1. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
Schematic of (a) PFMS process and (b) puddle region

2. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

3. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

4. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

5. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

6. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

7. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

8. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

9. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

10. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

11. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

12. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

13. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.

14. From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
Date of download: 10/27/2017
Copyright © ASME. All rights reserved.
From: Substrate Heating in the Planar-Flow Melt Spinning of Metals
J. Thermal Sci. Eng. Appl. 2014;6(4): doi: /
Figure Legend:
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.