes has led to improvements in process control, product quality, and conservation of energy and natural resources. Two examples are the modeling of (1) heat transfer across the interface between solid and liquid silicon in the Czochralski process to grow high-quality silicon single crystals, and (2) heat flow in aluminium and its alloys in casting processes. Both of these have a decisive effect on the quality of the products. In the on-going development of these models, one of the primary requirements at the moment is for accurate values for thermal conductivities of the materials in liquid state. The paucity of reliable thermal conductivity data for commercial materials involved in these processes is a reflection of the difficulties in measuring accurate values for molten metals, especially at high temperatures. Thermal conductivities of molten metals have often been measured conventionally using steady-state methods,[1] particularly using the concentric cylinder method due to instrument simplicity.[2,3,4] In this method, the instrument consists of two concentric cylinders, where a sample is placed between the outer and inner cylinders and the former is usually heated. The thermal conductivity of the sample can be determined from the generated heat and temperature difference between the two cylinders after the steady state is attained. However, it has been known that in steady-state methods, convection has a significant effect on thermal conductivities of liquids even at room temperature, leading to overestimation of thermal conductivity values. The problem of convection is much more serious at high temperatures, because accurate temperature control becomes progressively more difficult as temperature increases. Transient techniques, such as the laser flash method and the nonstationary hot wire method, have proved useful in minimizing thermal conductivity errors due to convection.[1,5] In recent years, the laser flash method has been EIJI YAMASUE, Graduate Student, and MASAHIRO SUSA, Associate Professor, Department of Metallurgical Engineering, and HIROYUKI FUKUYAMA, Associate Professor, and KAZUHIRO NAGATA, Professor, Department of Chemistry and Materials Science, are with the Tokyo Institute of Technology, Tokyo 152-8552, Japan. Manuscript submitted September 15, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
used to determine thermal conductivities of molten metals by holding the melt in silica cassettes.[6,7] This is a wellestablished method for solid metals, but for molten metals, the following problems could be encountered. (1) Precise measurements of the heat capacity and density are difficult for molten metals at high temperatures, although these data are required to determine the thermal conductivity. (2) Errors due to convection are possible. (3) Nonwetting conditions tend to cause difficulty in maintaining the shape of molten metal samples. (4) Carbon on the sample surface used to eliminate reflection of the laser may no
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