Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method

<table>Variation of the dimensionless vortex intensity <svg height="14.8125" id="M200" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 20.5 14.8125" width="20.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8125)">
<g transform="translate(72,-60.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ψ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.62,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑅</tspan>
</text>
</g>
</g>
</svg> with respect to <svg height="10.8125" id="M201" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜆</tspan>
</text>
</g>
</g>
</svg> when <svg height="10.9125" id="M202" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 59.012501 10.9125" width="59.012501" 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">R</tspan>
<tspan style="font-size: 12.50px; " x="8.3395014" y="0">e</tspan>
<tspan style="font-size: 12.50px; " x="19.442165" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="31.482553" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.734055" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="40.859802" y="0">0</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

fig7

Figure 7

Figure 7: Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method 