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

<table>The normalized draining flow rate (<svg height="21.9125" id="M132" style="vertical-align:-4.59964pt" version="1.1" viewbox="0 0 58.799999 21.9125" width="58.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.9125)">
<g transform="translate(72,-54.47)">
<text transform="matrix(1,0,0,-1,-71.95,59.08)">
<tspan style="font-size: 12.50px; " x="0" y="0">∫</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.25,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝛿</tspan>
<tspan style="font-size: 8.75px; " x="-2.25" y="11.46">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.26,59.11)">
<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>
<tspan style="font-size: 12.50px; " x="21.342621" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="27.994217" y="0">𝜂</tspan>
</text>
</g>
</g>
</svg>) and the normalized lateral flow rate (<svg height="21.9125" id="M133" style="vertical-align:-4.59964pt" version="1.1" viewbox="0 0 57.212502 21.9125" width="57.212502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.9125)">
<g transform="translate(72,-54.47)">
<text transform="matrix(1,0,0,-1,-71.95,59.08)">
<tspan style="font-size: 12.50px; " x="0" y="0">∫</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.25,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝛿</tspan>
<tspan style="font-size: 8.75px; " x="-2.25" y="11.46">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.26,59.11)">
<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>
<tspan style="font-size: 12.50px; " x="20.067314" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="26.71891" y="0">𝜂</tspan>
</text>
</g>
</g>
</svg>) obtained by the 8th-order approximation of the HPM. </table>

Journal of Applied Mathematics

fig4

Figure 4

Figure 4: Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method 