Mathematical Extrapolating of Highly Efficient Fin Systems

<table>Effects of the fin dimensionless length <svg height="10.325" id="M176" 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">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑋</tspan>
</text>
</g>
</g>
</svg> and thermal length <svg height="10.45" id="M177" 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">
<g transform="matrix(1.25,0,0,-1.25,0,10.45)">
<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>
</text>
</g>
</g>
</svg> on the effective thermal length <svg height="14.2375" id="M178" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 33.037498 14.2375" width="33.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<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>
</text>
<text transform="matrix(1,0,0,-1,-54.22,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">∞</tspan>
</text>
</g>
</g>
</svg>  for exponential straight fin and the maximum available efficiency ratio <svg height="16.637501" id="M179" 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">
<g transform="matrix(1.25,0,0,-1.25,0,16.6375)">
<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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<text transform="matrix(1,0,0,-1,-57.1,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">𝜂</tspan>
</text>
<text transform="matrix(1,0,0,-1,-47.37,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg> for triangular and parabolic straight fins, <svg height="20.4125" id="M180" style="vertical-align:-4.13007pt" version="1.1" viewbox="0 0 94.175003 20.4125" width="94.175003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.4125)">
<g transform="translate(72,-55.67)">
<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>
<path d="m -35.96,70.71 39.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<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">𝐻</tspan>
</text>
<text transform="matrix(1,0,0,-1,-1.33,56.71)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑏</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

Mathematical Extrapolating of Highly Efficient Fin Systems

Figure 3