Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study

<table>Temporal shear stress distribution (<svg height="16.6" id="M209" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 57.737499 16.6" width="57.737499" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="6.3765302" y="0">𝑢</tspan>
<tspan style="font-size: 12.50px; " x="12.302952" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="15.778786" y="0">𝜕</tspan>
<tspan style="font-size: 12.50px; " x="22.167818" y="0">𝑦</tspan>
<tspan style="font-size: 12.50px; " x="28.369307" y="0">|</tspan>
</text>
<text transform="matrix(1,0,0,-1,-41.07,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑦</tspan>
<tspan style="font-size: 8.75px; " x="4.340992" y="0">=</tspan>
<tspan style="font-size: 8.75px; " x="10.336112" y="0">0</tspan>
</text>
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</g>
</svg>) with <svg height="16.6" id="M210" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 56.924999 16.6" width="56.924999" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
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<text transform="matrix(1,0,0,-1,-62.42,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑝</tspan>
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<text transform="matrix(1,0,0,-1,-54.17,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">1</tspan>
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</svg>, <svg height="13.9875" id="M211" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 50.537498 13.9875" width="50.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.9875)">
<g transform="translate(72,-60.81)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.26,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
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<text transform="matrix(1,0,0,-1,-49.91,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">5</tspan>
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</svg>, <svg height="14.6" id="M212" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 56.049999 14.6" width="56.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
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<text transform="matrix(1,0,0,-1,-62.42,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">0</tspan>
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</svg>, and <svg height="14.6" id="M213" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 53.424999 14.6" width="53.424999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
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<text transform="matrix(1,0,0,-1,-64.52,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">7</tspan>
</text>
</g>
</g>
</svg> for the effect of the Grashof number (<svg height="14.475" id="M214" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.6875 14.475" width="16.6875" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.42)">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝐺</tspan>
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<text transform="matrix(1,0,0,-1,-62.77,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
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Advances in Numerical Analysis

fig7

Figure 7

Figure 7: Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study 