Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

<table>The normalized velocity profiles for the draining flow (<svg height="13.55" id="M129" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 26.8125 13.55" width="26.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="6.7766261" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.940125" y="0">𝜂</tspan>
<tspan style="font-size: 12.50px; " x="17.179123" y="0">)</tspan>
</text>
</g>
</g>
</svg>) and lateral flow (<svg height="13.55" id="M130" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 25.225 13.55" width="25.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑠</tspan>
<tspan style="font-size: 12.50px; " x="5.5013199" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">𝜂</tspan>
<tspan style="font-size: 12.50px; " x="15.903816" y="0">)</tspan>
</text>
</g>
</g>
</svg>) obtained by the 8th-order approximation of the HPM in comparison with the numerical solution, when <svg height="10.9125" id="M131" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 46.912498 10.9125" width="46.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛿</tspan>
<tspan style="font-size: 12.50px; " x="9.7523403" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.792728" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.04423" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.169979" y="0">8</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

fig3

Figure 3

Figure 3: Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method 