Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

<table>Temperature profile for different values of <svg height="9.2749996" id="M117" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.3125 9.2749996" width="13.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.275)">
<g transform="translate(72,-64.58)">
<text transform="matrix(1,0,0,-1,-71.95,64.63)">
<tspan style="font-size: 11.21px; " x="0" y="0">𝑁</tspan>
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</svg> at <svg height="12.1625" id="M118" style="vertical-align:-2.05875pt" version="1.1" viewbox="0 0 32.325001 12.1625" width="32.325001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.1625)">
<g transform="translate(72,-62.27)">
<text transform="matrix(1,0,0,-1,-71.95,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">𝛽</tspan>
<tspan style="font-size: 11.21px; " x="9.3586798" y="0">=</tspan>
<tspan style="font-size: 11.21px; " x="20.151983" y="0">1</tspan>
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</svg> and three profiles of the straight fin.</table>

Mathematical Problems in Engineering

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Figure 5

Figure 5: Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity 