Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid

<table>Plot of <svg height="14.3625" id="M172" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 21.5375 14.3625" width="21.5375" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
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<text transform="matrix(1,0,0,-1,-59.38,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑐</tspan>
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</g>
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</svg>  versus <svg height="12.925" id="M173" style="vertical-align:-1.90608pt" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.925)">
<g transform="translate(72,-61.66)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑄</tspan>
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</svg>  for different temperature gradients with <svg height="14.75" id="M174" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 58.4375 14.75" width="58.4375" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-52.96,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
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<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
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<text transform="matrix(1,0,0,-1,-61.31,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">5</tspan>
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<text transform="matrix(1,0,0,-1,-52.96,63.5)">
<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">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">0</tspan>
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</g>
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</svg>. </table>

International Journal of Differential Equations

fig4

Figure 4

Figure 4: Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid 