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TECHNICAL PAPERS: Bubbles, Particles, and Droplets

# Predicting Thermal Contact Resistance Between Molten Metal Droplets and a Solid Surface

[+] Author and Article Information
Yoav Heichal

Departmental of Mechanical & Industrial Engineering,  University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8

Sanjeev Chandra1

Departmental of Mechanical & Industrial Engineering,  University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8chandra@mie.utoronto.ca

1

Corresponding author.

J. Heat Transfer 127(11), 1269-1275 (Jun 09, 2005) (7 pages) doi:10.1115/1.2039114 History: Received February 08, 2005; Revised June 09, 2005

## Abstract

Thermal contact resistance between molten metal droplets (aluminum alloy 380 and bismuth) and solid plates (steel and brass) was measured experimentally. The diameter of the droplets was $4mm$, and droplet impact velocity ranged between 1 and $3m∕s$. Substrate temperature was varied from $25to300°C$ and roughness from $0.06to5.0μm$. Substrate temperature variation under impacting droplets was measured using fast temperature sensors that had a response time of $40ns$ and recorded substrate temperatures at five different radial locations under each droplet. Thermal contact resistance during the first few milliseconds of impact was obtained by matching measured surface temperature variation with an analytical solution of the one-dimensional transient heat conduction equation. An analytical model of the deformation of a free liquid surface in contact with a rough solid was used to calculate the true area of contact between them and, thereby, the thermal contact resistance. Test results agreed well with predictions from the analytical model. Thermal contact resistance values ranged from $10−7to3×10−6m2K∕W$, increasing with surface roughness and decreasing with rising impact velocity.

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## Figures

Figure 1

Schematic diagram of a thin-film thermocouple. The inset shows a photograph of three thermocouples spaced 1.15mm apart.

Figure 2

Surface temperature variation of a H-13 tool steel substrate during the impact of an aluminium 380 alloy droplet with an initial temperature of 630°C. Initial substrate temperature 25°C, droplet impact velocity 3m∕s, and surface roughness 0.5μm.

Figure 3

Estimation of contact resistance by curve fitting to experimentally measured surface temperature variation

Figure 4

Thermal contact resistance values between molten aluminium 380 and H-13 tool steel substrate

Figure 5

A scan of the H-13 tool steel substrate with Ra=2.7μm taken by an optical surface profilometer (on left) and an idealized model of it (on right)

Figure 6

Heat transfer from the molten metal at temperature Td to (a) an idealized rough surface and (b) a perfectly smooth surface. The temperature of the reference plane is Ts. Heat conduction takes place through a solid layer of thickness Ra.

Figure 7

Molten metal layer of thickness h in contact with an idealized rough surface

Figure 8

Thermal contact resistance values for molten metal droplets impacting with V0=3m∕s on steel and brass plates. Lines represent predicted values from Eq. 12.

Figure 9

A comparison between the analytical model predictions and tests results for different impact velocities. Solid lines represent predictions from Eq. 12.

Figure 10

Average thermal contact resistance variation with surface temperature for aluminium 380 droplets impacting with a velocity of 3m∕s on oxidized and nonoxidized H-13 tool steel substrates with two different surface roughness values.

Figure 11

Average thermal contact resistance for aluminium 380 droplets impacting with a velocity of 3m∕s on H-13 tool steel substrates covered with a thin film of oil or die-lube. Droplet impact velocity=3m∕s and surface roughness 0.5μm.

Figure 12

Comparison of measured contact resistance values (represented by data points) with predictions (solid line) from Eq. 13

## Errata

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