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

<table>Spatial velocity distribution (<svg height="7.1624999" id="M249" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑢</tspan>
</text>
</g>
</g>
</svg>) with <svg height="14.6" id="M250" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 63.424999 14.6" width="63.424999" 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">𝐺</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-55.23,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="24.530886" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">0</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.9875" id="M251" 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>
</text>
<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>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M252" 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>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.88,63.5)">
<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>
</text>
</g>
</g>
</svg>, and <svg height="14.6" id="M253" 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>
</text>
<text transform="matrix(1,0,0,-1,-64.52,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-56.98,63.5)">
<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">7</tspan>
</text>
</g>
</g>
</svg> for the effect of radiation-conduction parameter (<svg height="14.2375" id="M254" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.125 14.2375" width="17.125" 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">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
</text>
</g>
</g>
</svg>).</table>

Advances in Numerical Analysis

fig13

Figure 13

Figure 13: Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study 