On the heat transfer to the wheel in planar-flow melt spinning
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I.
INTRODUCTION
I N planar-flow spin casting, in contrast to the chill-block method, the nozzle slot from which the molten metal is forced under pressure is brought so close to the chill wheel that the nozzle face interferes with the puddle of liquid metal on the wheel. This feature leads to better control and stability of the flow and to the ability to produce much wider r i b b o n s - - a characteristic which has distinguished the planar-flow technique and which is widely recognized. On the other hand, it may not be sufficiently appreciated that this modification of the chill-block configuration also significantly changes the heat-transfer characteristics of the planar-flow process; in particular, it increases the demands on the efficiency of heat transfer to the wheel. The purpose of this note is to show that lower bounds on the heat transfer to the chill wheel, obtained by elementary heat-balance arguments, give technologically useful restrictions on the heat-transfer coefficient. Heat-transfer coefficients typically account for combined modes of heat exchange in situations where a detailed description of the thermal physics would be rather complicated. In planar-flow melt spinning, the coefficient of heat transfer to the wheel, H , is defined as the ratio of the heat flux from the metal (liquid or solid) across its boundary (interface) with the wheel, q, to the difference between the temperature at that boundary, T, and the nominal steady temperature of the chill wheel, T~ (Figure 1). q = n ( x ) ( T - Tr
[1]
This coefficient includes conduction and radiation of heat (it can depend on temperature) as well as any convective effects. In particular, influences of nonideal contacting, such as air entrainment at the metal/chill interface, are also included. Such combinations of heat-transfer modes are difficult to model even if one knows which effects are operable. Furthermore, values of the heat-transfer coefficients are difficult to measure with confidence. Techniques range from those based on photocalorimetric or pyrometric measurements to those based on dendritic arm or interJ.K. CARPENTER, formerly with Comell University, is with Rohm and Haas Company, Bristol, PA, 19007. P.H. STEEN, Associate Professor, is with the School of Chemical Engineering, Cornell University, Ithaca, NY 14853. Manuscript submitted June 26, 1989. METALLURGICAL TRANSACTIONS B
lamellar spacings, t1'2} None of these methods is particularly accurate; measurements often have an order of magnitude uncertainty, t3} In view of these difficulties, the estimates developed in this note may be useful as checks on measurements and predictions, as well as design criteria. The main difference between the chill-block and planarflow techniques, as far as heat transfer is concerned, involves the heat flux on the top side of the puddle. In planar flow, the molten metal is confined on top by the hot nozzle face which, being a good heat conductor (e.g., graphite or quartz) relative to the surrounding atmosphere ( e . g . , air or argon), may be taken
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