Mathematical Analysis of Inclusion Removal from Liquid Steel by Gas Bubbling in a Casting Tundish

<table>The critical film thickness (<svg height="14.8125" id="M89" style="vertical-align:-3.22281pt" version="1.1" viewbox="0 0 18.262501 14.8125" width="18.262501" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.74,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">c</tspan>
<tspan style="font-size: 8.75px; " x="3.8858881" y="0">r</tspan>
</text>
</g>
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</svg>) calculated as a function of the inclusion diameter (<svg height="16.475" id="M90" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 14.4125 16.475" width="14.4125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.475)">
<g transform="translate(72,-58.82)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.3,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑝</tspan>
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</svg>),  (a) alumina inclusion and (b) silica inclusion [<a href="/journals/jam/2012/534275/#B13">13</a>].</table>

Journal of Applied Mathematics

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Figure 1

Figure 1: Mathematical Analysis of Inclusion Removal from Liquid Steel by Gas Bubbling in a Casting Tundish 