Mathematical Extrapolating of Highly Efficient Fin Systems

<table>Effects of the fin dimensionless length <svg height="10.325" id="M181" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.4125 10.325" width="13.4125" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
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</svg> and thermal length <svg height="10.45" id="M182" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 22.2875 10.45" width="22.2875" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-63.64)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="8.8771296" y="0">𝐿</tspan>
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</g>
</svg> on the maximum available efficiency ratio <svg height="16.637501" id="M183" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 38.862499 16.637501" width="38.862499" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-58.69)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜂</tspan>
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<text transform="matrix(1,0,0,-1,-65.7,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">∞</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">𝜂</tspan>
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<text transform="matrix(1,0,0,-1,-47.37,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑓</tspan>
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</svg> for exponential, triangular and parabolic pin fins, <svg height="20.4125" id="M184" style="vertical-align:-4.13007pt" version="1.1" viewbox="0 0 86.900002 20.4125" width="86.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.4125)">
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<text transform="matrix(1,0,0,-1,-71.95,59.84)">
<tspan style="font-size: 12.50px; " x="24.389999" y="0.88">√</tspan>
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="12.340461" y="0">=</tspan>
</text>
<g>
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<text transform="matrix(1,0,0,-1,-35.96,59.84)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="13.465731" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="16.941565" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="23.718191" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-7.14,56.71)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑏</tspan>
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</g>
</svg>.</table>

Mathematical Problems in Engineering

Mathematical Extrapolating of Highly Efficient Fin Systems

Figure 4