Heat Flow Model for Surface Melting and Solidification of an Alloy
- PDF / 883,274 Bytes
- 9 Pages / 603.28 x 788 pts Page_size
- 49 Downloads / 192 Views
I.
INTRODUCTION
g number of investigations have addressed the heat flow problems in a semi-infinite substrate material subjected to stationary and moving high intensity heat fluxes. Major criticisms of the models developed include the use of temperature independent thermal properties, neglection of the heat of fusion and the inability to address the problem of an alloy substrate that melts and solidifies over a range of temperatures. In this investigation, an earlier model for the stationary transient heat flow problem during rapid melting and solidification of a pure material was extended to an alloy system with a "mushy" zone in which the heat of fusion is absorbed and liberated over a range of temperatures. The equations and solution methodology developed are general enough to be applicable to a variety of other solidification processing problems. In general, most mathematical formulations of surface melting have been aimed at the determination of the thermal fields, especially the position and shape of the liquid/solid interface in a pure substrate material. A one-dimensional analog computer program was developed by Cohen ~to investigate the temperature distribution in the molten surface layer and solid substrate during melting of a semi-infinite solid subjected to a step function heat input. These thermal profiles were subsequently used by other investigators to estimate average cooling rates during solidification by neglecting the heat of fusion. 2 A one-dimensional heat flow model that accounts for the heat of fusion was recently proposed by Hsu et al. 3 This model employs the "approximate integral technique" coupled with the numerical technique developed by Murray and Landis4 for the melting and solidification of a pure metal. For the case of a moving heat flux, Cline and Anthony5 constructed a solution by J.A. SEKHAR is Senior Development Engineer, Howmet Turbine Components Corporation, Whitehall, MI 49461; S. KOU is Assistant Professor, Department of Metallurgical and Materials Science, CarnegieMellon University, Pittsburgh, PA 15213; and R. MEHRABIAN is Director, Center for Materials Science, National Bureau of Standards, Department of Commerce, Washington, DC 20234. Manuscript submitted September 24, 1981. METALLURGICALTRANSACTIONS A
superimposing the solution of a point source at different times and positions. They, however, neglected the effect of the heat of fusion and assumed identical thermal conductivities for the solid and the liquid. More recently Gnanamuthu et al 6 used equations given in Carslaw and Jaeger7 to develop a numerical solution for heating and cooling of a steel substrate. Finally, other schemes for pulsed or continuous heat sources, which also neglect the heat of fusion, have been proposed. 8'9 In two recent papers, S.C. Hsu et a/l~ developed numerical solutions for melting and solidification of the surface layer of a pure metal by uniform and Gaussian heat flux distributions using an enthalpy model proposed by Shamsundar and Sparrow.~2 In this model, the enthalpy is used as a d
Data Loading...
