Research Papers

Substrate Heating in the Planar-Flow Melt Spinning of Metals

[+] Author and Article Information
Anthony L. Altieri

School of Chemical and
Biomolecular Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: Anthony.L.Altieri@gmail.com

Paul H. Steen

School of Chemical and
Biomolecular Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: phs7@cornell.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received November 7, 2013; final manuscript received May 29, 2014; published online June 27, 2014. Assoc. Editor: Ranganathan Kumar.

J. Thermal Sci. Eng. Appl 6(4), 041011 (Jun 27, 2014) (9 pages) Paper No: TSEA-13-1185; doi: 10.1115/1.4027809 History: Received November 07, 2013; Revised May 29, 2014

Planar-flow spin casting is a rapid solidification process used in the manufacture of thin, metallic ribbon, and foil. Liquid metal is solidified against a cool, rotating wheel which absorbs the super heat and latent heat of the metal. Industry typically implements an actively cooled wheel. However, validation of unsteady models requires observations from unsteady experiments. Experiments from our laboratory with an uncooled wheel show different temperature–time traces at different positions. Given a specified heat loading, a full conduction model predicts temperature fields within the wheel as they evolve with time. In this paper, we obtain reduced-order conduction models which take account of the various relevant length- and time-scales, with guidelines as to their validity. Model validation compares against measured temperatures from our casting machine. Finally, the model is modified to include internal cooling of the wheel to predict steady state behaviors. Spin casting can freeze molten metal sufficiently rapidly to achieve metallic glasses for a number of alloys whose properties in that state enable ultra-efficient energy conversion devices, alloys of increasing importance to energy conservation/harvesting.

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Fig. 1

Schematic of (a) PFMS process and (b) puddle region

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Fig. 2

Temperature measured within wheel at depths 2 mm (upper) and 9 mm (lower) from upper wheel surface. Black line drawn to highlight curvature of overall temperature rise.

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Fig. 3

Control volume of width W, length L, and thickness ξ. Time-dependent heat source footprint of length xs and width zs acts on upper surface. Direction definitions: x (circumferential) in rotation direction; y (radial) beginning at inner wheel surface, directed outward; and z (axial) beginning at wheel center, directed parallel to the axis of rotation.

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Fig. 4

Measured gap (upper) and thickness (lower) within a cast. Both decrease overall and have some periodicity per revolution, coinciding with circumferential out-of-roundness of the wheel. Solid lines serve to guide the eye.

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Fig. 5

Simplified two- and one-dimensional views of the control volume, neglecting circumferential direction. Numbers 1–6 represent TC positions which will be referred to repeatedly.

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Fig. 6

2D-model temperature prediction at various radial and axial locations, under typical casting conditions, Table 1. Radial temperature gradients are pronounced directly beneath the puddle.

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Fig. 7

2D-model temperature prediction at upper and lower wheel surfaces. Temperature rises by >100 K at the upper surface and then rapidly decays as heat conducts radially into the wheel.

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Fig. 8

A1D-model temperature prediction. Dotted (thick) lines: temperature when cyclic heat source is applied; solid (thin) lines: temperature when heat source is averaged in time. To the left of dashed line, t < tc, wheel acts as a semi-infinite solid. To the right of the dashed line, t > tc, the LS is felt and overall temperature growth is linear with time.

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Fig. 9

2D- (thin) and A1D-model (thick) predictions compared. Temperature growth is linear tc < t < 2tc, but then axial conduction (absent in (A1D)) causes downward curvature in the overall temperature.

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Fig. 10

2D-model temperature prediction as thickness τ decreases from 150 to 50 μm over 20 revolutions. The effect is to decrease the temperature rise per revolution, contributing to the overall concave-down shape of the traces.

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Fig. 11

2D-model temperature prediction as puddle length xs increases from 1 to 2 cm over 20 revolutions. The effect is to increase the heating time that the control volume experiences, increasing the temperature rise per revolution, contributing to an overall concave-up shape of the traces. Although xs has been observed to increase during a cast, such a pronounced concave-up shape has never been observed in the data.

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Fig. 12

2D-model temperature prediction for wheel speed U = 6 m/s (left) and U = 10 m/s (right). For slower speeds, heating phase is longer per revolution, yielding a greater overall temperature rise. Cooling times are also longer, so TC traces approach each other at the end of each revolution. For faster speeds, heating phase is shorter per revolution, yielding lower overall temperature rise. Cooling times are also shorter, so large radial gradients persist.

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Fig. 13

Measured (dots) versus predicted (line) temperature. Here, xs was assumed to be constant and the cast was chosen for τ decreasing steadily (i.e., no sudden changes in τ). Since xs was not measured, exact agreement is not expected.

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Fig. 14

Wheel outer surface temperature with internal cooling present at the inner surface as a function of time, for Biot number B = 1. Temperatures rapidly rise and fall as with the insulated case, but the overall temperature rise goes to zero.



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